 ## Math 219 Introduction to Differential Equations (Spring 2014)

#### 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, 9th ed., 2010.

 Week 1: Feb.17-21 1 Introduction, Directional FieldsChapter 2. First Order Differential Equations§2.2: Separable equations    (also homogeneous equations - see p49 #30). 2 §2.1: Linear equations; Method of integrating factors. §2.3: Modeling with first order equations    (tank problems). Week 2: Feb.24-28 3 §2.4: Differences between linear and nonlinear equations    (existence and uniqueness theorems). 4 §2.6: Exact equations and integrating factors. Week 3: Mar.3-7 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.10-14 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. §7.6: Complex eigenvalues. Week 5: Mar.17-22 9 §7.7: Fundamental matrices. 10 §7.8: Repeated eigenvalues. §7.9: Nonhomogeneous linear systems   (variation of parameters only). Midterm 1: Thursday, 20 March at 17:40 Week 6: Mar.24-28 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: Mar.31-Apr.4 13 Chapter 3. Second Order Linear Equations§3.2: Fundamental solutions of linear homogeneous equations. 14 §3.3: Linear independence and the Wronskian. §3.4: Complex roots of the characteristic equation. Week 8: Apr.7-11 15 §3.5: Repeated roots; Reduction of order. 16 §3.6: Nonhomogeneous equations; Method of undetermined coefficients. Week 9: Apr.14-18 17 §4.3: The method of undetermined coefficients. 18 §3.7: Variation of parameters. Week 10: Apr.21-25 19 §3.8: Mechanical and electrical vibrations. Holiday: Wed., 23 April 20 §3.9: Forced Vibrations. Week 11: Apr.28-May 2 21 Chapter 6. The Laplace Transform§6.1: Definition of the Laplace transform. 22 §6.2: Solution of initial value problems. §6.3: Step functions. Holiday: Thu., 1 May Midterm 2: Saturday, 3 May at 15:40 Week 12: May 5-9 23 §6.4: Differential equations with discontinuous forcing functions. 24 §6.5: Impulse functions. §6.6: The convolution integral. Week 13: May 12-16 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: May 20-23 Holiday: Mon., 19 May 27 §10.4: Even and odd functions. 28 §10.5: Separation of variables, heat conduction in a rod. FINAL EXAM: Saturday, 31 May at 9:00