D. Definite Integral Solutions

G. Graphical and Numerical Methods

C. Complex Numbers

IR. Input Response Models

O. Linear Differential Operators

S. Stability

I. Impulse Response and Convolution

H. Heaviside Coverup Method

LT. Laplace Transform

CG. Convolution and Green's Formula   

LS.1. Linear Systems: Review of Linear Algebra

LS.2. Homogeneous Linear Systems with Constant Coefficients

LS.3. Complex and Repeated Eigenvalues

LS.4. Decoupling Systems

LS.5. Theory of Linear Systems

LS.6. Solution Matrices

GS.1-6. Graphing ODE Systems

GS.7-8. Structural stability

LC. Limit Cycles

FR. Frequency Response

P. Poles and Amplitude Response

1. First Order ODE's   Solutions

2. Higher Order ODE's   Solutions

3. Laplace Transform   Solutions

4. Linear Systems   Solutions

5. Graphing Systems   Solutions

6. Power Series   Solutions

7. Fourier Series   Solutions

8. Extra Problems   Solutions

Supplementary Notes (Haynes Miller - Spring 2012 versions)

#0. Preface

#1. Notation and language

#2. Modeling by first order linear ODEs

#3. Solutions of first order linear ODEs

#4. Sinusoidal solutions

#5. The algebra of complex numbers

#6. The complex exponential

#7. Beats

#8. RLC circuits

#9. Normalization of solutions

#10. Operators and the exponential response formula

#11. Undetermined coefficients

#12. Resonance

#13. Time invariance

#14. The exponential shift law

#15. Natural frequency and damping ratio

#16. Frequency response

#17 Resonance, not: the Tacomah Narrows Bridge

#18 Linearization: the phugoid equation as example

#19 The Wronskian

#20 More on Fourier series

#21 Steps, impulses and generalized functions

#22 Generalized functions and differential equations

#23 Impulse and step responses

#24 Convolution

#25 Laplace Transform technique: coverup

#26 The Laplace Transform and generalized functions

#27 The pole diagram and the Laplace Transform

#28 Amplitude response and the pole diagram

#29 The Laplace Transform and more general systems

#30 First order systems and second order equations

#31 Phase portraits in two dimensions

Concourse 18.03 Linear Algebra Supplements (Robert Winters, Spring 2014)

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

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 Linear Coordinates, Alternate Bases, and Evolution Matrices

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

Nonlinear Systems and Linearization

Concourse 18.03 Lecture Notes (Robert Winters)

Lecture #1 Notes (revised Feb 2, 2020)

Lecture #2 Notes (revised Feb 5, 2020)

Lecture #3 Notes (may be revised)

Lecture #4 Notes (may be revised)

Lecture #5 Notes (revised Feb 19, 2020)

Lecture #6-7 Notes (may be revised)

Lecture #8 Notes (revised Feb 26, 2020)

Lecture #9 Notes (may be revised)

Lecture #10 Notes (revised Mar 17, 2020)

Lecture #11 Notes (may be revised)

Lecture #12 Notes (revised Mar 27, 2020)

Lecture #13 Notes (may be revised)

Lecture #14 Notes (revised Mar 27, 2020)

Lecture #15 Notes (new, Apr 7, 2019)

Lecture #16 Notes (new, Apr 21, 2019)

Lecture #17-18 Notes (revised, May 27, 2019)

18.03 Supplementary Notes (Haynes Miller, Spring 2010)

These notes (Spring 2010 version) were written by Prof. Haynes Miller and were designed to supplement the Edwards & Penney textbook. They are available as individual chapters below or compiled into a complete set. (PDF - 1.5MB)