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Math 383: Linear Algebra and Differential Equations

NOTE: the date of test 1 has changed!

Syllabus (PDF)
Office Hours: Mondays from 3:00 - 4:30 PM and Thursdays from 5:00 - 6:00 PM in Phillips 314
Many of you have said the book is not yet available so this is the first sections scanned in: Sections 1.1 - 2.1 (PDF)

Lecture 1 (01/10): (1.1-1.2) Introduction, falling object example

Lecture 2 (01/15): (1.1-1.3) Falling object example, radioactive decay case study, classification of DEs
Radioactive Decay Case Study
HW 1 DUE: 01/22 (before class!)

Lecture 3 (01/17): (1.3-2.2) Classification of DEs, method of integrating factors, and separable equations

Lecture 4 (01/22): (2.2-2.3) Separation of Variable and Mathematical Modeling
HW 2 DUE: 01/29 (before class!)

Lecture 5 (01/24): (2.3) Mathematical modeling examples and Quiz
Integral from Example 3 in Section 2.3

Lecture 6 (01/29): (2.4-2.5) Differences between linear and nonlinear equations (existence and uniqueness) and Autonomous equations
HW 3 DUE: 02/05 (before class!)

Lecture 7 (01/31): (2.5) Autonomous equations and population dynamics
Population Dynamics: Critical Threshold Model
Install Matlab by next Thursday - Feb 7, you can get the software from UNC software acquisition

Lecture 8 (02/05): (2.6) Exact Equations and Integrating Factors
HW 4 DUE: Thursday 02/14 (before class!)
2.7 homework worksheet

Matlab Files for Numerical ODE solver
Solver (use numerical_ode_solver to start applet)
Solver v2 (use numerical_ode_solver2 to start applet)
Forward Euler
Runge Kutta 2
Runge Kutta 4

Lecture 9 (02/07): (2.7 + more) Numerical Methods for first order ODEs

Lecture 10 (02/12): (2.7 + more) Numerical Methods for first order ODEs (worked on HW 2.7 worksheet in class as well) and Quiz

Lecture 11 (02/14): (3.1) Introduction to second order ODEs and homogeneous equations with constant coefficients

Lecture 12 (02/19): Test 1 - covers all material in Chapters 1 and 2 (including the extra material on numerical methods covered in class)
Review Session: Monday, February 18, 5:00 - 6:00 PM, Phillips 332

Lecture 13 (02/21): (3.2) Linear homogeneous equations and the Wronskian
HW 5 DUE: 02/28 (before class!)

Lecture 14 (02/26): (3.2 + more) Linear homogeneous equations and the Wronskian

Lecture 15 (02/28): (3.3-3.4) Homogeneous equations with constant coefficients: complex roots and repeated roots
HW 6 DUE: 03/07 (before class!)

Lecture 16 (03/05): (3.4-3.5) Homogeneous equations with constant coefficients: repeated roots and Nonhomogenous equations: Method of undetermined coefficients

Lecture 17 (03/07): (3.5-3.6) Nonhomogenous equations: Method of undetermined coefficients and Variation of parameters
HW 7 DUE: 03/21 (before class!)

Lecture 18 (03/19): Review of second order equations and (3.7) Mechanical vibrations
Review Worksheet

Lecture 19 (03/21): (3.7) Mechanical vibrations without forcing
HW 8 DUE: 04/02 (before class!)

Lecture 20 (03/26): (3.7-3.8) Mechanical vibrations without and with forcing

Lecture 21 (03/28): Test 2 - focus will be on Chapter 3 (3.1 - 3.7) (up to and including the material that was covered on 3/21)
Review Session: Monday, March 25, 6:00 - 7:00 PM, Phillips 332

Lecture 22 (04/02): (4.1) Higher Order Linear Equations
HW 9 DUE: 04/09 (before class!)

Lecture 23 (04/04): (Determinants + 4.2) Determinants and Homogenous Equations with Constant Coefficients
Test 2 was returned - for bonus points you can redo problem 5: DUE: 04/11 (before class!)
Determinant Example

Lecture 24 (04/09): (4.2 + 4.3 + 4.4) Nonhomogenous Equations: Method of Undetermined Coefficients and Variation of Parameters
HW 10 DUE: 04/16 (before class!)

Lecture 25 (04/11): (5.1-5.2) Introduction to systems of ODEs and Review of Matrices

Lecture 26 (04/16): (5.3) Systems of Equations, Linear Independence, Eigenvalues and Eigenvectors
HW 11 DUE: 04/23 (before class!)

Lecture 27 (04/18): (5.3 - 5.4) Eigenvectors and Eigenvalues and Theory of Systems of First Order Equations

Lecture 28 (04/23): (5.5 - 5.6) Homogeneous Linear Systems with Constant Coefficients - Real and Complex Eignevalues
Practice Problems Does not need to be turned in

Lecture 29 (04/25): Examples from 5.5 and 5.6

Final Exam Tuesday, April 30, 2013 8:00 AM - 11:00 AM - cumulative exam up to and including 5.6
Review Session I: Wednesday, April 24, 5:00 PM - 6:00 PM, Phillips 332
Review Session II: Monday, April 29, 3:00 - 4:00 PM, Phillips 332

Matlab Help
Introduction and Plotting
Matlab Session:
Introduction handout from the session