[September 6, 2020] These are notes for 3rd-semester calculus. They were written during Spring, 2018. I need to write up a introductory section on vector fields, but the rest of the notes are in reasonable shape.

Latest changes:

- [January 13, 2022] I corrected the problem with the stylesheet URL, so the web pages should display better now. I made some revisions to the notes on Lagrange multipliers to improve the explanations.
- [January 18, 2022]Minor typo fixed in the notes on gradient, divergence, and curl.
- [January 22, 2022]The notes on conservative fields have been revised. I'm no longer regarding curves as vector functions, and will gradually update the other notes to reflect this.
- [October 14, 2023] I fixed an error in one of the spherical coordinate examples.

- Points in 2 and 3-dimensional Euclidean space

[PDF file] - Vectors

[PDF file] - Dot products

[PDF file] - Matrices

[PDF file] - Determinants

[PDF file] - Cross products

[PDF file] - Lines and planes

[PDF file] - Distance problems involving lines and planes

[PDF file] - Surfaces

[PDF file] - Parametric surfaces

[PDF file] - Vector functions

[PDF file] - Parametric curves

[PDF file] - Velocity and acceleration

[PDF file] - Arc length

[PDF file] - Unit tangent, unit normal, binormal; curvature; osculating circle

[PDF file] - Functions of several variables

[PDF file] - Limits and continuity

[PDF file] - Partial derivatives

[PDF file] - Tangent planes and normal lines

[PDF file] - Derivatives of functions of several variables

[PDF file] - The Chain Rule for functions of several variables

[PDF file] - Taylor series for functions of several variables (brief description - no proofs)

[PDF file] - Directional derivatives and gradients

[PDF file] - Maxima and minima for functions of two variables

[PDF file] - Lagrange multipliers

[PDF file] - Double integrals

[PDF file] - Volumes by double integrals

[PDF file] - Double integrals in polar

[PDF file] - Interchanging the order of integration

[PDF file] - Surface area

[PDF file] - Triple integrals

[PDF file] - Change of variables in multiple integrals

[PDF file] - Cylindrical coordinates

[PDF file] - Spherical coordinates

[PDF file] - Center of mass

[PDF file] - Gradient, divergence, curl

[PDF file] - Path integrals

[PDF file] - Conservative fields and path independence

[PDF file] - Green's theorem

[PDF file] - Scalar and vector surface integrals; flux

[PDF file] - The Divergence Theorem

[PDF file] - Stokes' Theorem

[PDF file]

Copyright 2020 by Bruce Ikenaga