2005 Spring - Math 251

Math 251: Ordinary and Partial Differential Equations

Instructor: Ming-Hsuan Kang

Office: 012 McAllister Building

Office Hour: MTWF 2:30~3:30 or by appointment

Website: http://www.math.psu.edu/kang_m/

Course description:

First and second order equations, numerical methods, Laplace transform, Fourier series and partial differential equations

Prerequisite:

Math 141, or equivalent courses.

Time Schedule Homework Quiz Practice Exam

Textbook:

W.E.Boyce and R.C.DiPrima: ,Elementary Differential Equations and Boundary Value Problems , 8th Edition.

Grade:

Homework = 50 points, (count best 10)

Quizzes = 50 points, (count best 10)

    Midterm 1 = 100 points,
    Midterm 2 = 100 points,
    Final Exam = 150 points.
    Total = 450 points.

Exam:

Midterm 1, 6:30-7:45 pm, 2-28, Sparks 010

Conflict 5:05-6:20 pm, 2-28, Chambers 102

Makeup 6:30-7:45 pm, 3-5, Willard 360

Range: Chapter I-IV

Midterm 2, 6:30-7:45 pm, 4-07-2008

Final Exam, TBA

ACADEMIC INTEGRITY STATEMENT:

All Penn State policies regarding ethics and honorable behavior apply to this course. For more information see: http://www.science.psu.edu/academic/Integrity/index.html

Applets for plotting direction fields: Dfield and pplane

Common integral formula

Homework back to top

HW1 (due to Jun, 23)
   1.1 #1,2,11,12,15,16,26(Using Dfield)
   1.2 #1,7,8
1.3 #1,2,3,4,7,8,15,16,25
   2.1 #1,2,10,13,16,22
   2.2 #1,3,4,9,10

HW2 (due to Jun, 30)
   2.3 #1, 2, 4, 7, 8
   2.4 #1, 2, 3, 7, 10, 12
2.5 #9, 10, 11, 12, 15

   HW3 (due to Feb, 6)
   2.6 #2, 4, 7, 9, 10, 13, 15
p.133 #36, 37, 42, 47, 49, 51
3.1 #9, 10, 11, 15, 16, 17, 23

HW4 (due to Feb, 14)
3.2 #3, 6, 7, 9, 13, 16, 17, 18
3.3 #1, 2, 5, 10, 15, 20, 21
3.4 #1, 3, 5, 17, 18, 19, 20

HW5 (due to Feb, 21)
3.5 #11, 12, 14, 16, 23, 24, 28
3.6 #13, 14, 19 ~ 23(only setup the form of particular solution)

HW6 (due to Feb, 28)
3.8 #1, 2, 3, 5, 6, 7, 11
3.9 #5, 6, 9, 10, 18(a)
4.2 #11, 12, 14
4.3 #13, 14, 15

HW7 (due to 3, 20)
6.1 #5
6.2 #1, 3, 8, 9, 11, 12, 13, 21, 22
6.3 #1, 2, 6, 7, 8, 9, 10, 13, 14, 15
6.4 #1, 2, 3, 9, 10, 11
6.5 #1, 2, 3, 4

HW8(due to 3, 27)
7.5 #1~10, 15, 16
7.6 #1~6, 9~12

Applets for plotting direction fields: pplane

HW9(due to Apr, 3)
7.1 #1~7
7.8 #1~4,7~10
9.3 #5~10
9.5 #1,3

HW10(due to Apr, 17)
10.1 #1, 3, 5, 7, 9, 15, 17, 19
10.2 #13, 14, 15, 16, 18

HW11(due to Apr, 24)
10.3 #1, 2, 5
10.4 #1, 2, 5, 6, 7, 8, 9 15, 17, 18, 19
10.5 #1, 3, 5, 7, 8, 9, 11

HW12(due to May, 1)
10.6 #1, 2, 4, 6, 9(a)(b), 10(a)(b)
10.7 #4(a), 8(a)
10.8 #1, 2

Quiz back to top

Quiz1 (Jun, 24) 1.1~2.2

Quiz2 (Jun, 31) 2.3~2.5

Quiz3 (Feb, 7) 2.6~3.1

Quiz4 (Feb, 14) 3.2~3.4

Quiz5 (Feb, 21) 3.5~3.6

Quiz6 (Feb, 27) 3.8~4.3

Quiz7 (Mar, 20) 6.1~6.5

Quiz8 (Mar, 27) 7.5~7.6

Quiz9 (Apr, 2) 6.1~6.5

Quiz10 (Apr, 3) 7.7~9.6

Quiz12 (Apr, 17) 10.1~10.2

Quiz11 (Apr, 24) 10.3~10.5

Time Schedule back to top

INTRODUCTION

1.1 Direction fields (1)
1.2 Solutions of Some DE's (1/2)
1.3 Classification of DE's (1/2)

FIRST ORDER DE's

2.2 Separable Equations (1)
2.1 Linear Equations with Variable Coefficients (2)
2.3 Modeling with First Order Equations (3) (do mixture, interest and air resistance)
2.4 Differences Between Linear and Nonlinear Equations (1)
2.5 Autonomous Equations, Population Dynamics (1) (cover stability and concavity)
2.6 Exact Equations (omit integrating factors) (1)

SECOND ORDER LINEAR EQNS

p.133 The case of the missing y and the case of the missing t (1)
3.1 Homogeneous Equations with Constant Coefficients (2) (cover the equations with missing y or missing t, show how to solve initial value problems with data is specified not at 0)
3.2 Fundamental Solutions of Linear Homogeneous Equations (1)
3.3 Linear Independence and the Wronskian (1)
3.4 Complex Roots of the Characteristic Equations (also review complex arithmetic) (2)
3.5 Repeated Roots; Reduction of Order (1)
3.6 Nonhomogeneous Equations; Method of Undetermined Coefficients (3)
3.8 Mechanical Vibrations (omit electrical vibs) (2)
3.9 Forced Vibrations (no damping) (1)

THE LAPLACE TRANSFORM

6.1 Definition of the Laplace Transform (2)
6.2 Solution of Initial Value Problems (2)
6.3 Step Functions (1)
6.4 Differential Equations (1) with Discontinuous Forcing Functions
6.5 Impulse Functions (1)
7.1 Introduction to Systems of Differential Equations (1)
7.5-9 Classification of critical points and sketching (2) phase portraits.

NONLINEAR DIFFERENTIAL EQUATIONS AND STABILITY

9.1 Phase portraits and stability (1)
9.2 Phase portraits for Nonhomogeneous Linear systems (1)
9.5 Linearize a nonlinear system at each of its critical points. Phase portrait for predator-prey eqn (1)

PARTIAL DIFFERENTIAL EQUATIONS AND FOURIER SERIES

10.1 Two Point Boundary Value Problems (1)
10.2 Fourier Series (2)
10.3 The Fourier Theorem (2)
10.4 Even and Odd Functions (2)
10.5 Separation of Variables; Heat in a Rod (2)
10.5 Other Heat Conduction Problems (2)
10.6 The Wave Equation: Vibrations of an Elastic String (1)
10.7 Laplace's Equation (1)