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Differential Equations >> Content Detail



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Calendar

The calendar below provides information on the course's lecture (L) and recitation (R) sessions.

 
SES #TOPICSKEY DATES
I. First-order Differential Equations
L0Simple Models and Separable Equations
R1Natural Growth and Decay
L1Direction Fields, Existence and Uniqueness of Solutions
R2Direction Fields, Integral Curves, Isoclines
L2Numerical Methods
L3Linear Equations: Models
R3Numerical Methods; Linear Models
L4Solution of Linear Equations, Variation of ParameterProblem set 1 due
R4First Order Linear ODEs: Models and Solutions
L5Complex Numbers, Complex Exponentials
L6Roots of Unity; Sinusoidal Functions
L7Linear System Response to Exponential and Sinusoidal Input; Gain, Phase Lag
R5Complex Numbers, Complex Exponentials
L8Autonomous Equations; The Phase Line, StabilityProblem set 2 due
L9Linear vs. Nonlinear
R6Using the Complex Exponential; Autonomous Equations
L10Hour Exam I
II. Second-order Linear Equations
R7Solutions to Second Order ODEs
L11The Spring-mass-dashpot model; Superposition
Characteristic polynomial; Real Roots; Initial Conditions
L12Complex Roots; Damping Conditions
R8Homogeneous Second Order Linear Equations
L13Inhomogeneous Equations, Superposition
R9Second Order Linear Equations
L14Operators and Exponential SignalsProblem set 3 due
L15Undetermined Coefficients
R10Operators, Exponential Response, Exponential Shift, Undetermined Coefficients
L16Frequency Response
R11Superposition, Frequency Response
L17Applications: Guest Appearance by EECS Professor Jeff LangProblem set 4 due
L18Exponential Shift Law; Resonance
R12Review
L19Hour Exam II
III. Fourier Series
R13Fourier Series: Introduction
L20Fourier Series
L21Operations on Fourier Series
R14Fourier Series: Playing Around
L22Periodic Solutions; Resonance
R15Fourier Series: Harmonic Response
IV. The Laplace Transform
L23Step Function and Delta FunctionProblem set 5 due
L24Step Response, Impulse Response
R16Step and Delta Functions, and Step and Delta Responses
L25Convolution
R17Convolution
L26Laplace Transform: Basic PropertiesProblem set 6 due
L27Application to ODEs; Partial Fractions
R18Laplace Transform
L28Completing the Square; Time Translated FunctionsProblem set 7 due
L29Pole Diagram
R19Hour Exam Review
L30Hour Exam III
V. First Order Systems
R20Systems of First Order Equations
L31Linear Systems and Matrices
L32Eigenvalues, Eigenvectors
R21Eigenvalues and Eigenvectors
L33Complex or Repeated Eigenvalues
R22Complex or Repeated Eigenvalues
L34Qualitative Behavior of Linear Systems; Phase PlaneProblem set 8 due
L35Normal Modes and the Matrix Exponential
R23Qualitative Analysis of Linear Systems
L36Inhomogeneous Equations: Variation of Parameters Again
R24Matrix Exponentials and Inhomogeneous Equations
L37Nonlinear SystemsProblem set 9 due
L38Examples of Nonlinear Systems
R25Qualitative Analysis of Nonlinear Systems
L39Chaos
R26Review
L40Final Exam

 








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