Lecture notes
Lecture 1: Introduction and population growth models
Lecture 2: Logistic equation, separation of variables, mixing problem
Lecture 3: Slope fields and Euler's method
Lecture 4: Euler's method and Phase lines for Autonomous equations
Lecture 5: Existence and uniqueness theorems
Lecture 6: Integrating factors, recap of existence and uniqueness theorems, phase lines
Lecture 7: One parameter families of ODEs and bifurcation
Lecture 8: Properties of linear equations, method of undetermined coefficients, and miscellania from chapter 1
Lecture 9: Introduction to systems
Lecture 10: Direction fields for systems, autonomous systems, uniqueness for systems
Lecture 11: Introduction to planar linear systems, superposition principle, and linear independence of solutions
Lecture 13: Planar linear systems, straight line solutions, and phase portraits for real distinct eigenvalues
Lecture 14: Planar linear systems - complex eigenvalues and their phase portraits
Lecture 15: Shape of phase portraits for complex eigenvalues, introduction to repeated eigenvalues
Lecture 16: Repeated eigenvalues, generalized eigenvectors
Lecture 17: Trace determinant plane, 3d systems, and extra details from 3.4 and 3.5
Lecture 18: Second order linear equations, damped harmonic oscillators, and two perspectives of the solutions
Lecture 19 and 20: Overdamped, underdamped, and critically damped oscillators. Forced oscillations and method of undetermined coefficients.
Lecture 21: Sinusoidal forcing, variation of parameters
Lecture 22: Beats, pure resonance, practical resonance - how does the steady state response vary with the external force frequency?
Lecture 23: Non-linear equations and linearization at equilibria
Lecture 24: Nullcline analysis
Quiz and exam solutions
Quiz 1: Modeling and separation of variables
Quiz 2: Slope fields, Euler's method, and phase lines for autonomous equations
Quiz 3: Integrating factors, existence and uniqueness of solutions
Quiz 4: Bifurcation diagrams, mixing problem variable volume
Quiz 5: Systems of equations, direction fields, equilibria
Midterm 1 solutions
Quiz 6: Planar linear systems: Real distinct eigenvalues
Quiz 7: Complex eigenvalues
Quiz 8: Repeated eigenvalues and the trace-determinant plane
Midterm 2 solutions
Quiz 9 solutions (corrected version)
Quiz 10 solutions (corrected version)
Quiz 11 solutions