METU-NCC Math

    Math 219 Introduction to Differential Equations (Summer 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:
Jun.30-Jul.4
1 Introduction, Directional Fields
Chapter 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).
3 §2.4: Differences between linear and nonlinear equations
   (existence and uniqueness theorems).
4 §2.6: Exact equations and integrating factors.
Week 2:
Jul.7-11
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.
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.
Short Exam 1: July 9 at 17:40
Week 3:
Jul.14-18
9 §7.7: Fundamental matrices.
10 §7.8: Repeated eigenvalues.
§7.9: Nonhomogeneous linear systems
  (variation of parameters only).
11
Chapter 4. Higher Order Linear Equations
§4.1: General theory of nth order linear equations.
12 §4.2: Homogeneous equations with constant coefficients.
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 4:
Jul.21-25
15 §3.5: Repeated roots; Reduction of order.
16 §3.6: Nonhomogeneous equations; Method of undetermined coefficients.
17 §4.3: The method of undetermined coefficients.
18 §3.7: Variation of parameters.
19 §3.8: Mechanical and electrical vibrations.
20 §3.9: Forced Vibrations.
Short Exam 2: July 23 at 17:40
Week 5:
Aug.04-08
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.
23 §6.4: Differential equations with discontinuous forcing functions.
24 §6.5: Impulse functions.
§6.6: The convolution integral.
Week 6:
Aug.11-15
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).
27 §10.4: Even and odd functions.
28 §10.5: Separation of variables, heat conduction in a rod.
FINAL EXAM