METU-NCC Math

    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