Calculus series
This is a series of calculus guides based off my calculus notes at RPI. Starting at a high school algebra/precalculus level, they build up to encompass most of the contents of a multi-year set of courses in calculus, including (ordinary) calculus, multivariable calculus, vector calculus, differential equations, and more.
The guides in the series are listed below:
- Precalculus guide - a review of the essentials of high school-level algebra before starting calculus.
- Calculus in one variable - the basics of calculus, including the concept of a limit, derivative, and integral in one dimension, how to compute derivatives and integrals, as well as infinite series. These topics are typically covered in a college-level Calculus I and Calculus II course.
- Multivariable calculus - extensions of single-variable calculus to multiple dimensions, including multiple integrals, partial derivatives, optimization of multivariate functions, line integration, and vector derivatives.
- Vector calculus and beyond - a more advanced treatment of the topics in multivariable calculus, as well as Green's theorem, Stoke's theorem, and the Divergence Theorem. This also covers topics beyond a standard vector calculus class, including the calculus of variations and tensor calculus.
- Introduction to differential equations - an introductory guide to the theory of differential equations, covering mostly ODEs (ordinary differential equations). The topics covered including classifying ODEs, applying the basic solution techniques to various types of ODEs, and solving eigenvalue problems.
- Partial differential equations - a more advanced guide that specifically covers partial differential equations (PDEs). This includes a deep dive into the standard PDEs of mathematical physics (wave equation, diffusion equation, and Laplace's equation), as well as solving a variety of boundary-value problems.
- For a crash course in PDEs, see the mini-guides solving separable PDEs and solving the wave equation