Math 415

 

Home
Research
Teaching
Curriculum Vitae
Links
Contact Me

 
bullet

Syllabus: Click here for details in a PDF file

bullet

Course: Math 415, Ordinary and Partial Differential Equations, MWF 3:30pm, Pomerene Hall

bullet

Texts: (1) Elementary Differential Equations & Boundary Value Problems (8th Ed) by Boyce and Diprima

bullet Topics: Solutions to first order, second order and higher order ordinary differential equations and partial differential equations; Phase plane analysis; Fourier series; Boundary value problems.
bullet Office Hours: MW 4:30-5:30pm @MW410  and by appointment
bullet Grading: first midterm (Mon. Apr 19, 20%), second midterm (Mon. May. 17, 25%), final exam( Thur. Jun 10 3:30pm,30%), class participation (5%), and homework and quiz (20%). The letter grade will be with an approximately 90(A)-80(B)-70(C)-60(D) scale.
bullet  Policy: NO make-up exams without doctor's excuse. Late Homework will be no credit.
bullet Tentative Schedule: updated regularly

The HW problems need to be turned in. HW due every Thursday in TA section. It includes all assignments given in the previous week (Mon, Wed, Fri). 

 

Monday Wednesday Friday
Mar 29 (Spring Classes Begin)

Chapter 1: Introduction

Chapter 1.2: Solutions of some ODEs

HW: 1.1 (11), 1.2(11)

Mar 31

Chapter 1.2: Solutions of some ODEs

Chapter 1.3: Classification of DEs

HW: 1.3(2,3,13,22,23,28)

Apr 2

Chapter 2.1 & 2.2

HW:2.1 (6,10,15,18,28)

HW 2.2(4,11,25,33)

Linear Equation: Method of Integrating Factors

Separable Equations

Chapter 2.2

Separable Equations

Apr 5

Chapter 2.2

Separable Equations

Chapter 2.3

Modeling with First Order Equations

HW 2.3(4,9,14,23)

Apr 7

Chapter 2.3

Modeling with First Order Equations

Chapter 2.4

Differences Between Linear and Nonlinear Equations

Apr 9

Chapter 2.4

HW: 2.4(11,22,28)

Differences Between Linear and Nonlinear Equations


Apr 12

Chapter 2.5

Autonomous Equations and Population Dynamics

HW 2.5:(3,7,9,17)

Apr 14

Chapter 2.5

Autonomous Equations and Population Dynamics

3.1 Homogeneous Equations with Constant Coefficients

 

 

Apr 16

3.1 Homogeneous Equations with Constant Coefficients

HW: 3.1 (6 13 19 20)

Apr 19

Chapter 3.2

Fundamental solutions, linear independence

HW: 3.2 (2,8,11,13,23)

Apr 21

First Exam: Ch1 and Ch2 to 2.5

 

Apr 23

Chapter 3.3: the Wronskian

HW: 3.3 (3,4,15,16,20)

 

Apr 26

Chapter 3.4

Complex Roots of the Characteristic Equation

HW: 3.4 (2,3,21)

 

Apr 28

Chapter 3.5

HW:3.5(3,11,12,20,25,30)

Repeated Roots; Reduction of Order

 

Apr 30

Chapter 3.6

Nonhomogeneous equations: method of undetermined coefficients

HW:3.6 (3,8,14,24)

 

 

May 3

Chapter 3.8

Mechanical and electrical vibrations

HW:3.8 (2,6,9,13)

May 5

Chapter 3.9

Mechanical and electrical vibrations

HW 3.9 (5,6,7(a,c),10)

May 7

Chapter 10.1,Two-Point Boundary Value Problems

HW: 10.1 (2,3,4,14,16)

 

May 10

Chapter 10.2, Fourier Series

HW: 10.2 (3,4,15,18)

 

May 12

Chapter 10.3

The Fourier Convergence Theorem

HW: 10.3 (2,3)

May 14

Chapter 10.4 Even and Odd Functions

HW: 10.4 (3,6,7,15,18,35)

May 17

Chapter 10.5: Heat equation with zero boundary conditions

HW 10.5: 3,5,8,10

 

May 19

Second Exam

Chapter 3 and 10.1-10.2

May 21

Chapter 10.6: Other Heat Conduction Problems

HW10.6: 2,3,9(a)

May 24

Chapter 10.7

Wave equation

HW 10.7: 1(a),6(a)

May 26

Chapter 10.7,8

Wave equation, Laplace’s equation

HW 10.8: 1(a,b),2,5

 

May 28

Chapter 10.8, Chapter 7.1

Laplace’s equation,Systems of first order equations: Linearization at equilibrium – the problem of stability

HW 7.1: 2,5

 

May 31 (Memorial Day - no class) June 2

Chapter 7.3, ex 4, 7,4 Thm1, 2 , 7.5

Eigenvalues, eigenvectors, General solution of X' = PX, homogeneous liear systems with constant coefficients

HW 7.3(15,17,19), 7.5 (1,4)

June 4

 

Chapter 7.4-7.5:

Homogeneous linear systems with constant coefficients

 

Chapter 7.6:

Complex eigenvalues

HW: 7.6 (2,6)

Review

 


June 7

Final exam week

June 9

Final exam week

June 11

Final exam week

Spring commencement