 
 Syllabus:
Click here for details in a
PDF file 

Course: Math
415, Ordinary and Partial Differential Equations, MWF 11:30am 

Texts:
(1) Elementary Differential Equations & Boundary Value Problems (7th Ed) by
Boyce and Diprima 

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. 

Office Hours: MWF 10:3011:30am
@MW410 and by
appointment 

Grading: first midterm
(Fri. Oct 5, 20%), second midterm (Fri. Nov. 2, 25%), final exam( Mon. Dec
3 11:30am, 30%), class participation (5%), and homework (20%). The letter
grade will be with an approximately 90(A)80(B)70(C)60(D) scale. 

Policy:
NO makeup exams without doctor's excuse. Late Homework will be no credit. 

Tentative Schedule: updated regularly 
The HW problems need to
be turned in. HW due every Wednesday in class. It includes all assignments given in the
previous week (Mon, Wed, Fri).
Monday 
Wednesday 
Friday 
Sept 17 
Sept
19 (Autumn Classes Begin)
Chapter 1:Introduction
HW: 1.1 (11), 1.2(11),1.3(13,28)

Sept 21
Chapter 2.1 & 2.2
Linear Equation: Method of Integrating Factors
Separable Equations
HW: 2.1 (6,10,15,18,28)

Sept 24 Chapter 2.2,2.3
Separable Equations
Modeling with First Order Equations
2.2(4,11,25,33)

Sept 26
Chapter 2.3,2.4
HW:2.3(4,9,16,21,24)
Differences Between Linear and Nonlinear Equations 
Sept 28
Chapter 2.4, 2.5
HW:2.4(11,17,22,28)
Autonomous Equations and Population Dynamics

Oct 1
Chapter 2.5
HW:2.5(3,7,9,17) 
Oct 3
Chapter 2.6
HW2.6(7,9,19,26,27)

Oct 5
Chapter 2.6

Oct 8
Chapter 2.7
Numerical Approximations and Population Dynamics
HW2.7(3,15,18(too much computation, I decide not to give this question as HW))

Oct 10
First Exam 
Oct 12
2.8 The Existence and Uniqueness Theorem
HW 2.8(4,7,11)

Oct 15
Chapter 3.1
Homogeneous Equations with Constant Coefficients
Fundamental Solutions of Linear Homogeneous Equations
HW: 3.1 (6 13 19 20)

Oct 17
Chapter 3.2
Linear Independence and the Wronskian
HW: 3.2 (2,8,11,13,23)

Oct 19
Chapter 3.3

Oct 22
Chapter 3.4, 3.5
HW: 3.3 (2,3,4,15,16,20) HW 3.4 (2,3,21)
Complex Roots of the Characteristic Equation 
Oct 24
Chapter 3.5
HW: 3.5 (3,11,12,20,25,30)
Repeated Roots; Reduction of Order

Oct 26
3.6,3.7
HW 3.6 (3,8,14,24), HW 3.7(2,5,14,17)
Nonhomogeneous Equations: Method of Undetermined Coefficients
Variation of Parameters

Oct 29
3.8,3.9
Mechanical and Electrical Vibrations
HW 3.8 (2,6,9,13), HW 3.9(5,7,10)

Oct 31
Supplement Material:
Systems of ODEs
HW 3.2 supplement (11(a),16,19
Click here for a PDF file of supplement material

Nov 2
Supplement Material:
3.3 Homogeneus Linear Systems with constant coefficient
HW 3.3 supplement (3,14 without drawing the direction field and phase portrait)

Nov 5
Supplement Material:
Stability

Nov 7
Second Exam

Nov 9
Supplement: Chapter 3.4 Complex eigenvalues
HW:Solve (1)y''+9y=0 and (2) 16y''8y'+145y=0 y(0) = 2 and y'(0)=1 by reformulating (a) and (b) to first order system equations and draw the phase portrait 
Nov 12 (Veteran's Day. No Classes) 
Nov 14
Chapter 10.1,TwoPoint Boundary Value Problems
HW 10.1: 2,3,4,11,13
Chapter 10.2 Fourier Series 
Nov 16
Chapter 10.2, Fourier Series
HW 10.2: 3,4,15,18

Nov 19
Chapter 10.3
The Fourier Convergence Theorem
HW 10.3: 2,3
Chapter 10.4 Even and Odd Functions 
Nov 21
Chapter 10.4 Even and Odd Functions
HW 10.4: 3,6,7,15,18,35
Chapter 10.5
Separation of Variables; Heat Conduction in a Rod

Nov 23 (Columbus Day. No Classes)

Chapter 10.5,10.6
Other Heat Conduction Problems
HW 10.5: 3,5,8,10
HW 10.6: 2,3,9(a)

Nov 28
Chapter 10.7: 1(a),6(a)
The Wave Equation : Vibrations of an Elastic String 
Nov 30
Chapter 10.8: 1(a,b),2,5
Laplace's Equation

Dec 3 Final Exams Week

Dec 5 Final Exams Week

Dec 7 Final Exams Week

