Math 321: Vector and Complex Calculus for the Physical Sciences

Fall 2011 course information

Earth from r ≃ 42156 km, θ =45°, φ = - 90° Prereq: Math 221, Math 222 .

Current Textbook None! Course notes are posted below. Some of the material is covered in your Calculus book (Math 222, 234), so you'll use that book again, hopefully you didn't throw it away!

Common Latin Abbreviations used in scientific and technical literature.

Quick Outline (Detailed Outline)

Vector, Matrix (and Tensor) Algebra (in 3D Euclidean space)
Vector Calculus
Complex Calculus

Lecture notes

(Fall 2011: These notes are somewhat out of date and do not include some material covered in class. Take you own notes in class and complete by reading these notes.)

Vectors and Matrices, (2008/09/01)
- dv/dt = b x v solutions (motion of charged particle in a constant magnetic field; uniform rotation) (2006/02/11)
Vector Calc (2006/11/14 draft) Extra notes on Gradient (2008/03/14 draft)
Complex Calc (updated 2009/04/20) Draft + complex maps examples (updated 2008/04/29)

Supplementary information

There are all sorts of good things available in other books and on the web... although don't believe everything you read!

Basics of vectors in 3D space and generalizations of the vector concept (scroll down to `Representation of a vector' first. Unfortunately that page uses the old fashioned i, j, k notation and refers too much to that orthogonal basis [not anymore, I replaced i, j, k by e₁, e₂, e₃ (2007/01/23)], but all these things have geometric interpretations that are important, so focus on the pictures not the formula.) The Summation convention page explains why you should forget about i, j, k and replace them in your mind with e₁, e₂, e₃, as we always do in Math 321, and beyond.
These vector concepts and the boldface notation are due to Josiah Willard Gibbs , yep, the same fellow that you have heard about in Chemistry, Physics, Thermodynamics, Statistical Mechanics,... Here's a link to the paper where Einstein introduced the summation convention . This is his paper on the foundation of general relativity. The summation convention is introduced at the bottom of page 158.