Calculus

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Lessons
These are my notes for lessons on everything in a standard calculus curriculum, as well as many things that go beyond an introductory calculus course. These notes are meant to be concise: they don't gloss over any important information but they also aren't painfully long. However, even if you have read the notes, I still strongly suggest doing the practice problem in order to fully comprehend the topic.
Limits


Introductory Derivatives


Implicit Differentiation and Related Rates


Logarithmic Differentiation and Optimization


Antiderivatives


Integration by Parts


Definite Integrals


Integral Applications
Problems
These problems were selected from previous Mu Alpha Theta tests, primarily January regionals, transcribed and arranged (mostly) in order of difficulty. As of now, these problems encompass all the different kinds of problems you may encounter on such exams. If you feel comfortable with them, then you should have no problem competing. Remember to practice on your own: speed is key!
Limits


Tangent Lines and Methods of Derivation


Antiderivatives and $u$-subsitution


Definite Integrals and the FTC


Solutions
Comprehensive solutions created by yours truly. I have attempted to explain in as much detail as possible, so they are a bit lengthier than you may be used to, but cover all the descrepincies Mu Alpha Theta solutions ommit.
Limits


Tangent Lines and Methods of Derivation


Antiderivatives and $u$-substitution


Definite Integrals and the FTC