Math E-21c Lecture Notes (Robert Winters)

Lecture #1 Notes (revised Sept 12, 2024)

Lecture #2 Notes (revised Feb 25, 2022)

Lecture #3 Notes (revised Sept 18, 2020)

Lecture #4 Notes (revised Sept 30, 2021)

Lecture #5 Notes (minor revision Oct 8, 2024)

Lecture #6 Notes (revised Oct 6, 2021)

Lecture #7 Notes (revised Oct 21, 2024)

Lecture #8 Notes (revised Oct 13, 2021)

Lecture #9 Notes (revised Oct 31, 2024)

Lecture #10 Notes (minor edits Nov 6, 2024)

Lecture #11 Notes (revised Nov 20, 2021)

Lecture #12 Notes (revised Nov 16, 2022)

Lecture #13 Notes (minor edits Dec 4, 2024)

Lecture #14 Notes (revised Dec 8, 2023)

Math E-21c Supplements (Robert Winters)

Basic Calculus Notes - Derivatives, Linear Approximation, and Higher Order Approximation

Systems of Linear Equations and Row Reduction

Matrices and Vectors – Meaning of Columns of a Matrix

Matrix Algebra and Inverse Matrices

Subspaces, Span, Linear Independence, Basis of a Subspace; Images and Kernel of a Matrix

Coordinates Relative to a Basis; Matrix of a Linear Transformation Relative to Bases

General Linear Spaces (Vector Spaces) and Solutions of ODEs

Linear nth Order ODE Cookbook (may be revised)

A Worked Example of a 2nd Order Linear System with Sinusoidal Input Signal

Laplace Transform Facts

Worked Examples of Laplace Transform and Convolution

Notes on Convolution

Sampler of Phase Plane diagrams

Supplement on Evolution Matrices

Supplement on Representation of Functions in Different Coordinates

Supplement on Linear Coordinates, Alternate Bases, and Evolution Matrices

Matrix Methods for Solving Systems of 1st Order Linear Differential Equations

Continuous Dynamical Systems – Part 1

Continuous Dynamical Systems – Part 2

Nonlinear Systems and Linearization