Math 210 – Differential Equations, Winter 2016


Instructor: Anatolii Grinshpan
Office hours:  Tu 12-1 and Th 12-2, Korman 249.

Course information   Terrell’s notes   Academic calendar    Tutoring center  

Week 1. First-order equations. Slope field. Slope field plotter. Phase line.

              Stationary solutions.  Banker’s equation. A gallery of  equations.

              Isoclines. Separable equations. Homogeneous equations. Bernoulli’s equation.

              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.

               Reduction of order. Resonance. Example. Quiz 4 (Chapters 9, 10). Multiple spring-mass systems.

               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). 

                Phase portrait generator. Problems.

 

Week 10.  Classification of phase portraits. Purely imaginary eigenvalues. Quiz 7 (Chapters 21-23).

                 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.