Instructors: Matthew Ellison, Dimitrios Giannakis

Course on canvas.dartmouth.edu.

## Course Schedule

Sections and problems are from Boyce & DiPrima, 11th edition.

 Lectures Sections Description Tentative Homework Week 1: Th Jan 4 1.1, 1.2, 1.3 Introduction to differential equations; classification of ODEs 1.1: #5, 6, 8, 18, 201.2: #5, 10 (Hint: do (b) first), 11 Week 2: T Jan 9 2.1, 2.2 Integrating factors; separable equations 2.1: #9, 12, 20, 232.2: #6,15, 20 Week 2: Th Jan 11 2.3, 2.4 Modeling with differential equations; existence-uniqueness theorems 2.3: #2, 6 (Hint: solve 6(c) numerically), 112.4: #8, 10, 18, 21, 24, 27 Week 3: T Jan 16 2.5, 2.6 Autonomous equations; exact equations 2.5: #3, 8, 152.6: #2, 10, 12 Week 3: Th Jan 18 3.1, 3.2 Second-order constant coefficient equations with distinct roots; the Wronskian 3.1: #11, 16, 17, 20 3.2: #8, 15, 17,21, 27 Week 4: T Jan 23 3.3, 3.4 Complex conjugate roots; repeated roots and reduction of order 3.3: #4, 8, 14, 263.4: #5, 9, 22 Week 4: Th Jan 25 3.5, 3.6 Inhomogeneous equations; method of undetermined coefficients and variation of parameters 3.5: #7, 10, 11, 223.6: #9, 12 Week 4: F Jan 26 Midterm Exam 1 Material through 3.3 Week 5: T Jan 30 7.1, 7.2 7.3 Review of matrices; systems of ODEs 7.1: #6,127.2: #2, 12, 167.3: #9, 19 Week 5: Th Feb 1 7.4, 7.5 Existence and uniqueness of solutions of systems of ODEs; systems with distinct real eigenvalues 7.4: #8 (only (a,b,c)), 11, 12(only (a,b))7.5: #6, 12, 18, 21 Week 6: T Feb 6 7.6, 7.7 Systems with complex eigenvalues; fundamental solutions 7.6: #8, 9, 237.7: (TBD) Week 6: Th Feb 8 7.8, 7.9 Systems with repeated eigenvalues; inhomogeneous linear systems 7.8: #8, 13, 17 (only (a,b,c,d))7.9: # 2, 3, 7, 10 (only verify the general solution of the corresponding homogeneous part) Week 7: T Feb 13 9.1, 9.2 The phase plane; autonomous systems and stability 9.1: #15, 17, 189.2: #3, 7 (only (a,b,c)), 19 Week 7: Th Feb 15 9.3 Locally linear systems 9.3: #3, 7, 17, 24 Week 7: F Feb 16 Midterm Exam 2 Material from 3.4 through 7.9 Week 8: T Feb 20 9.4, 9.5 Competing species; predator-prey equations 9.4: #3, 69.5: #4, 12 Week 8: Th Feb 22 6.1, 6.2 Laplace transform and the IVP 6.1: #2, 11, 186.2: #12, 18, 21, 24 Week 9: T Feb 27 6.3 Step functions 6.3: #12, 14, 17 Week 9: Th Feb 29 6.4, 6.5 Discontinuous forcing functions, impulse functions 6.4: #5, 126.5: #6, 10, 14 Week 10: T Mar 5 6.6 The convolution integral 6.6: #1, 2, 13, 16 March 8 Final Exam Exam covers material from the whole course