This week in calc we primarily went over Chapter 7.3 along with the t-shirt ideas.We took the whole week to go over Chapter 7.3 because of the longevity of that section in addition to the different topics which were apart of it.
Since the new year,it seems that I would rather be doing anything else other than blog posts such as math homework or even studying for calc. It.It seems that blog posts are bringing out the worst in me as far as writing is concerned.I was kidding:I just wanted to avoid the boring this week we learned about blah blah as my introduction.The topic of discussion this week was Slope Fields and anti-differentiation by substitution.Both of these units were familiar but felt difficult to understand and so I took the time to study those topics better through the homework assignments.Since I began regularly doing my homework assignments,I have noticed an increase in grade in Calc which has thought me the importance of getting the homework done on time.
The fundamental theorem was a great unit because it combined topics I enjoyed studying in calc and made it more simple than I would have imagined.While the fundamental theorem is a great unit it also serves as the bridge between integration and differentiation.To understand it better,this theorem has been divided into two portions: one of which deals with the chain rule to substitute and another which deals with finding the area by evaluating the integral. Learning this unit was suprisingly difficult for me,intially.I think it's because I failed to see the lack of connection on problems using the chain rule.I simply assumed it was going but how ?This question was answered completly soon after I began watching several videos which taught me a pattern per say to manuever through the problem
This week we began chapter 5 and we started with an activity on finding the areas of iregular polygonsand shapes.Some of the polygons/shapes were combinations of triangles, trapezoids, rectangles, and circles and so in order to find the areas of one such example one would use the appropriate polygon.For each of the shapes one could use a rectangle to find the area,which is why finding area is measured in square units.This directly led us into the topic of RAM or rectangular approximation method.
This was the final week of school of 2014 and it went out with a bang with the way we were able to conclude with chapter four.After chapter four we had a quiz on the chapter along with the previous topics we discussed such as limits and derivatives.I had some trouble with finding the critical points and the other information we had learned in the last chapter about graphing.However,I was able to solve this problem by remembering how to do problems such as these with a trick.So for local max/mins,you in the numbers you found in the 1st derivative(critical numbers) to the second derivative to find the local max or min.For a local max if the value of the second derivative is less than zero then it is a local max and if the value of the second derivative is greater than zero it is a local min.In a special case where the value of the second derivative equals zero then anything is possible.
This week was primarily focused on reviewing Chapter 4,which I have found to be one of the most challenging units we have had so far but now I have grasped the concept a little better.The modeling and optimization was simply figure out the the lengths of the sides,plug it into a formula,solve that formula for one variable and plug that variable into a formula you are given to solve it.After all of this you take the derivative and set the equation where you solve for the value.When you solve for the value,you plug in the number into the original equation. The related rates
I thought related rates were much more difficult than optimization.While it combined the analytical problem solving in optimization,it also had the additional piece of information such as the volume and side changing with respect to time.A way I then began remembering in order to solve a problem such as those were to first identify the variables,develop a model of the problem,write an equation relating the rate of change being looked for to the variable which is being seeked
We simply learned about finding the derivative of functions and the transformations of a single function with the function being the square root function for the first problem and it enduring changes such as a shift downwards,upwards and even a stretch of the function.We saw how related the slope of the tangent line was when we shifted it down or up and I came to a conclusion that it may apply to all functions which are differentiable because shifting it up and down will similar to doing that to the slope which in turn will match that pattern.