My Calculus 2 Review Guide (Florida Polytechnic University)

Introduction:

Hello Guys! So if you don't know me already my name is Jonathan Gan and I am currently enrolled in Florida Polytechnic University for my major in Computer Engineering!

Now if you don't know already Engineering majors have to do a lot of math and right now Im getting my ass kicked in Calculus 2 class so to prepare for my final on Monday Im writing this study guide that will be everything on the Syllabus ( or at least as far as it seems my final will be focused on)

My advise:

So being a student in the field of computer engineering, its hard to say the best approach since not all majors will need math as heavily as I will but good notes and keeping your old exams are my best advise. I wish I had spent more time studying for each exam instead of slacking until now but thats beside the point.

The basic skills you will need:
Memorize all derivative and integral rules that you will need, each topic will rely heavily on those so it's better you hear it now than to realize it the hard way. Also get good at visualizing your problems and understanding what it is that you're trying to solve. I struggled with and still do with a lot of these topics but by posting my study material all in one place, I feel it will help anyone that may come across this stuff one day!

Course Info

Course Title: Analytic Geometry & Calculus 2
Course Number: MAC 2312 Section 1
Credit Hours: 4
Instructor: Burbank
Textbook: Thomas Calculus Early Transcendentals 14/E Pearson 978-0134764528

Learning outcomes:

1. Ability to calculate an integral using integration by parts
2. Ability to calculate an integral using Trigonometric Substitution
3. Ability to calculate the volume of a solid of revolution
4. Deduce whether a given series converges or diverges
5. Calculate the Taylor Series for a given differentiable function

Terms & Vocabulary

Integration:
it is a branch of mathematics concerned with the theory and applications (as in the determination of lengths, areas, and volumes and in the solution of differential equations) of integrals and integration

U- substitution:
integration by substitution, also known as u-substitution, is a method for finding integrals. Using the fundamental theorem of calculus often requires finding an antiderivative. For this and other reasons, integration by substitution is an important tool in mathematics. It is the counterpart to the chain rule for differentiation.

Sequence
So a sequence is basically just a list so by utilizing a sequence of numbers you can use it to create a series (hence why the two are taught together. By adding a summation in from a sequence, you basically turn it into a series.

Series
So a series is a summation of an infinite sequence which as defined above, you can use a sequence to figure out properties of the series like its limit and how it behaves as far as tests of convergence and divergence are concerned.

Taylor Series
So when ever you're given an integral, you can basically write the integral as an infinite series and this allows you to determine a lot about the summation. The Taylor series in its most basic way of explaining it, is a method of using the derivatives and the point of a integral to estimate the summation of how a series will behave to an infinite number of terms as integral without bounds are basically a series. The Taylor series has a formula but as long as you understand the idea/concept of what you're solving.

First Exam Problems w/ solution

1.        ∫ 2x/√(1−x^2)
   
           u=1-x^2
           du= 2xdx
   
         =  ∫ 1/(u^1/2) du
         = ∫ u^-1/2)du
             
              -1/2 + 2/2 = 1/2
               a/b / c/d = a/b * d/c
               
          = 2u^1/2 = 2(1-x^2)^1/2 + c
   

Still being worked on...