<p>Hey guys,</p>
<p>So before I go on I would just like to say that I really don't want to be left waiting next year for the tests. I have had "exposure" to Calculus since the beginning of my year and am very adept at its notation and philosophy even if i'm not too ahead in the book. </p>
<p>Here's what I have so far:</p>
<p>Derivatives
- Sum Rule
- Power Rule
- Chain Rule
- Quotient Rule
- Reciprocal Rule
- Function Exponentiation Rule
- Inverse-Function Rule
- Implicit Differentiation
- Logarithmic Chain-Differentiation(I think its logarithmic differential formally but idk for sure)
- Multivariable Derivatives - Multivariable Delta Process
- Derivatives of functions based on Taylor/Maclaurin Series Expansions...</p>
<p>Limits
- L'Hopital's Rule
- Squeeze Theorem
- Division Series Expansion Theorem (idk the formal name but its the alternative to L'Hopital's Rule... Obviously i'm making this name up but in its jist you divide numerator by the denominator (taylor series if necessary) and expand the series that you get its useful for situations where derivation for lack of a better word is a pain in the ass)</p>
<p>What I need help with is learning the delta/epsilon definition and mastering integrals... Plus anything else I might have missed. Quite frankly I have know background in integrals besides their applications and the fundamental theorem/calculating area. Also do you know if we have to master the gamma function? n-nomial expansion? and n-dimensional vectors? I know i'll have to learn 2D vectors atleast.</p>
<p>What's your advice on how to study and get going. I'm using Barron's Calculus the Easy Way, Study Island Calculus AB and BC, Kaplan AP Calculus AB and BC... Plus the wonderful tool of the internet*</p>
<p>*Credits to Wolfram Mathworld, PhysicsForms, and Wikipedia [look up mathematics there you will be amazed the level of depth although its a little bit frustrating when it gets too complex]</p>