# Lecture Notes

Below are the lecture notes for every lecture session. Some lecture sessions also have supplementary files called "Muddy Card Responses." Students pick up half pages of scrap paper when they come into the classroom, jot down on them what they found to be the most confusing point in the day's lecture or the question they would have liked to ask. Responses are then made available to all students on the class Web site.

SES # TOPICS
I. First-order Differential Equations
L0 Simple Models and Separable Equations
L1 Direction Fields, Existence and Uniqueness of Solutions (PDF)
L2 Numerical Methods (PDF)
L3 Linear Equations: Models (PDF)
L4 Solution of Linear Equations, Variation of Parameter (PDF)
L5 Complex Numbers, Complex Exponentials (PDF)
L6 Roots of Unity; Sinusoidal Functions (PDF)
L7 Linear System Response to Exponential and Sinusoidal Input; Gain, Phase Lag (PDF)
L8 Autonomous Equations; The Phase Line, Stability (PDF)

Muddy Card Responses (PDF)
L9 Linear vs. Nonlinear (PDF)
L10 Hour Exam I
II. Second-order Linear Equations
L11 The Spring-mass-dashpot Model; Superposition Characteristic Polynomial; Real Roots; Initial Conditions (PDF)

Muddy Card Responses (PDF)
L12 Complex Roots; Damping Conditions (PDF)
L13 Inhomogeneous Equations, Superposition (PDF)
L14 Operators and Exponential Signals (PDF)

Muddy Card Responses (PDF)
L15 Undetermined Coefficients (PDF)
L16 Frequency Response (PDF)
L17 Applications: Guest appearance by EECS Professor Jeff Lang (PDF)

Supplementary Notes

Driving Through the Dashpot (PDF)
L18 Exponential Shift Law; Resonance (PDF)
L19 Hour Exam II
III. Fourier Series
L20 Fourier Series (PDF)
L21 Operations on Fourier series (PDF)

Muddy Card Responses (PDF)
L22 Periodic Solutions; Resonance (PDF)
IV. The Laplace Transform
L23 Step Function and delta Function (PDF)
L24 Step Response, Impulse Response (PDF)
L25 Convolution (PDF)
L26 Laplace Transform: Basic Properties (PDF)

Muddy Card Responses (PDF)
L27 Application to ODEs; Partial Fractions (PDF)
L28 Completing the Square; Time Translated Functions (PDF)

Muddy Card Responses (PDF)
L29 Pole Diagram (PDF)
L30 Hour Exam III
V. First Order Systems
L31 Linear Systems and Matrices (PDF)
L32 Eigenvalues, Eigenvectors (PDF)
L33 Complex or Repeated Eigenvalues (PDF)
L34 Qualitative Behavior of Linear Systems; Phase Plane (PDF)
L35 Normal Modes and the Matrix Exponential (PDF)
L36 Inhomogeneous Equations: Variation of Parameters Again (PDF)

Muddy Card Responses (PDF)
L37 Nonlinear Systems (PDF)
L38 Examples of Nonlinear Systems (PDF)
L39 Chaos (PDF)
L40 Final Exam