## Math 219 Introduction to Differential Equations (Spring 2022)

#### This page is for archival purposes only! Students should use ODTU-Class

The table below is a rough guideline for the content of course lectures. Professors may reorder their lectures as necessary/desired. Section and page numbers below are from the textbook, Elementary Differential Equations and Boundary Value Problems, Boyce and DiPrima, 10th ed.

 Week 1: Mar.7-11 1 Introduction, Directional Fields 2 Chapter 2. First Order Differential Equations§2.2: Separable equations    (also homogeneous equations - see #30 on page 49). §2.1: Linear equations; Method of integrating factors. Week 2: Mar.14-18 3 §2.3: Modeling with first order equations    (tank problems). 4 §2.4: Differences between linear and nonlinear equations    (existence and uniqueness theorems). §2.6: Exact equations and integrating factors. Week 3: Mar.21-25 5 Chapter 7. Systems of First Order Linear Equations§7.1: Introduction. §7.2: Review of matrices. 6 §7.3: Systems of linear algebraic equations;    Linear independence, eigenvalues, eigenvectors. Week 4: Mar.28-Apr.1 7 §7.4: Basic theory of systems of first order linear equations. §7.5: Homogeneous linear systems with constant coefficients. 8 §7.5: Homogeneous linear systems with constant coefficients (continued). §7.6: Complex eigenvalues. Week 5: Apr.4-8 9 §7.7: Fundamental matrices. 10 §7.8: Repeated eigenvalues. §7.9: Nonhomogeneous linear systems   (variation of parameters only). Week 6: Apr.11-15 11 Chapter 4. Higher Order Linear Equations§4.1: General theory of nth order linear equations. 12 §4.2: Homogeneous equations with constant coefficients. Week 7: Apr.18-22 13 Chapter 3. Second Order Linear Equations§3.2: Linear independence and the Wronskian. 14 §3.3: Complex roots of the characteristic equation. Week 8: Apr.25-29 15 §3.4: Repeated roots; Reduction of order. 16 §3.5: Nonhomogeneous equations; Method of undetermined coefficients. HOLIDAY: Mon-Wed, 2-4 April Week 9: May 9-13 17 §4.3: The method of undetermined coefficients. 18 §3.6: Variation of parameters. Week 10: May 16-20 19 §3.7: Mechanical and electrical vibrations. 20 §3.8: Forced Vibrations. Holiday: Thursday, 19 May Week 11: May 23-27 21 Chapter 6. The Laplace Transform§6.1: Definition of the Laplace transform. §6.2: Solution of initial value problems. 22 §6.3: Step functions. Week 12: May 30-June 3 23 §6.4: Differential equations with discontinuous forcing functions. 24 §6.5: Impulse functions. §6.6: The convolution integral. Week 13: June 6-10 25 Chapter 10. Partial Differential Equations and Fourier Series§10.A: Derivation of the Heat Conduction Equation. §10.1: Two-point boundary value problems. 26 §10.2: Fourier series. §10.3: The Fourier convergence theorem (briefly). Week 14: June 13-17 27 §10.4: Even and odd functions. 28 §10.5: Separation of variables, heat conduction in a rod. FINAL EXAMS: 20 June -- 2 July