Math 385, Section D2, Fall 2006

Course news  Homework assignments  Approximate Schedule Table of common integrals
Answer of Exam2;   Answer of Exam1   Answer of Quiz of HW6   Answer of Quiz of HW7, Answer of Quiz of HW10, Answer of Exam3;
  Score Reports, 
 
Review slides for Final 
  Contens and examples of the final (in updating...... 
 

• Lectures: MWF 11:00-11:50 in 245 ALTGELD
• Instructor: Tao Mei, mei@math.uiuc.edu
• Course homepage: www.math.uiuc.edu/~mei/math385.html
• Office & Telephone: ALTGELD Hall 221, 217-244-2478
• Office Hours: MW 4:00-5:30 PM
• Textbook (required): C. H. Edwards and D. E. Penney, Differential equations and boundary value problems: Computing and modeling, 3rd edition.

Slides of section3.5

　

Course Description:

This course is an introduction to differential equations, with particular emphasis on boundary value problems and series solutions. We will cover most of Chapter 1,3,9 and section 2.1,2.3, which include homogeneous and nonhomogeneous linear equations, boundary value and eigenvalue problems, and Fourier series methods.The prerequisite for this course is completion of one of the multivariable calculus courses (242 or 243).　

Tentative exam dates: There will be three hour-long exams during the semester and a final exam.  Books, notes, calculators are not allowed on exams. 

Exam #1 -  Monday, Sept. 18, 7:00-8:00pm , room 314 Altgeld Hall.
Exam #2 -  Friday, Oct. 20,  11:00-11:50 am in Class. Regular class room (245 Altgeld Hall).

Contents covered : Chapter 3 excepte section 3.7. The matirial you should know includes: Linear independent; Wronskian; general solution of homogenous differentail equation with constant coifficients; particular solution of nonhomogenous differential equation by the method of undertermined coifficients and by the method of variation of parameters;  general solution of nonhomogenous differential equations; pariticular solution satisfying intial conditions; eigenvalues and associated eigenfunctions.
A reiview will be given on Wednesday Oct. 18th.

Exam #3 -  Nov. 15th, 7:00-8:00Pm, usual classroom (245, Altgeld), conflict exam will be from 5:30-6:30pm, meet in my office

Contents covered: Exam 3 will cover Chapter 9, including Periodic functions(period of a function, orthogonal functions), Fourier series of piecewise continous functions, Fourier Sine and Cosine series of functions defined on [0,L](odd extension, even extension), Convergence of Fourier series, Integral and Derivative of Fourier series, Solve differential equations by fourier series(In class, we did Example 1 on page 602 of the textbook, make sure you can do problems similar to it.); Solve parial differential equations by fourier sine or cosine series: Heat conduction(typical example: Example 2,3 of Section 9.5 on the textbook); Vibrating strings(typical example: exercise #2,4,6(to easy your work, replace x(\pi-x) by x), #7of section 9.6);Dirichelet problems for the "semi-infinite strip" ("infinite square").

　
Final Exam- 8:00-11:00 AM, Monday, December 11, in our usual classroom, room 245 Altgeld Hall. The final exam will cover the entire course. Note: Please arrange any travel, etc., so that you can take the final on this date.   Math 385 has a "non-combined" final exam.  There will be no conflict exam given except for those few individuals who meet the official university criteria given here in the student code. 

Missed exams:  If you miss an exam, you will receive a 0 for your grade.  The only exception is if you have a valid excuse for missing, such as academic conference, major illness or a serious emergency - if so, you must inform me before the exam, preferably by email. And you need a note from your academic advisor or your doctor. Notify me no later than one day after the test to set up a time for a make up. 

Homework: We will have a homework assignment each week. Written homework is due at the beginning of class on the due date. 

Homework Rules: (1)Print your name, section at the top of the paper. (2) Staple the papers together if your homework takes more than one page. (3) Work out the problems, the answer only will not be accepted.(5)Be neat and legible.

No late homework: Homework must be turned in to me at the beginning of class on the due date.  Late homework will not be accepted. 

Grading Policy: Your course grade will be determined as follows:
Weekly Homework (around 15 homework, only 12 of them will be count)    24%
Exam #1        15%
Exam #2         15%
Exam #3         15%
Final Exam(8:00–11:00 AM, Monday, December 11)     31% 

The follow scale describes approximately how the course grades will be assigned.  The instructor reserves the right to adjust this scale slightly (for the whole class, not for individual students): 

90%  or above = A+, A or A-
80%-89% = B+, B or B-
65%-79% = C+, C or C-
55%-64% = D
below 55% = F 

You will be able to check your homework and exam grades at Score Reports, which is the Math Department's gradebook program.  This will be available beginning approximately two weeks into the semester.  All your h/work, quiz and exam grades will be posted there. You will be prompted for your NetID and NetID password after following the Score Reports link. Please check score reports regularly to make sure your grades have been correctly reported and tell me promptly about any errors.  You are responsible for keeping all of your graded homework and exams so that any discrepancies in recorded grades can be settled.  

Approximate Course Schedule

Chapter 1. First Order Differential Equations (6 lectures, Aug. 23-Sept.8) 

　

1.1 Differential Equations and Mathematical Models

1.2 Integrals as General and Particular Solutions

1.3 Direction Fields and Solution Curves (3) (Emphasize the existence/uniqueness theorem, and the gemetric interpretation and applications of slope fields.)

1.4 Separable Equations and Applications (The material on exponential growth and decay is covered in Math 120 and can be skipped or quickly reviewed.)

1.5 Linear First Order Equations

1.6 Substitution Methods and Exact Equations (3) (The material on exact equations has been de-emphasized.)

　 Chapter 2. Mathematical Models and Numerical Methods (2 lectures, Sept. 11-13) 

　

2.1 Population Models

2.3 Acceleration-Velocity Models (Cover one of these in detail. The other can be covered briefly, time permitting.)

Exam1 Sept. 18 Chapter 3. Linear Equations of Higher Order (14 lectures, Sept 15, Sept 20-Oct.20) 

　

3.1 Introduction: Second-Order Linear Equations

3.2 General Solutions of Linear Equations (3) (Emphasize the second order case but introduce the idea of linear independence and the Wronskian for higher order equations.)

3.3 Homogeneous Equations with Constant Coefficients (2) (Include factorization of constant coefficient operators.)

3.4 Mechanical Vibrations (2)

3.5 Inhomogeneous Equations and the Method of Undetermined Coefficients (3) (Include variation of parameters.)

3.6 Forced Oscillations and Resonance (2)

3.8 Boundary Value Problems and Eigenvalues (2) (May be covered between 9.4 and 9.5 instead)

Exam2 Oct. 25 Chapter 9. Fourier Series Methods (12 lectures, Oct. 23, Oct 27-Nov. 29) 

　

9.1 Periodic Functions and Trigonometric Series (3)

(Strongly emphasize the concept of orthogonality. This will be good preparation for students taking Math 342.) 

9.2 General Fourier Series and Convergence (1)

9.3 Fourier sin and cos series (1)

9.4 Applications of Fourier Series (1)

3.8 Endpoint Problems and Eigenvalues (2) (Section 3.8 should be covered now if it was not covered in Chapter 3.)

9.5 Heat Conduction and Separation of Variables (2)

9.6 Vibrating Strings and the One-dimensional Wave Equation (2)

9.7 Steady-State Temperature and Laplace's Equation (3) (Covers the Dirichlet problem for the disk. Provides another example of substitution methods, this time for a PDE.)

Exam 3 Nov.  15th

Chapter 10. Eigenvalues and Boundary Value Problems (5 lectures, Nov. 27th-Dec.) 

　

10.1 Sturm-Liouville Problems and Eigenfunction Expansions (2)

10.2 Application of Eigenfunction Series (2)

10.3 Steady Periodic Solutions and Natural Frequencies (1)

　 Examinations, review and leeway (5 lectures) 

Total: 44 lectures

Course News

• As of Aug. 31(Thursday) the Math 385 free Tutoring is available:

• Our second midterm exam will be on 
• The final exam will take place from 8:00-11:00 AM, Monday, December 11, in our usual class room, room 245 Altgeld Hall.　
• The pre-exam office hours will be the following:

• Assignment #1 (due on monday, Aug. 28th, 11:00am) Exercise of section 1.1 of the textbook, #9,10,13,15,23,24,31,36; Section 1.2:#8,10,21,29.
• Assignment #2 (due Wed. Sept. 6) : (i)Draw slope field of the differential equation: dy/dx=-y by hand and sketch the solution curve pass through (0,1);

(ii)Section 1.3:#15,16; 

(iii)Find a general solution and any sigular solution of the differentail equation dy/dx=y(2-y). Find a particular solution for it with the initial condition y(1)=1. 

(iv)Section 1.4:#11,#22,28; Section 1.5:#17,30. 

Assignment #3 (due Wed. Sept. 13) :(i) Section 1.5:#36,38; (ii) Section 1.6:#1,17,24; (iii)Review of Ch 1, Page 76, #32,34,35; Section 2.1: 29(a),(b). 

Assignment #4 (due Fri. Sept. 22) : Section 2.3,#4, Section 3.1, #4,5,33,37, Section 3.2, #1,8,19,31 

Assignment #5 (due Friday Sept.29) : Section 3.3, #16,22,25,30,31,38; Section 3.4, # 4, 10; Hint of problem #31,38: ``exp(3x) is a solution of the differential equation" tell us that 3 is a root of the correspondent characteristic equation. Then (r-3) is a factor of it. 

Assignment #6 (will NOT be graded, a quiz with probs from hw6 will run in class and the grade goes to your hw6 grade): Section 3.5, #2,13,25,26,31,41,43,64; Section 3.6: #1,#3 (Just solve the equation with the given initial condition, no need to follow the instruction to graph and express as a trignometric functions) 

Answer of even number problems of hw6:section 3.5:#2:y=-(5+6x)/4;#26:y=x[A e^(3x) sin2x + B e^(3x) cos2x + C xe^(3x) sin2x + Dx e^(3x) cos 2x];#64:y=-xCosx+Sinx; Section 3.6:#3:y_p=3 cos5t+4 sin 5t; y_g=A cos10t+ B sin 10t+3 cos 5t+ 4 sin 5t; the solution satisfy the initial condition is y=372 cos 10t -2 sin 10t +3 cos 5t +4 sin 5t.

HW #7 (will NOT be graded, a quiz with probs from Chapter 3 will run Friday Oct. 13th): Section 3.8, #2, 3, 14; Section 3.5: #27,33,35,37, 47, 53