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Differential Equations >> Content Detail



Lecture Notes



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
L0Simple Models and Separable Equations
L1Direction Fields, Existence and Uniqueness of Solutions (PDF)
L2Numerical Methods (PDF)
L3Linear Equations: Models (PDF)
L4Solution of Linear Equations, Variation of Parameter (PDF)
L5Complex Numbers, Complex Exponentials (PDF)
L6Roots of Unity; Sinusoidal Functions (PDF)
L7Linear System Response to Exponential and Sinusoidal Input; Gain, Phase Lag (PDF)
L8Autonomous Equations; The Phase Line, Stability (PDF)

Muddy Card Responses (PDF)
L9Linear vs. Nonlinear (PDF)
L10Hour Exam I
II. Second-order Linear Equations
L11The Spring-mass-dashpot Model; Superposition Characteristic Polynomial; Real Roots; Initial Conditions (PDF)

Muddy Card Responses (PDF)
L12Complex Roots; Damping Conditions (PDF)
L13Inhomogeneous Equations, Superposition (PDF)
L14Operators and Exponential Signals (PDF)

Muddy Card Responses (PDF)
L15Undetermined Coefficients (PDF)
L16Frequency Response (PDF)
L17Applications: Guest appearance by EECS Professor Jeff Lang (PDF)

Supplementary Notes

Driving Through the Dashpot (PDF)
L18Exponential Shift Law; Resonance (PDF)
L19Hour Exam II
III. Fourier Series
L20Fourier Series (PDF)
L21Operations on Fourier series (PDF)

Muddy Card Responses (PDF)
L22Periodic Solutions; Resonance (PDF)
IV. The Laplace Transform
L23Step Function and delta Function (PDF)
L24Step Response, Impulse Response (PDF)
L25Convolution (PDF)
L26Laplace Transform: Basic Properties (PDF)

Muddy Card Responses (PDF)
L27Application to ODEs; Partial Fractions (PDF)
L28Completing the Square; Time Translated Functions (PDF)

Muddy Card Responses (PDF)
L29Pole Diagram (PDF)
L30Hour Exam III
V. First Order Systems
L31Linear Systems and Matrices (PDF)
L32Eigenvalues, Eigenvectors (PDF)
L33Complex or Repeated Eigenvalues (PDF)
L34Qualitative Behavior of Linear Systems; Phase Plane (PDF)
L35Normal Modes and the Matrix Exponential (PDF)
L36Inhomogeneous Equations: Variation of Parameters Again (PDF)

Muddy Card Responses (PDF)
L37Nonlinear Systems (PDF)
L38Examples of Nonlinear Systems (PDF)
L39Chaos (PDF)
L40Final Exam

 








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