**Instructors:** Longmei Shu

**Course on canvas.dartmouth.edu.**⇗

## Syllabus

Course Summary: Date Details Mon Sep 12 1.1, 1.2 Basic mathematical models, Solutions of some differential equations Wed Sep 14 1.2, 1.3 Solutions of some differential equations, Classification of differential equations Fri Sep 16 2.1, 2.2 Linear first order differential equations, Separable equations Mon Sep 19 2.4 Existence and uniqueness theorems Wed Sep 21 2.3 Modeling with differential equations Thu Sep 22 Homework 1 due by 11:59pm Fri Sep 23 2.5 Autonomous equations and population dynamics Mon Sep 26 2.6 Exact equations Tue Sep 27 Homework 2 due by 11:59pm Wed Sep 28 3.1, 3.2 Second order constant coefficient equations with distinct roots, the Wronskian Fri Sep 30 3.3 Complex conjugate roots Mon Oct 3 3.4 Repeated roots and reduction of order Wed Oct 5 3.5, 3.6 Nonhomogeneous equations: Method of undetermined coefficients and variation of parameters Thu Oct 6 Homework 3 due by 11:59pm Fri Oct 7 7.1, 7.2 Review of matrices Mon Oct 10 7.3, 7.4 Systems of ODEs, Existence and uniqueness of solutions of systems of ODEs Wed Oct 12 7.5 Constant coefficient systems with distinct real eigenvalues Thu Oct 13 Homework 4 due by 11:59pm Fri Oct 14 7.6, 7.7 Constant coefficient systems with complex conjugate eigenvalues, Fundamental matrices Mon Oct 17 7.8 Repeated eigenvalues Wed Oct 19 7.9 Nonhomogeneous linear systems Thu Oct 20 Homework 5 due by 11:59pm Fri Oct 21 9.1 The phase plane Mon Oct 24 9.2 Autonomous systems and stability Wed Oct 26 9.3 Locally linear systems Fri Oct 28 9.4 Competing species Mon Oct 31 9.5 Predator-prey equations Tue Nov 1 Homework 6 due by 11:59pm Wed Nov 2 6.1, 6.2 Laplace transform and the IVP Thu Nov 3 Midterm 2 due by 11:59pm Fri Nov 4 6.3 Step functions Mon Nov 7 6.4, 6.5 Discontinuous forcing functions, Impulse functions Tue Nov 8 Homework 7 due by 11:59pm Wed Nov 9 6.6 The convolution integral Fri Nov 11 Review of Chapter 6 Mon Nov 14 Review Tue Nov 15 Homework 8 due by 11:59pm Tue Nov 22 Final due by 11:59pm