math 340 - Differential Equations

News | Office Hours | Schedule | Syllabus | Textbook | Homework | Links

Travis A Olson
18A Weber Building
(970) 491-????
taolson@rams.colostate.edu

News

   FINAL: Tuesday May 12, 3:40-5:40 in EDDY 212 
      A good review of chapter 9 can be here: Chp9review.pdf
         My finals from last 2 summers: math340su08finalsol.pdf , m340su07final.pdf
         A general review of main material for this test: math340 final notes.pdf
  
   The main class website: http://www.math.colostate.edu/m340/
    You can see tests from last semester in there.


    The m files for the Feb 17 lab are: m340sec61euler1.m, m340sec61euler2.m, m340sec62RungKut1.m
    The m-file for the lab Jan 27 is: here (PlotLabJan272009.m)
    pplane and dfield come in two types.  A matlab program found at: http://math.rice.edu/~dfield/index.html
    or java versions for those without matlab at: http://math.rice.edu/~dfield/dfpp.html

Office Hours

Monday and Tuesday and Wednesday at 9am, Wednesday at 11am, and by appointment.

Course Outline

Part I: First Order Equations
Chapter 1: Introduction to Differential Equations 1.1, 1.2, 1.3
• Chapter 2: First-order Equations. Solution techniques for linear and separable equations, exact equations, models of motion, autonomous equations and stability of equilibrium solutions 2.1, 2.2, 2.3, 2.4, 2.6, 2.7, 2.9
• Chapter 3: Modeling and Applications. Population Modeling 3.1,  Electrical Circuits 3.4
• Chapter 6: Numerical Methods. Euler method 6.1,  Runge Kutta Methods 6.2
Part II: Systems of First Order Equations
• Chapter 7: Matrix Algebra. Vectors, matrices, linear systems of equations, subspaces, determinants 7.1, 7.2, 7.3, 7.4, 7.5, 7.6, 7.7
• Chapter 8: Introduction to Systems. Definition, geometric interpretation, linear systems, phase-plane portraits 8.1, 8.2, 8.3, 8.4, 8.5
• Chapter 9: Linear Systems with Constant Coefficients. Eigenvalue-eigenvector solutions of homogeneous systems and matrix exponential, phase-plane portraits and trace-determinant plane, qualitative analysis and stability, inhomogenous systems 9.1, 9.5, 9.6 (9.2: planar systems), 9.3, 9.4, 9.7, 9.9
Part III: Linear Second and Higher Order Equations
• Chapter 9.8: Higher Order Equations. Linear Dependence/Independence, Wronskian, fundamental set of solutions 9.8, 4.3
• Chapter 4: Second-Order Equations. Homogenous and inhomogenous equations, variation of parameters and undetermined coefficients methods, forced and unforced harmonic motio. 4.2, 4.4, 4.5, 4.6, 4.7
• Chapter 5: The Laplace Transform. Definition and properties, application to differential equations, discontinuous forcing terms, Delta function, convolution 5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7
Part IV: Nonlinear Systems
• Chapter 10: Nonlinear Systems. Linearization, long-term behaviour of solutions, mechanical systems, population models.

Syllabus

Please review the course Syllabus (PDF).

Textbook

Differential Equations (2nd edition)
J. Polking, A. Boggess, D. Arnold
Prentice Hall 2005, ISBN 0-13-143738-0

Supplementary Text: J. Polking, D. Arnold: Ordinary Differential Equations using Matlab

Homework

Date Due	Assignment	Solutions
Jan 28	HW1	HW1solutions
Feb 4	HW2	HW2solutions
Feb 11	HW3	HW3solutions
Feb 18	HW4	HW4solutions
Feb 25	HW5	HW5solutions
Mar 4	HW6	HW6solutions
Mar 25	HW7	HW7solutions
Apr 1	HW8	HW8solutions
Apr 8	HW9	HW9solutions
Apr 15	HW10	HW10solutions Note: problem 1c has sign errors problem 4b is not done, but is another like 4a
Apr 22	HW11	HW11solutions
May 6	HW12	HW12solutions
Problem sheet	math340problems2ndhalf

Section	Suggested
1.1	2,3,6,7,10
1.2	8,9,11,12,14,17,19,21
1.3	2,5,11,13,16,17,20,22
2.1	5,8,10,13,,18,23,25,27,33
2.2	5,7,12,15,16,21,26
2.3	3,6,9,10,13
2.4	6,13,16,19,36,43
2.5	select a couple
2.6	3,7,10,13,23
2.7	1,2,4,5,11,27
2.9	2,5,8,9,12,20,21,25
3.1	4,7,11,10,13,16
3.3	4,8,10
6.1	4,7,8,10,11
6.2
7.1	32,34,38,44
7.2	6,7,13,18,23,24
7.3	4,18,20,32
7.4	4,12,20
7.5	6,14,22,30
7.6	10,18,32
7.7	28,32
8.1	6,8,14
8.2	18,22
8.3	4,8
8.4	8,14,20
8.5	6,10,12
9.1	8,14,44
9.2	4,10
9.5	8,14,20,38,46
9.6	2,14,18,26
9.3	20,22
9.4	6,12,20
9.7	4,10
9.9	4,6
9.8
4.3
4.2/4.4	13,24/14
4.5	4,22
4.6	12
4.7	4,6,18,32
5.1
5.2	20,24,40
5.3	14,20
5.4	24
5.5
5.6
5.7

Useful Links

As the semester progresses, this will be a growing list of resources.

• An interesting article on brain growth and learning that basically refinforces the old saying that there's nothing more common than a talented failure (aka its more how hard you work than how talented you are)How to raise smart kids.