Math 286 Spring 2009 (Intro to Diffy Qs Plus)

https://faculty.math.illinois.edu/~jlebl/math286-s09.html

Section X1: MTWR 12:00-12:50 pm in 156 Henry


Homework
Handouts / Extra material:


Class notes

These are the notes I am lecturing from. Please do not print the whole file, it is a LOT of paper. Do tell me of any mistakes / typos / suggestions.


Lecturer: Jiří Lebl
Web: https://faculty.math.illinois.edu/~jlebl/
Office: 105 Altgeld
E-mail: jle...@math.uiuc.edu
Phone: 3-3143
Office hours: MW 1:00pm-1:50pm, W 3:00 - 3:50pm, and by appointment

Lab I:
Dates: Lab I: Thursday Jan 22nd
Place: Engineering Hall rooms 406B1 and 406B8, normal class time (12:00pm-12:50pm)
See https://faculty.math.illinois.edu/iode/materials.html for the Lab I guide.

Lab II:
Dates: Tuesday Feb 3rd
Place: Digital Computer Lab rooms L440 and L520, normal class time (12:00pm-12:50pm)
See https://faculty.math.illinois.edu/iode/materials.html for the Lab II guide.

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

Quiz: Wednesday, February 11, 10% of your grade.

Exam 1: Thursday, March 19, 20% of your grade.

Exam 2: Tuesday, April 28, 20% of your grade.

Final Exam: Wednesday, May 13, 7-10 PM, 40% of your grade. (Same room as class)

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 works for sure, version 3 maybe). 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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