Math 286 Fall 2008 (Intro to Differential Eq Plus)

https://faculty.math.illinois.edu/~jlebl/math286-f08.html

Section G1: MTWR 3:00-3:50 pm in 333 Armory


Lab I: Wednesday Aug 27:

In Grainger Engineering Library room 57, normal class time (3pm-3:50pm)

See https://faculty.math.illinois.edu/iode/materials.html for the Lab I guide.

Lab II: Tuesday Sep 9:

In Grainger Engineering Library room 57, normal class time (3pm-3:50pm)

See https://faculty.math.illinois.edu/iode/materials.html for the Lab II guide.

Lab/Project III: Monday Sep 29:

In Grainger Engineering Library room 57, normal class time (3pm-3:50pm)

Jeremy Tyson will be there instead of me.

See https://faculty.math.illinois.edu/iode/materials.html for the Project III (mechanical vibrations).


Homework 1 (due Wed Sept 3. beginning of class)
1.1: 9, 16, 20, 23, 32, 42
1.2: 3, 8, 17
1.3: Project I (direction fields)

Homework 2 (due Wed Sept 10. beginning of class)
1.4: 15, 17, 25, 47
1.5: 9, 13, 18, 38
1.6: 14, 16, 23, 61
2.2: 1, 3, 23

Homework 3 (due Wed Sept 17. beginning of class)
2.4: Project II
3.1: 5, 12, 19, 27, 36, 37, 48
3.2: 6, 9, 25, 26

Homework 4 (not due, but do it anyway)
3.3: 7, 8, 22, 26, 42, 43

Homework 5 (due Wed Oct 1. beginning of class)
Project III
3.4: 3 (write 20cm as 0.2m), 5 (first read the instructions above the problem, and read pages 183-184), 6 (this means the pendulum takes 24 hours 2 minutes and 40 seconds at the equator to complete as many cycles as it does during 24 hours at Paris), 13, 14 (And for # 13, 14: determine whether the system is overdamped, critically damped, or underdamped.), 23 (here m=100, and you should express omega in radians per second)
3.5: 3, 4, 6

Homework 6 (due Wed Oct 8. beginning of class)
3.5: 10, 22, 26, 29, 34, 43, 50
3.6: 5, 6, 11, 18, 24, 25
3.8: 3, 16

Homework 7 (due Wed Oct 15. beginning of class)
4.1: 5, 24
5.1: 2, 3, 6, 12, 20, 22, 31 (no need for wronskians in 22, just check that when t=0, you can't write one as a constant multiple of the other).
5.2: 4, 8, 11, 20, 29

Homework 8 (not due but you should do it anyway)
5.3: 3, 9, 12, 14
5.4: 7, 11

Homework 9 (due Wed Oct 29. beginning of class)
5.5: 9, 19, 23, 27, 32
5.6: 2, 4, 14, 16, 25

Homework 10 (due Wed Nov 5. beginning of class)
5.6: 7, 10
9.1: 1, 8, 9, 12, 19, 25

Homework 11 (due Wed Nov 12. beginning of class)
Project 4 (Fourier series)
9.2: 8, 13, 25
9.3: 6, 11

Homework 12 (due Wed Nov 19. beginning of class)
9.4: 4, 14
9.5: 3, 9, 14, optionally: 19, 22
9.6: 3, 11, 14

Homework 13 (due Wed Dec 10. beginning of class)
9.7: 4
10.1: 1, 8, 11
10.2: 2, 6, 9
10.3: 1, 2, 8


Handouts:


Lecturer: Jiří Lebl
Web: https://faculty.math.illinois.edu/~jlebl/
Office: 105 Altgeld
E-mail: jle...@math.uiuc.edu
Phone: 3-3143
Office hours: MTW 4:00 - 4:50 pm
Hat: Barmah Squashy (no I'm not australian)

Grades/Curve: Grades will be based on the percentages below. Curve will be applied if needed.

Midterm 1: Monday, September 22, 10% of your grade.

Midterm 2: Wednesday, October 22, 20% of your grade.

Midterm 3: Thursday, November 20, 20% of your grade.

Final Exam: 7:00-10:00 PM, Friday, December 12, 40% of your grade.

Homework: Assigned every week. Worth 10%, possibly spot checked (spot checked means: some spot(s) of each homework checked, and all will be collected). Lowest homework grade dropped. Some homework will be iode based (see below).

Iode: Iode is a free software package tailored for this course. We will spend some time in the computer lab learning this software and you will be assigned some homework using it. See https://faculty.math.illinois.edu/iode/. Iode requires Matlab or Octave (version 2, not 3). Matlab is available in the lab and Octave is free so you need not purchase anything.

Test Policies: No books, notes, calculators or computers allowed on the exams or the final.

Text: C.H. Edwards & D.E. Penney, Differential Equations and Boundary Value Problems: Computing and Modelling, 4th edition, Prentice Hall 2008.

Syllabus: (Approximately)

 Chapter 1. First Order Differential Equations (6 lectures)

    1.1 Differential Equations and Mathematical Models 
    1.2 Integrals as General and Particular Solutions 
    1.3 Slope Fields and Solution Curves 
    1.4 Separable Equations and Applications 
    1.5 Linear First-Order Equations 
    1.6 Substitution Methods and Exact Equations 

Chapter 2. Mathematical Models and Numerical Methods (3 lectures)

    2.2 Equilibrium Solutions and Stability
    2.4 Numerical Approximation: Euler's Method

Chapter 3. Linear Equations of Higher Order (13 lectures)

    3.1 Introduction: Second-Order Linear Equations 
    3.2 General Solutions of Linear Equations 
    3.3 Homogeneous Equations with Constant Coefficients 
    3.4 Mechanical Vibrations 
    3.5 Nonhomogeneous Equations and Undetermined Coefficients 
    3.6 Forced Oscillations and Resonance 
    3.8 Endpoint Problems and Eigenvalues 

Chapter 4. Introduction to Systems of Differential Equations (1 lecture)

    4.1 First Order Systems and Applications 

Chapter 5. Linear Systems of Differential Equations (13 lectures)

    5.1 Matrices and Linear Systems 
    5.2 The Eigenvalue Method for Homogeneous Systems 
    5.3 Second-Order Systems and Mechanical Applications 
    5.4 Multiple Eigenvalue Solutions 
    5.5 Matrix Exponentials and Linear Systems 
    5.6 Nonhomogeneous Linear Systems 

Chapter 9. Fourier Series Methods (12 lectures)

    9.1 Periodic Functions and Trigonometric Series 
    9.2 General Fourier Series and Convergence 
    9.3 Fourier Sine and Cosine Series 
    9.4 Applications of Fourier Series 
    9.5 Heat Conduction and Separation of Variables 
    9.6 Vibrating Strings and the One-Dimensional Wave Equation 
    9.7 Steady-State Temperature and Laplace's Equation 

Chapter 10. Eigenvalues and Boundary Value Problems (5 lectures)

    10.1 Sturm-Liouville Problems and Eigenfunction Expansions 
    10.2 Applications of Eigenfunction Series 
    10.3 Steady Periodic Solutions and Natural Frequencies 

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