This is the first big idea in AP Calculus BC, and it lays the basis for most of Calculus. So Calculus is interested in finding the values of things that are infinitesimally small ( like the slope of a point or the area under a curve) and to find these values limits are used. Take for instance the area under the curve, to approximate it you can divide the curve into rectangles, but the area will only be that an approximation. The smaller the width and the more rectangles there were the better the approximation would be. So what calculus does is take the limit of the sum of the rectangles as the width of the rectangles approaches zero ( or the number of rectangles approaches infinity ) which is the exact area. I'll write more on finding areas under curves when I get to big idea 3 Integration.
So a limit of a function as the input approaches some value is really the value the output or the function approaches. So the function doesn't have to be defined at a point to have a limit there.
There are many ways to find limits of function, including using graphs and just plain algebra. Limits can come from two different directions , the negative direction ( or from the left side of the graph , i.e. the value the function approaches from input values less then the value you are taking the limit at ) and the Positive direction ( from the right side of the graph with values larger than the desired input value ). The notation for the two different types of limits looks like this:
lim f(x) = L lim f(x) = L
x→c - x→c +
From the negative direction Positive Direction
So the → means approaches and the x→ c means as x approaches c . The Limits from each side do not have to be the same, and when they are not there is a weird jump in the function.
Some times to approximate limits algebraically you just have to plug in the c value for x in the function and it gives you the limit. But if this limit is undefined ( ∞/∞ or 0/0 ) then you are going to have to try some different methods. If the function has a quotient , then divide the top and bottom by the highest power of x , and then take the limit. There is also a way that you can factor a function out and then cancel expressions leaving a defined limit. A very useful rule for evaluating limits with indeterminate form ( +∞/∞ or 0/0 ) is L'Hopitals rule which states that if you have a limit in indeterminate form , then you can take the derivative of the top and bottom ( separately ) and then take the limit of it.
lim f(x) =+∞/∞ or 0/0 then lim f(x) =lim f '(x)
x→c g(x) x→c g(x) x→c g'(x)
A function is continuous if ( all of the following conditions are met ):
lim f(x) = lim f(x) = L
x→c - x→c +
( so the lim f(x) is defined and equals L )
x→c
lim f(x) = L =f(c)
x→c
( or in other words the function must be defined at x=c, and the limit of the function as x approaches c must be defined and equal the function's value at x=c )
A point that needs to be covered here is that if the limits of the function from the right hand and the left hand are not the same than the limit of the function at that point is not defined ( the limits from either side have to equal each other for the whole limit to be defined. )
Asymptotes are places where either the limit as x approaches infinity equals that value ( for y value asymptotes or horizontal asymptotes ) or the limit as x approaches that value equals infinity ( for x values , or vertical asymptotes )
Continuity allows us to have some theorems, like the intermediate value theorem and the extreme value theorem ,and later on the Mean value and Rolles theorem. The Intermediate value theorem states that if a function is continuous on the interval [a,b] then there is some value c that if between the values f(a) and f(b) for the function. The extreme value theorem states that if a function is continuous on an interval it will hit a highest value on an interval. The Means value theorem ( MVT ) and Rolles theorem which is a special case of MVT have to do with derivatives.
There are different types of discontinuity , jump, removable and infinite discontinuities:
jump discontinuities happen when the right hand and the left hand limits don't equal each other ( the function " jumps " at the discontinuity )
removable discontinuous are when the limits equal each other but not the functions defined value.
Infinite discontinuities happen when functions approach positive or negative infinity at a point ( which actually means that their limit and value are undefined )
Tuesday, May 30, 2017
Wednesday, May 24, 2017
Why Calculus ?
So you may have heard that I took the AP Calculus BC exam a little while back. Your reaction could have been ugggh ! that stuff is so boring and complicated , why would you ever do that?
( or it could have been Awesome that stuff is so cool! If it was something like that then you do not have to read this but you still can ) I mean when would you EVER have to use that in regular life ?
My article today strives to answer at least part of this question " why calculus " and how it is awesome!
Calculus , like any topic, can be made boring and dissatisfying through mental prejudice and unenthusiasm. When you put it into your brain ( quite unfairly ) that this is not going to be fun and it will never be fun , in a nutshell that you dislike it. This approach must not be the way you look at calculus if you ever want to come to love it and have fun doing it, but rather you at least have to have a open approach to the subject. Preferably you should have a positive, optimistic approach to the subject having a hope that it will be fun and exciting.
What makes Calculus fun is that with knowledge you can solve problems, thereby thereby using your brainpower to get answers. Calculus is really not fun when you do not know how to do it, so learning it is an essential part of the process. Learning can be hard at times and so you need to press forward continue trying and rely on the infinite grace and mercy of our Heavenly Father to learn and understand calculus. Once you learn the material , answering problems becomes easy ( or at least doable) and the excitement of being able to find the answer emerges.
Learning Calculus can be fun to though , once you finally understand a new definition , or theorem it enables you to do something new in math that you did not know how to do before. It opens new doors in your ability to solve problems , and things that seemed impossible now become second nature.
For example , say you knew basic algebra and how to find the slope of a graph, but then you think of a curved graph ( say ln(x) ) and wonder how to find out its slope at a defined point. You can increasingly approximate the slope at the point but not quite reach it using algebra, but with differential calculus you can literally find the slop of a point of a curved graph. For example at x=2 dy/dx of y=ln(x) or the infinemestial slope at the point x=2 of the natural log of x is equal to the 1/2.
While I was learning how to take the volume of irregular solids, I wondered if you could somehow use related rates to find the rate of change of the volume of an irregular solid where the upper integrand is changing. So what this means is that say you have a graph of a function ( for example y=x2) and then you rotate the graph around an axis ( say the x ) so what you get is a solid with a volume that can be determined using integration and the property that each slice of the solid is a circle. The area of each of the circles is 𝛑r² and the one thing that changes between the each of the circles is the radius. The radius at each point or for each circle is equal to the value of the function at that point ( since the diameter is twice the function value ) or x2
If you sum the areas of every circle in the range that you want ( say from 0 to 2 , which numbers are called the lower and upper bounds of integration, or the integrands ) then you get the volume. To sum the areas of every circle you have to use an integral which is and the limit as the number of circles approaches infinity or the limit as the width of the cylinders approaches zero of the sum of each of the cylinders. It would be 𝛑∫(x²)²dx since 𝛑(x²)² is the area of one circle and the sum of all of them is the integral. Using integration rules ( ∫xn=
xn+1
from 0 to 2. The rate of change of this volume was a bit hard for me to determine how to find when given that the upper integrand was changing at some rate, but I eventually got it , with Heavenly Father's help. So the fundamental theorem of Calculus state that the derivative of an integral of a function with respect to the changing upper integrand is equal to the function of the integrand.
By the chain rule the derivative of a composite function f(g(x)) with respect to x is equal to the derivative of f(g(x)) with respect to g(x) multiplied by the derivative of g(x) with respect to x. So say that you were given the rate of change of the upper integrand and asked for the rate of change of an irregular volume produced by rotating f(x) around the x axis. The way to do this is multiply f(x) by dx/dt or the function of x multiplied by the rate of change in x. This is a simpler way than what I did. I used a differential equation to solve for the upper integrand in terms of t and then plugged that into the integral as the integrand and than applied the fundamental theorem and the chain rule.
Once you have mastered Calculus answering problems gives you a "zing" to the brain and it can get mildly addictive, so do not do it to much.
( or it could have been Awesome that stuff is so cool! If it was something like that then you do not have to read this but you still can ) I mean when would you EVER have to use that in regular life ?
My article today strives to answer at least part of this question " why calculus " and how it is awesome!
Calculus , like any topic, can be made boring and dissatisfying through mental prejudice and unenthusiasm. When you put it into your brain ( quite unfairly ) that this is not going to be fun and it will never be fun , in a nutshell that you dislike it. This approach must not be the way you look at calculus if you ever want to come to love it and have fun doing it, but rather you at least have to have a open approach to the subject. Preferably you should have a positive, optimistic approach to the subject having a hope that it will be fun and exciting.
What makes Calculus fun is that with knowledge you can solve problems, thereby thereby using your brainpower to get answers. Calculus is really not fun when you do not know how to do it, so learning it is an essential part of the process. Learning can be hard at times and so you need to press forward continue trying and rely on the infinite grace and mercy of our Heavenly Father to learn and understand calculus. Once you learn the material , answering problems becomes easy ( or at least doable) and the excitement of being able to find the answer emerges.
Learning Calculus can be fun to though , once you finally understand a new definition , or theorem it enables you to do something new in math that you did not know how to do before. It opens new doors in your ability to solve problems , and things that seemed impossible now become second nature.
For example , say you knew basic algebra and how to find the slope of a graph, but then you think of a curved graph ( say ln(x) ) and wonder how to find out its slope at a defined point. You can increasingly approximate the slope at the point but not quite reach it using algebra, but with differential calculus you can literally find the slop of a point of a curved graph. For example at x=2 dy/dx of y=ln(x) or the infinemestial slope at the point x=2 of the natural log of x is equal to the 1/2.
While I was learning how to take the volume of irregular solids, I wondered if you could somehow use related rates to find the rate of change of the volume of an irregular solid where the upper integrand is changing. So what this means is that say you have a graph of a function ( for example y=x2) and then you rotate the graph around an axis ( say the x ) so what you get is a solid with a volume that can be determined using integration and the property that each slice of the solid is a circle. The area of each of the circles is 𝛑r² and the one thing that changes between the each of the circles is the radius. The radius at each point or for each circle is equal to the value of the function at that point ( since the diameter is twice the function value ) or x2
If you sum the areas of every circle in the range that you want ( say from 0 to 2 , which numbers are called the lower and upper bounds of integration, or the integrands ) then you get the volume. To sum the areas of every circle you have to use an integral which is and the limit as the number of circles approaches infinity or the limit as the width of the cylinders approaches zero of the sum of each of the cylinders. It would be 𝛑∫(x²)²dx since 𝛑(x²)² is the area of one circle and the sum of all of them is the integral. Using integration rules ( ∫xn=
xn+1
from 0 to 2. The rate of change of this volume was a bit hard for me to determine how to find when given that the upper integrand was changing at some rate, but I eventually got it , with Heavenly Father's help. So the fundamental theorem of Calculus state that the derivative of an integral of a function with respect to the changing upper integrand is equal to the function of the integrand.
By the chain rule the derivative of a composite function f(g(x)) with respect to x is equal to the derivative of f(g(x)) with respect to g(x) multiplied by the derivative of g(x) with respect to x. So say that you were given the rate of change of the upper integrand and asked for the rate of change of an irregular volume produced by rotating f(x) around the x axis. The way to do this is multiply f(x) by dx/dt or the function of x multiplied by the rate of change in x. This is a simpler way than what I did. I used a differential equation to solve for the upper integrand in terms of t and then plugged that into the integral as the integrand and than applied the fundamental theorem and the chain rule.
Once you have mastered Calculus answering problems gives you a "zing" to the brain and it can get mildly addictive, so do not do it to much.
Monday, May 15, 2017
AP Physics C:Mechanics
I took the AP Physics C:Mechanics exam last week, and it was a bit challenging, but I am pretty sure I passed ( for BYU that means get at least a 4 ). You see I had not studied it nearly as weel or as much or as enthusiastically as Calculus and I did not understand it as well and Calculus BC. The Physics exam had more than just math ( unlike the AP Calculus BC exam did ) it had theory and laws and you had to know how to solve the problems. Which luckily I did ( most of them ) but there were still some that had me a bit confused. The Free response especially , which had a whole question on the rolling motion of a ball , was confusing. But I believe that I wrote enough and got enough of the Multiple choice correct to get a 4.
The Exam is separated into two sections: multiple choice and free response , where the MC part has ~35 questions which you have to fill in a letter on a answer sheet, and the FR part has 3 questions where you have to write. You are given 45 minutes for both parts, and so an hour and a half for the whole exam.
The Exam tests kinematics, forces and newtons laws, work and energy, linear momentum , impulse and center of mass, rotational motion, gravitation, and oscillations.
Kinematics deals mainly with the study of motion, how things move ( velocity, displacement, acceleration and the equations that relate these quantities and time ) and is only up to two-dimensional in AP Physics c mechanics with projectile motion. In this course both kinematics under constant acceleration and kinematics under varying acceleration are covered ,where in the first case the kinematic equations are used and in the second case calculus is used.
Forces and newtons laws deal with why objects move and the forces that make them move. The method of drawing free body diagrams and solving newtons second law equations (F=ma) are covered as are the 3 laws ( inertia , F net = ma, action reaction pairs ). Inclined planes and force trigonometry is used to find components of forces in different directions. Different types of force, such as the normal force, the gravitational force, the frictional force and centripetal force are covered.
Linear Momentum is the mass of an object times its velocity or the integral of force with respect to time for varying forces. Impulse if equal to momentum as stated in the impulse-momentum theorem, and calculations are done on these equations. Conservation of linear momentum is covered and so are the different types of collisions ( elastic , inelastic and completely inelastic ). The method for calculating the center of mass of both a system of particles and a continuous body are also covered.
Work and energy deal with the integral of force with respect to distance ( for varying force), Mechanical , Potential , and Kinetic energy, potential energy graphs, conservation of mechanical energy, non conservative energy, basic gravitational and spring potential energy, work energy theorem , and power.
Rotational motion deals with the rotational analogous of the fore covered topics of kinematics and dynamics when rotating around a fixed axis ( so it can only rotate in two directions ), and how to solve problems with this. These include but are not limited to angular displacement , velocity, and acceleration, arc length , torque , rotational inertia, and rotational kinetic energy.
Gravitation deals with Kepler's 3 laws,Newtons law of gravity, actual gravitational acceleration, the equating of centripetal force and gravitational force for circular orbits, the finding of the gravitational force inside a sphere, the actual gravitational potential energy and the discovery of escape velocity, and the like
Oscillation deals with springs, the restoring force for simple harmonic motion, potential energy for springs, period and frequency, the model for sinusoidal simple harmonic motion of position, velocity and acceleration, pendulums and the simple harmonic motion equations for ones that are displaced a small angle of theta.
It is so awesome how newton discovered these laws that rule the motion of objects ! Our Heavenly Father loves it when we strive to find the truth and with his help we do. He helped me learn Physics and I am so thankful for this.
Kinematics deals mainly with the study of motion, how things move ( velocity, displacement, acceleration and the equations that relate these quantities and time ) and is only up to two-dimensional in AP Physics c mechanics with projectile motion. In this course both kinematics under constant acceleration and kinematics under varying acceleration are covered ,where in the first case the kinematic equations are used and in the second case calculus is used.
Forces and newtons laws deal with why objects move and the forces that make them move. The method of drawing free body diagrams and solving newtons second law equations (F=ma) are covered as are the 3 laws ( inertia , F net = ma, action reaction pairs ). Inclined planes and force trigonometry is used to find components of forces in different directions. Different types of force, such as the normal force, the gravitational force, the frictional force and centripetal force are covered.
Linear Momentum is the mass of an object times its velocity or the integral of force with respect to time for varying forces. Impulse if equal to momentum as stated in the impulse-momentum theorem, and calculations are done on these equations. Conservation of linear momentum is covered and so are the different types of collisions ( elastic , inelastic and completely inelastic ). The method for calculating the center of mass of both a system of particles and a continuous body are also covered.
Work and energy deal with the integral of force with respect to distance ( for varying force), Mechanical , Potential , and Kinetic energy, potential energy graphs, conservation of mechanical energy, non conservative energy, basic gravitational and spring potential energy, work energy theorem , and power.
Rotational motion deals with the rotational analogous of the fore covered topics of kinematics and dynamics when rotating around a fixed axis ( so it can only rotate in two directions ), and how to solve problems with this. These include but are not limited to angular displacement , velocity, and acceleration, arc length , torque , rotational inertia, and rotational kinetic energy.
Gravitation deals with Kepler's 3 laws,Newtons law of gravity, actual gravitational acceleration, the equating of centripetal force and gravitational force for circular orbits, the finding of the gravitational force inside a sphere, the actual gravitational potential energy and the discovery of escape velocity, and the like
Oscillation deals with springs, the restoring force for simple harmonic motion, potential energy for springs, period and frequency, the model for sinusoidal simple harmonic motion of position, velocity and acceleration, pendulums and the simple harmonic motion equations for ones that are displaced a small angle of theta.
It is so awesome how newton discovered these laws that rule the motion of objects ! Our Heavenly Father loves it when we strive to find the truth and with his help we do. He helped me learn Physics and I am so thankful for this.
Saturday, May 13, 2017
AP Calculus BC !
I took the AP Calculus BC exam last Tuesday and it was awesome!
I had studied for it for about 4 months before and It was quite fun to take it. I know that I could never have taken it without my Heavenly Father's help.
The free response questions ( released on college board here ) were harder than the past few FRQs that I have taken ( like the 2013, 2012, and 2016 ones).
For example the first calculator one ( or #1) did not ask for a estimation of a derivative ( as the earlier ones usually do) and asked for the rate of change of a volume that required an integral, which I had pondered about earlier while I was taking the course. Because I had learned about related rates for objects and shapes that had well defined formulas for area , volume and length ( circles, right triangles, cubes and the like), and I started learning how to take volumes of irregular shapes using integrals ( like volumes of rotation using discs and washers, and volumes with cross sections that had known areas ). So I wondered, If you knew the rate at with the upper bound of integration was increasing , could you solve for the rate at which the volume was changing ? I was not able to figure it out right then, and I still wondered it as a kept learning calculus.
But later on ( like 1-2 weeks before the exam ) it came to me! All I had to do was solve a basic differential equation, sub the solved value for the upper bound of integration as a function of time into the integral, and then use the chain rule and fundamental theorem to solve it !
It was a wonderful blessing from my Father in Heaven to allow me to figure this out, and have it on the exam!
The second FRQ was crazy!! it was a BC topic only that involved two polar functions and their graphs and had some really interesting parts. Part a was basic as it had you take the area of one of the polar graphs in the first quadrant, which since a calculator was allowed was not to complicated after you set up the integral.
Part b was cool because it asked you to write an equation that had a ray k that separated one of the graphs into two equal areas in the first quadrant. But parts c and d were where it got me really thinking !
Part c had two functions whose x and y coordinates were determined by functions ( which was basically a parametric form).The x coordinate of the first was determined by the a function of theta that equaled one of the polar functions, while the other was determined as a function of theta that equaled the other polar one. Both of the y coordinated were determined as theta. The question asked me to find an function in terms of theta that was the distance between the two graphs at any theta. The way I went about this problem was to use the vector formula for distance ( sqrt(x^2+y^2) ) and then minus the one with greater x coordinate from the one with lesser x coordinate.
Then the question asked for the average value ( over an interval ) for the function I had written , which made my have to plug in a whole bunch of notation into my calculator and then use it to integrate. The last part of the question was where I had to take a derivative at a point of the function and determine if the function was increasing or decreasing. I remember urging my calculator on when it was taking to long to integrate the function
There were some hard parts on the exam that I did not really know how to do, but overall the exam was good. I had time left during Section I after finishing so I wrote James 1:5-6 from memory and my testimony.
The AP Calculus BC exam ( and AB ) was (were ) changed this school year to include a few more topics and with a different format. This exam I think made students think more and use multiple things they learned to answer questions.
Calculus was fun and I hope to get a 5 on the exam with Heavenly Father's help.
The course had 4 big ideas:
2. Derivatives
I will be posting about every week on AP Calulus BC topics ( Limits, Derivative, Integrals, Differential Equations, and Series ).
Calculus was awesome and fun to do ( once I learned the rules ) but it also has some practical and useful applications, since it allows you to find areas and slopes of things not defined in regular algebra and geometry. Graphs of thins like membership versus time , or profit versus time usually are not straight lines and perfect circles, and calculus enables you to find the instantaneous rate at with your membership ( or profit) is growing. With differential equations you can also find the population at some time in the future if given a solvable differential equation for the rate of growth of the population, and an initial t=0 population.
I had studied for it for about 4 months before and It was quite fun to take it. I know that I could never have taken it without my Heavenly Father's help.
The free response questions ( released on college board here ) were harder than the past few FRQs that I have taken ( like the 2013, 2012, and 2016 ones).
For example the first calculator one ( or #1) did not ask for a estimation of a derivative ( as the earlier ones usually do) and asked for the rate of change of a volume that required an integral, which I had pondered about earlier while I was taking the course. Because I had learned about related rates for objects and shapes that had well defined formulas for area , volume and length ( circles, right triangles, cubes and the like), and I started learning how to take volumes of irregular shapes using integrals ( like volumes of rotation using discs and washers, and volumes with cross sections that had known areas ). So I wondered, If you knew the rate at with the upper bound of integration was increasing , could you solve for the rate at which the volume was changing ? I was not able to figure it out right then, and I still wondered it as a kept learning calculus.
But later on ( like 1-2 weeks before the exam ) it came to me! All I had to do was solve a basic differential equation, sub the solved value for the upper bound of integration as a function of time into the integral, and then use the chain rule and fundamental theorem to solve it !
It was a wonderful blessing from my Father in Heaven to allow me to figure this out, and have it on the exam!
The second FRQ was crazy!! it was a BC topic only that involved two polar functions and their graphs and had some really interesting parts. Part a was basic as it had you take the area of one of the polar graphs in the first quadrant, which since a calculator was allowed was not to complicated after you set up the integral.
Part b was cool because it asked you to write an equation that had a ray k that separated one of the graphs into two equal areas in the first quadrant. But parts c and d were where it got me really thinking !
Part c had two functions whose x and y coordinates were determined by functions ( which was basically a parametric form).The x coordinate of the first was determined by the a function of theta that equaled one of the polar functions, while the other was determined as a function of theta that equaled the other polar one. Both of the y coordinated were determined as theta. The question asked me to find an function in terms of theta that was the distance between the two graphs at any theta. The way I went about this problem was to use the vector formula for distance ( sqrt(x^2+y^2) ) and then minus the one with greater x coordinate from the one with lesser x coordinate.
Then the question asked for the average value ( over an interval ) for the function I had written , which made my have to plug in a whole bunch of notation into my calculator and then use it to integrate. The last part of the question was where I had to take a derivative at a point of the function and determine if the function was increasing or decreasing. I remember urging my calculator on when it was taking to long to integrate the function
There were some hard parts on the exam that I did not really know how to do, but overall the exam was good. I had time left during Section I after finishing so I wrote James 1:5-6 from memory and my testimony.
The AP Calculus BC exam ( and AB ) was (were ) changed this school year to include a few more topics and with a different format. This exam I think made students think more and use multiple things they learned to answer questions.
Calculus was fun and I hope to get a 5 on the exam with Heavenly Father's help.
The course had 4 big ideas:
- Limits
- definition,
- evalutaion,
- L'Hoplitals rule,
- asymptoes ,
- continutity,
- types of discontinuty
- theorems
- definition( slope of a point )
- rules ( polynomial, exponential, trigonometric, logarithmic, chain, product, quotient )
- as a limit
- approximation
- theorems ( mean value, Rolle's )
- differentiability and continuity
- tangent line approxiamtion
- parametic differation
- polar differentiation
- related rates
- higher degree derivatives
- of inverse functions
- other applications ( maximum and minimum, points of inflection and concavity )
- movement of a particle ( distance, position, velocity, speed and acceleration)
- definition
- antiderivatives
- rules ( polynomial, exponential, trigonometric, logarithmic )
- fundamental theorem
- u-substitution
- by parts
- by partial fractions
- definite integral
- definite integral properties
- applications of integration
- areas under curves
- volumes of irregular solids
- approximation of using Riemann sums
- parametric integration
- polar integration
- movement of a particle ( distance, position, velocity, speed and acceleration)
- differential equations ( including logistic growth and euler's method )
- improper integrals
- definition ( sum of a sequence )
- geometric
- infinite
- interval and radius of convergence
- p-series
- tests for convergence ( nth term, comparison, limit comparison, ratio, integral etc. )
- error bound ( for alternating and with Lagrange error bound )
- expressing functions as a series
- Power series ( Taylor and Macluraian )
It is pretty hard to wait for my scores until July 5th but I can't do much about it.
I will be posting about every week on AP Calulus BC topics ( Limits, Derivative, Integrals, Differential Equations, and Series ).
Calculus was awesome and fun to do ( once I learned the rules ) but it also has some practical and useful applications, since it allows you to find areas and slopes of things not defined in regular algebra and geometry. Graphs of thins like membership versus time , or profit versus time usually are not straight lines and perfect circles, and calculus enables you to find the instantaneous rate at with your membership ( or profit) is growing. With differential equations you can also find the population at some time in the future if given a solvable differential equation for the rate of growth of the population, and an initial t=0 population.
Monday, September 26, 2016
The Slave Community Write Up
I did a Write Up on The Slave Community by John W. Blassingame For my U.S. History Course through BYU Independent study. Here it is:
Slavery
was a harsh and morally wrong system, with white masters denying slaves very
basic human rights and exploiting their labor with the bare minimum
requirements for survival in most instances.
A
field hand's life consisted of waking up before dawn, preparing a meal, eating,
feeding livestock and then getting out to the fields a bit before dawn. They
were whipped if they were late. Then they worked until dusk in a variety of
labors, depending on the season and the type of crop.
For
instance they could be planting the crops, preparing the fields, clearing the land,
getting rid of pests, or harvesting the crop.
Then
after sunset they put away livestock, and made their meal before going to bed,
but sometimes they worked till nine or later if they were ginning cotton or
boiling sugar.
The
domestic slave ate better food and wore better clothes than the field hands,
but they still had negatives like being under the constant watch of the whites,
absorbing white anger in the form of punching or whipping, and being at their
beck and call day and night.
According
to Nathaniel Ware, a slave could be sustained by $20 (in 1844, around $645
today) a year, while a free laborer needed $100 (~3,225 today) for food and
clothing alone for him and his family.
This
meant that slaves sometimes did not have enough food, and when this happened
they stole food. They also had wretched, crude, one room, and often crowed
cabins with holes and hard dirt floors. Basically the bare minimum.
Many
masters attempted to assure their authority over their slaves and that of all whites’
superiority over all blacks (very much against natural law). Most planters also
worked to make "their" slaves submissive and non-rebellious.
Planters
forced slaves to act happy about slavery and their exhausting labors, while truly
and inside they did barely felt any joy about these things.
Black
overseers had really strenuous lives because they were caught in the middle
between the slaves and the master. When they worked the slaves too hard, the master
was happy with them, while the slaves were not. On the other hand when they let
the slaves slack off and not really work that much, the master got mad and
usually whipped the overseer.
Domestic
servants acted as the secret police of the planter, they spied on the other
slaves and reported back to him. Masters were sometime very cruel to the slaves
in punishment, with extensive flogging and iron shackles to the slaves’ limbs.
Planters
also physically abused and even mutilated their slaves. Masters sometimes
killed slaves under punishment, whether accidentally or intentionally. But
while it was illegal for masters to kill their slaves, they were not usually held
accountable for any crimes by the white government if one died under
punishment.
There
were also some masters who were generally kind like Dr. Carson. Some of the
things kind masters did was that they abstained from flogging, giving enough
food and shelter, and leaving slave families together.
Some
kind masters became cruel when they were angry, but overall most of masters were
neither kind nor exceptionally cruel with the treatment of slaves.
While
planters extracted all the labor from their slaves that they could, they also
tried to act humanely and were forced to recognize the humanity of their slaves.
Planters
were kinder to their slaves sometimes because they were worried about public
opinion and/or they tried to apply Christian principles in their relations with
slaves.
Many
slaves limited their work so to try to speed up the work planters gave prize’s
to the best cotton pickers.
Slaves coped with this oppressive system in different ways. One of
the biggest ways slaves coped with it was through their culture which came
largely the oral traditions from West Africa.
Regional
Storytelling in West Africa included acting, and singing that was a favorite
evening entertainment. West African Folk tale culture was largely transplanted
to the South and the slaves’ culture. Patterns and symbols/symbolism of the
folktales can tell us a lot about the slaves’ thoughts and views.
These
attempted to explain natural phenomena and had heroes and morals. Often the
audience responded to questions and the tales were accompanied by drums.
West
African tales show us that they valued Families and knowledge. There were a lot
of Animal storied and Trickster figures- like the Nigerian Tortoise and the
Ghanaian spider and rabbit-are all over them. They are weaker than the other
animals but through cunning they outwit them and triumph over evil.
Folk
tales were not only an entertainment they were also a concentration of folk
wisdom, a manifestation of a slave’s dreams, hopes and personal experiences. They
were also used as instructional devices to teach young slaves how to live.
Folk
Tales were an area which was out of the whites’ control, and they allowed the
slave to convey hostility at his master and explain the plantation system.
In
animal tales the slaves identified themselves with the weaker animals, and were
fascinated with weakness overcoming strength. This could be a symbol of the
weak unarmed slaves overcoming the whites including their masters.
Sometimes
there were not just symbols of masters, overseers and slaves but direct
references, like with the John series.
This series is a very accurate and specific depiction of slavery in the folk
tales, where John longs for freedom, runs away, gets beaten, desires revenge
for his suffering and often defies his master.
John
symbolized the discontent of slaves, the many options for the slaves, a set of
survival techniques, and was a means of increasing self-worth.
Folk tales
prove that the hardships and cruelties of slavery were not enough to demolish
the creativity of the slaves and folk tales allowed the slave to view himself symbolically
and to find patience and hope when he talked about his fortune.
Folk tales
helped the slave cope with the hardships of slavery because they were mental
tools that helped channel emotions allowing them to talk about their resentment
of their masters and white people in ways that had little or no physical threat
and provided leisure, fun and creativity.
Slaves
also coped with their hardships through religion where he found hope of escape
of the brutalities of slavery.
Protestant
missionaries had taught thousands of slaves Christian doctrines, and slaves
believed God promoted freedom interpreting the freedom from bondage of Israel
to mean that they had a hope for freedom too.
The
Religious faith of the slave often conquered the slave’s fear of their master.
When slaves were whipped for going to church they continued because they
determined that their master could only harm their physical body and not their
soul.
Religious
services and activities also provided the slave with welcome rest from
constant, hard labor and gave him joy and companionship. By engaging in these activities the slave
could take his mind of his/or her hopeless condition and focus on the happy
future that awaited him.
The
Slave’s life was hard, and would have been practically unbearable had there not
been a black plantation culture separate from and out of the control of the
white people.
It
also helped the slaves form an appreciation for group protection and unity. Finally
the slave’s culture boosted his self-worth and joys, helping him have
enthusiasm in what was otherwise a very difficult and unpleasant life.
Thursday, September 1, 2016
Constitution Write-up and Common Sense discussion response
I did a Constitution write-up for my Course HIST-220 American History to 1877, about a modern - day issue and how the Constitution addresses or doesn't address it. Here it is:
One challenge currently facing American society today is the expansion of Federal and Presidential power. It is an issue because it threatens individual liberty and rights, which are protected when the Federal government has less power and has to “compete “with state Governments. Another Reason that it is an Issue is that when the Federal Government expands so much that it goes against Natural Law (Law that is higher than manmade law, including God’s Law and Scientific/Mathematical Laws) it brings decline to the Nation.
I also did a Common-Sense discussion board Response here it is:
One challenge currently facing American society today is the expansion of Federal and Presidential power. It is an issue because it threatens individual liberty and rights, which are protected when the Federal government has less power and has to “compete “with state Governments. Another Reason that it is an Issue is that when the Federal Government expands so much that it goes against Natural Law (Law that is higher than manmade law, including God’s Law and Scientific/Mathematical Laws) it brings decline to the Nation.
According to Fredric Bastiat’s famous essay The Law, this overreach brings about the
following consequences: People won’t truly respect the Law because it privileges
the federal or central government above the rights of the individual. This
leads to less respect for the Government and more lawbreaking. Which in turn leads
people to have less respect for each other and to believe that everyone is
dishonest and that they in turn should act dishonestly. Ultimately this leads
to widespread distrust and a decrease of freedom, equality and opportunity.
The United States Constitution seeks to address this issue
by limiting the power of the Federal Government and the President. It limits the power of the Federal Government
in multiple ways. One of the biggest is the 10th amendment, which
states: “The powers not delegated to the United States by the Constitution, nor
prohibited by it to the States, are reserved to the States respectively, or to
the people.”
This means that the Federal government only has the powers
delegated to it in the constitution and all other powers (as long as they
aren’t prohibited to the states, like ex post facto laws or bills of attainder)
go to the states.
Some examples are education, setting up schools and
determining if abortion and LBGT marriage is allowed or prohibited. The U.S. Constitution also limits the Federal
government by dividing the powers of government among the 3 Branches of the
Federal Government:
·
The Legislative Branch which is further divided
into the Senate and the House of Representatives, who each have unique powers
like the origination of all revenue bills in the House and the sole power to
judge impeachment cases for the Senate. But overall the Congress deals with the
lawmaking of the country.
·
The Executive Branch: the President and The VP which are elected by
another body, the Electoral College which in turn was instituted to protect the
office of the president from the majority “mob” rule of the people. The
Executive branch deals with enforcing the Law and it has a huge Federal
Bureaucracy to help do this.
·
The Judicial Branch which has the power of
interpreting the law of the Land, and
deciding disputes.
The three branches have checks and balances procedures and
powers that enable each branch to limit the power of the other branches and
force a compromise between all three. This prevents any one branch from getting
too much power, and prevents tyranny.
Congress, for example, is given the power to impeach and
convict Federal officials including Judges, SCOTUS Justices and the President
and VP. The President has the power to veto a law passed by Congress. Congress
on the other hand can override a presidential veto with a 2/3 vote. Congress
has the power to declare war, but the President has the power to command the
Military. The President nominates Supreme Court Justices and Congress holds the
power to confirm or reject them.
Presently however, the Federal Government has overstepped
these limits in multiple instances and thus it has gone against the Law of the
Land, and Natural Law. Some of the
instances include the Roe v. Wade and Oberfell v. Hodge SCOTUS Cases where the
SCOTUS went against the the 10th amendment of Constitution and Natural Law or
the idea that “all powers delegated to the government must be entrusted to the
lowest level of government that can effectively accomplish the desired goal*”
and the commandments of God in the Family
a Proclamation to the World.
The Federal Government has also expanded its power by
creating laws to “legally plundering” its people with the redistribution of
wealth. This also goes against Natural Law
The Powers of the POTUS and the oval office are also
expanding more than the Constitution gave it power to do as well. The
Constitution essentially gave the President 12 powers in Article II-2 & 3:
**
1.
He is the commander in chief of the
military.
2.
He may require written opinions from anyone
serving as head of a department in the executive branch.
3.
He can grant reprieves and pardons.
4.
He can make treaties, as long as
two-thirds of the Senate agrees.
5.
He can appoint ambassadors, justices of
the Supreme Court, and other federal officials, as long as two-thirds of the
Senate agrees.
6.
He can fill vacancies in federal
offices during recesses of the Senate.
7.
He shall from time to time give a
report and recommendations to the Congress.
8.
He may, in a time of extraordinary
circumstances, convene Congress and/or adjourn it (this was defined by the
framers mainly as a time when a declaration of war was needed).
9.
He can meet with foreign diplomats.
10.
He shall take care that all the laws
are faithfully executed.
11.
He shall commission all the officers of
the United States.
12.
He can veto Laws passed by Congress
(Article I-7)
Anything more than this goes against
the Constitution and takes away the freedom of people.
Examples include the Affordable Care
Act and Obamacare which force people to get insurance or pay a fee. The refusal
of giving a treaty by the President to the Senate to be Ratified also goes
against the Constitution (Article II Section II: “He shall have Power,
by and with the Advice and Consent of the Senate, to make Treaties, provided
two thirds of the Senators present concur“). This has happened the Framework
Convention on Climate Change Agreement***. Also an Executive order that forces
a state to stop transporting Illegal Immigrants out of the Country is unconstitutional
because the President can’t make laws, he can only enforce them.
Another Example of the President going against
the constitution is the Executive Order issued by Franklin Delano Roosevelt
that transported Japanese-Americans to Internment Camps. This affected tens of
thousands completely innocent people and had nothing to do with the Japanese
Fascists attacks on the U.S.A.
One final example of bending the constitution is
the use of Executive Agreements between the POTUS and a head of a foreign
country. Unlike treaties these are not sent to the Senate for ratification,
these are not binding to future Presidents and Presidents tend to use them a
lot to bypass Congress. They are
Unconstitutional however and are another example of Presidential expansion of power
from that which is in the Constitution.
As explained in this quote by Dallin H. Oaks “For checks and balances to work properly, and
for the fundamental principle of separation of powers to be honored and perform
its proper function, each branch of government must fulfill its duties fully,
and each must refrain from attempting to exercise the functions of the others”
the Judicial Branch and the Executive Branch should not make Laws just as the
Legislative Branch should not enforce the Law they made.
It may seem that the Federal Government is still expanding
notwithstanding the Constitution’s limits made to prevent tyranny, but the
Framers instituted a deciding check on Federal power. This limit is the power
of the people to elect their representatives, which forces the Federal
Government to follow public opinion closely enough to stay in office.
So to fix these problems that lead to Decline we
need to educate the People that we need to follow our constitution and Natural
law and so they can apply the necessary public pressure to the Government to
follow these things.
*We Hold These Truths
to be Self-Evident Oliver DeMille
**http://oliverdemille.com/2016/02/parties-cant-cooperate/
*** http://dailysignal.com/2016/04/22/obamas-violating-the-constitution-by-not-submitting-climate-treaty-to-senate/
I also did a Common-Sense discussion board Response here it is:
Common Sense is a pamphlet written by Thomas Paine in the 1776 to argue the case for independence from Britain to the American People. It appealed to the common people and not just the elites because
Paine argues that the King of England and Parliament had used their power oppressively against the people of America and that they have the right to discard them: In the Introduction on page 1: “a long and violent abuse of power…the King of England… Parliament…as the good people of this country [America] are grievously oppressed by the combination, they have an undoubted privilege to inquire into the pretensions of both, and equally to reject the usurpation of either”. This appealed to the common people and not just the elites because they, the common people, had been oppressed by the abuse of the King’s and Parliament’s power, and they liked the idea that they had the right to reject them, because that would ease their suffering.
The common people didn’t want another mortal person to be placed above them with power to control and oppress them without their consent, it being against their unalienable right to liberty. That is what a monarch is and there are multiple instances in Common Sensewhere Paine writes against monarchy and the king such as:
"the king…he hath shewn himself such an inveterate enemy to liberty”.
and
“ the crown…hath…eaten out the virtue of the house of commons…it is the Republican and not the Monarchical part of the Constitution of England which Englishmen glory in…choosing a House of Commons …when Republican virtues fail, slavery ensues...the Crown hath engrossed the Commons.”
Since the common people like choosing a House of Commons and the House of Commons itself, and the king had corrupted the House of Commons this frustrated the common people.
Paine argues the case for actual, equal and large representation: “the elected might never form to themselves an interest separate from the electors , the necessity of a large and equal representation ”.
The common people preferred actual representation (representatives serving the interest of the specific people who elected them, and not necessarily the common good of the whole nation), because it was what most colonists believed in.
Common people in the border country/frontier especially liked equal representation, where each district/area gets the same number of electors compared to the population of the area (like if the ratio was 1 representative to 2,000 people, then that ratio is equal for all districts), because they had a larger population than many eastern places in the colony but got a lower number of representatives in the colony legislature.
Common Sense also goes against hereditary succession which the common people didn’t like because, among other reasons, it gave them less opportunity than “high-born” people and maintained a caste system with less economic, social and political mobility.
The common people of the colonies wanted to prosper in commerce and economy, and Paine makes the case that if they stayed part of the British Empire, then they would prosper less in economy and commerce than they could have if they had become an independent separate people. Independence would allow them to conduct commerce with other nations besides the British Empire and they would not be limited in their economy by a king who wanted them to prosper less.
Common Sense appealed to the common people of the colonies through many means and it convinced countless colonists that separation of the colonies from Britain into a separate and independent Nation was necessary and expedient for them arguing that cause of America is the cause of all mankind.
Wednesday, July 6, 2016
Year in Review
So this year I did a physics course online through Coursera and then I started to focus a lot on Government and History.
After finishing a BYU Independent Study World History Course in November, I studied for and took the AP US Government exam at Triton in May. It was a lot of hard work and fun as I got to learn things about the our Federal Government all through the year. I got a 5 with Heavenly Father's wonderful help on the AP U.S. Government and Politics exam.
I also attended a town hall meeting, visited the local courthouse, created campaign signs and went canvassing during the primary elections. I only wish I wasn't still 5 years away from voting. My 18th birthday will be just a month after the 2020 election cycle (wretched). I found out what my AP score was on Saturday.
I am now taking a U.S. History Course also through BYU I.S. and I love it that I live in a place where I can visit a lot of the places I'm learning about. We went to Plymouth a few weeks back and I got to go to Plimoth plantation and talk with the Governor about the colony.
I also took an art class at Triton and got to do a lot of creative projects. My pencil portrait of the Prophet Lorenzo Snow won a prize at the Budding Artist Competition at the NAA. One of my favorite art projects this year was a driftwood Nativity I made for Christmas. I also did a 3D animation in blender through a Youth Digital class that was really interesting.
For math besides the Physics algebra I finished Trigonometry and I started working on Pre-Calculus on Khan Academy.
I am still playing soccer with the 7th and 8th graders and with my brother pretty much every day.
One of my favorite things about homeschooling is eating really good food every day. We grow a lot of kale every summer and I have been mixing it into green smoothies and all sorts of other meals as one of my favorite foods.
I've read a lot of classic books this year with our family as well as a lot about freedom and government like The Law by Bastiat and We Hold These Truths to be Self-Evident. I've also found some time for fun reading and got through all of Sherlock Holmes and recenlty got into the Wizard of Earthsea series this year. I can't wait til Brandon Mull publishes his new Dragonwatch series.
After finishing a BYU Independent Study World History Course in November, I studied for and took the AP US Government exam at Triton in May. It was a lot of hard work and fun as I got to learn things about the our Federal Government all through the year. I got a 5 with Heavenly Father's wonderful help on the AP U.S. Government and Politics exam.
 |
| My AP Scores |
I also attended a town hall meeting, visited the local courthouse, created campaign signs and went canvassing during the primary elections. I only wish I wasn't still 5 years away from voting. My 18th birthday will be just a month after the 2020 election cycle (wretched). I found out what my AP score was on Saturday.
I am now taking a U.S. History Course also through BYU I.S. and I love it that I live in a place where I can visit a lot of the places I'm learning about. We went to Plymouth a few weeks back and I got to go to Plimoth plantation and talk with the Governor about the colony.
I also took an art class at Triton and got to do a lot of creative projects. My pencil portrait of the Prophet Lorenzo Snow won a prize at the Budding Artist Competition at the NAA. One of my favorite art projects this year was a driftwood Nativity I made for Christmas. I also did a 3D animation in blender through a Youth Digital class that was really interesting.
For math besides the Physics algebra I finished Trigonometry and I started working on Pre-Calculus on Khan Academy.
I am still playing soccer with the 7th and 8th graders and with my brother pretty much every day.
One of my favorite things about homeschooling is eating really good food every day. We grow a lot of kale every summer and I have been mixing it into green smoothies and all sorts of other meals as one of my favorite foods.
I've read a lot of classic books this year with our family as well as a lot about freedom and government like The Law by Bastiat and We Hold These Truths to be Self-Evident. I've also found some time for fun reading and got through all of Sherlock Holmes and recenlty got into the Wizard of Earthsea series this year. I can't wait til Brandon Mull publishes his new Dragonwatch series.
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