Instructor: Anatolii Grinshpan
Office hours: Tu 12-1 and Th 12-2, Korman 249.
Week 1. First-order equations. Slope field. Slope field plotter. Phase line.
Stationary solutions. Banker’s equation. A gallery of equations.
Reading and exercises: Chapters 1, 2. Problems.
Week 2. Quiz 1 (Chapters 1, 2). A glimpse into PDE: transport equation.
Population dynamics. Existence and uniqueness of solutions. Leaking bucket.
Reading and exercises: Chapters 3-5. Problems.
Week 3. Quiz 2 (Chapters 3, 4). Newton’s law of cooling. Integrating factors. Exact equations.
Reading and exercises: Chapters 5-7. Problems.
Week 4. Euler’s numerical method. Example. Reading and exercises: Chapter 8.
Quiz 3 (Chapters 7, 8). Spring-mass oscillations. About Babylonian astronomers.
Week 5. Midterm 1 (Chapters 1-8). Spring-mass oscillations. Homogeneous second-order linear equations.
Space of solutions. Forced oscillations. Method of undetermined coefficients.
Reading and exercises: Chapters 9, 10. Problems.
Week 6. Linear equations with constant coefficients. Complex numbers. Complex and repeated characteristic values.
Reading and exercises: Chapters 11, 12. Problems.
Week 7. Multiple spring-mass systems. Boundary-value problems. Eigenvalues and eigenfunctions.
Quiz 5 (Chapters 11, 12). One-dimensional heat equation. Heat kernel.
Reading and exercises: Chapters 13, 14. Problems.
Week 8. Product solutions. Boundary-value problems for the heat equation.
Quiz 6 (Chapters 13, 14). One-dimensional wave equation. A drum model. Bessel’s equation. Series solutions.
Reading and exercises: Chapters 15, 16.
Week 9. Midterm 2 (Chapters 9-16). Systems of linear equations with constant coefficients. Two-dimensional case. Slope fields.
Methods of solution. Phase portrait. Reading and exercises: Chapters 14, 15, 21 (and 16-20 on Linear Algebra).
Nonhomogeneous systems (mixing in multiple tanks). Nonlinear systems (predator-prey).
3D systems (helical orbits, Lorenz attractor, Dzhanibekov effect).
Reading and exercises: Chapters 22-25.
Mar 11. Discussion session: 4:10-5:30+, Lebow 241.
Mar 15. Final exam (all lectures): 1-3 PM, Lebow 135.