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Math 219 Syllabus - Metu Math. Dept. 2013 Fall Semester

This document is the syllabus for Math 219 at METU for the Fall 2013 semester. It outlines the 15 weeks of topics to be covered from differential equations and boundary value problems. The course will focus on classification of differential equations, methods for solving first and second order linear equations, series solutions, Laplace transforms, systems of linear equations, and Fourier series. Students will have two midterm exams worth 30% each and a final exam worth 40% of the overall grade. To pass the course, students must score a total of at least 30 points on the two midterm exams combined.

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74 views

Math 219 Syllabus - Metu Math. Dept. 2013 Fall Semester

This document is the syllabus for Math 219 at METU for the Fall 2013 semester. It outlines the 15 weeks of topics to be covered from differential equations and boundary value problems. The course will focus on classification of differential equations, methods for solving first and second order linear equations, series solutions, Laplace transforms, systems of linear equations, and Fourier series. Students will have two midterm exams worth 30% each and a final exam worth 40% of the overall grade. To pass the course, students must score a total of at least 30 points on the two midterm exams combined.

Uploaded by

Anonymous 7PNVhPu
Copyright
© © All Rights Reserved
Available Formats
Download as PDF, TXT or read online on Scribd
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Math 219 Syllabus METU MATH. DEPT.

2013 Fall Semester



Boyce, di Prima, "Elementary Differential Equations and Boundary
Value Problems" (8th Edition)

Week 1 (23-27 Sept.)
1.1 Classification of differential equations
Direction Fields
1.2 Solutions of some differential equations
1.3 Classification of differential equations
2.1 Linear equations; Method of integrating factors

Week 2 (30 Sept-04 Oct.)
2.2 Separable equations
2.4 Differences between linear and nonlinear equations
2.5 Autonomous equations and population dynamics


Week 3 (7-11 Oct.)
2.6 Exact equations and integrating factors
(Make sure to give some examples of substitution
including Bernoulli equations and homogeneous equations)
2.7 Numerical approximations: Euler's method
2.8 The existence and uniqueness theorem

Week 4 (21-25 Oct.)
3.1 Homogeneous equations with constant coefficients
3.2 Fundamental solutions of linear homogeneous equations
3.3 Linear independence and the Wronskian
Complex numbers
3.4 Complex roots and the characteristic equation

Week 5 (28 Oct.-1 Nov.)
3. 5 Repeated roots; reduction of order
3. 6 Nonhomogeneous equations; method of undetermined coefficients
3. 7 Variation of parameters

Week 6 (4-8 Oct.)
4. 1 General theory of nth order linear equations
4. 2 Homogeneous equations with constant coefficients (be brief in the
first two sections stressing similarity with the second order
equations)
4. 3 The method of undetermined coefficients

Week 7 (11-15 Nov.)
5.1 Review of power series
5.2 Series Solution near an ordinary point, Part I
5.3 Series Solution near an ordinary point, Part II


Week 8 (18-22 Nov.)
5.4 Regular singular points
5.5 Euler Equations
5.6 Series Solution near a regular singular point, Part I

MIDTERM I (NOVEMBER 23)



Week 9 (25 Nov. - 29 Nov.)
6. 1 Definition of the Laplace transform
6. 2 Solution of initial value problems
6. 3 Step functions
6. 4 Differential equations with discontinuous forcing functions

Week 10 (2-6 Dec.)
6. 5 Impulse functions
6. 6 The convolution integral
7.1 Introduction
7.2 Review of matrices

Week 11 (9-13 Dec.)
7.3 Systems of linear algebraic equations; linear independence,
eigenvalues, eigenvectors
7.4 Basic theory of systems of first order linear equations
7.5 Homogeneous linear systems with constant coefficients

Week 12 (16-20 Dec.)
7.6 Complex eigenvalues
7.7 Fundamental matrices
7.8 Repeated eigenvalues

MIDTERM II (DECEMBER 21)

Week 13 (23-27 Dec.)
7.9 Nonhomogeneous linear systems
10.1 Two Point BVP
10.2 Fourier series

Week 14 (30 Dec. - 3 Jan.)
10.3 The Fourier Convergence Theorem
10.4 Even and odd functions
10.5 Separation of Variables: Heat Conduction in a Rod

Week 15 (6 - 10 Jan.)
10.6 Other Heat Conduction problems
10.7 The wave equation: Vibrations of an elastic string


Grading: Midterm I 30%
Midterm II 30%
Final 40%

Important Note: Those students whose two midterm grades (out of 100) do not add up to
thirty (30) will be not admitted to the final examination and thus will receive the letter grade
NA in Math 219. For example, a student with midterm scores 21 and 8, both out of 100, will
fail in the course receiving NA.

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