-------------------------------------------- Math. 316 Fall'08 - Homework Assignments -------------------------------------------- updated: Tue Nov 25 12:45:14 MST 2008 *************************************** ******************************* TA: Mr. Candelario Castaneda, , Hokona 309 TA office hrs: Mon 12-1, Wed. 11-12 Computer Lab: Mon. 3-4 (in DSH 141) (when there is matlab hwk) -------------------------------------------------------------------------------- Only problems not marked by (*) should be turned in. (starred problems are good training, and possible test leads). Homework is due at the begining of Thursday's class, following the week it was assigned. No late homework will be accepted after solutions are posted Class meets TTh 11:00-12:15 in DSH 224 Solutions for textbook problems can be found at: http://ereserves.unm.edu/courseindex.asp (you need a course password, which I will announce in class) -------------------------------------------------------------------------------- WEEK 1 1( 8/26) 1st order equations, Direction Fields, Euler's method. Ch.1(1,2,3,4) 2( 8/28) Linear equations & integrating factors; separable equations. Ch.2(1,2) HW1 due Thursday September 4: 1.1(2,4) using DIRFIELD.M to plot direction fields, 1.2(2) 1.3(1,2) using EULER.M 1.4(2,5,7,8,15) 2.1(13,15,16) 2.2(1,9,10) *******Due date extended to Tuesday, Sep. 9 -------------------------------------------------------------------------------- WEEK 2 3( 9/02) More on separable, linear equations. Autonomous case (y'=f(y)) and the phase line, qualitative behavior of solutions and uniqueness, interval of existence. [Sec. 2.5]; partial fractions (p.86). 4( 9/04) Euler's method from the integral equation and the associated local error using Taylor's Theorem, [Sec. 2.7]. Improved Euler's method from integral equation motivated from Simpson's method and local error, [Sec. 2.8]. HW2 due Thursday September 11: Sec.2.5 p.92(2,4,10,12) In problems 10 and 12 find the solution using the separable technique and partial fractions as illustrated on p.86 and in class and verify your sketch. Include a discussion of the interval of existence Sec.2.8 p.113. Verify the second row of table 2.8.1 (t=.1). (use euler.m and impeuler.m) -------------------------------------------------------------------------------- WEEK 3 5( 9/09) 3.1 2x2 linear systems. Discussion of Ax=b; vectors and matrices, Matrix-vector multiplication. Determinant. Cramer's rule and inverse. 6( 9/11) 3.1 Eigenvalues. Examples Review complex numbers! HW3 due Thursday September 18: I. Problem 3, p.72 Polking. You will need to download eul, rk2 and rk4 from Polking's web site (rk2 is the same as improved euler) II. Use the programs eul, rk2, rk4 from I to solve the IVP y' = t^2 + y^2, y(0)=1, on [0,1]; h = .1 and .01 and plot the solution you find from each method on the same plot (use different markers to distinguish plots). III. Solve the IVP's (a) y' = y^2 , and (b) y' = 1 + y^2, y(0) = 1. Discuss their intervals of existence for t>0. What can you say about the IVP in II? IV. Sec.3.1 (p.138-39) 14, 16, 18, 22, 34, 38* -------------------------------------------------------------------------------- WEEK 4 7( 9/16) 3.2 Systems of ODEs. Inhomogeneous u'=Au+b => u = U+e; Ae+b=0; U' = AU Solution in terms of eigenvalues/eigenvectors 8( 9/18) 3.3: real and complex eigenvalues HW4 due Thursday September 27 (1) #11 p.147 and #9 p.162 (2) #12 p.147, #11 p.162 and #16 p.162 (3) #2 p.162 and #13 p.162 (4) #18, p.163 (5) #20, p.163 (6)* #29, p.163 (7) #3 and #8 p.173 (8) #13, p.173 In problems 1,2,3 and 7 use PPLANE (as discussed in CH.7 of P&A, pp.95-96) to draw the direction fields and phase plane portraits. (I will discuss questions about it next Tuesday) -------------------------------------------------------------------------------- WEEK 5 9( 9/23) 3.4, 3.5 Complex eigenvalues; Equal eigenvalues 10( 9/25) Overview of Phase plane portraits Nonlinear systems. HW5 due Thursday October 2 (1) #10 and #15, p.162. (2) #2 and #7, p.173. (3) #10 p.173. (4) #7 and #8 p.186 All problems: include general solution and hand-drawn sketch of phase plane portrait ****(Midterm I on 10/9) WEEK 6 11( 9/30) 4.1 Second order equations 12(10/02) 4.1-2 No homework due next week; look on web page for practise exam which will be posted on Sunday. I recommend you study for the exam, then take the practise exam, using your text. Put any information you need to look up on the sheet of paper that you will bring with youse to the exam. I will give answers on Tuesday (instead of review; I will be covering new material to make up for the time we lost today) -------------------------------------------------------------------------------- WEEK 7 13(10/ 7) 4.2-3 Linear equations with constant coefficients 14(10/ 9) One page of notes allowed HW5 due Thursday October 23 (1-4) Sec. 4.2: 10, 20, 21, 24 (5-8) Sec. 4.3: 2, 6, 10, 28 (In 2, 6b sketch Phase Plane by hand; use PPLANE for 10b) (9-11) Sec. 4.4: 12, 14, 26 (12) explain why the spirals in the context of Sec. 4.4 are always clockwise. -------------------------------------------------------------------------------- WEEK 8 15(10/14) 4.3 Reduction of Order: equal roots; 4.4 Complex roots xx(10/16) Fall break -------------------------------------------------------------------------------- WEEK 9 16(10/21) 4.5-6 Vibrations; undetermined coefficients 17(10/23) 4.7 Forced Vibrations and Resonance HW6 due Thursday October 30 (1-2) Sec. 4.5: 7, 13 (3-7) Sec. 4.6: 2, 3, 8, 16, 18 (8-10) Sec. 4.7: 9, 16, 17 -------------------------------------------------------------------------------- WEEK 10 18(10/28) 4.7-8 Resonance; Variation of parameters 19(10/30) 5.1-2 Laplace Transforms and properties HW7 due Thursday November 6 (1-2) Sec. 4.7: 21 (3-7) Sec. 4.8: 2, 3, 14, 16 (8-10) Sec. 5.1: 1, 18, 21, 28, 29 -------------------------------------------------------------------------------- WEEK 11 20(11/ 4) 5.2-3 Inverse Laplace transforms and applications to ODEs 21(11/ 6) 5.3-4 Solving ODEs with L-transforms HW8 due Thursday November 13 (1-2) Sec. 5.2: 5, 9, 10 (3-7) Sec. 5.3: 4, 6, 8, 21 (8-10) Sec. 5.4: 6, 7, 12 -------------------------------------------------------------------------------- WEEK 12 22(11/11) 5.4 Laplace transforms for systems; 5.5 Step functions 23(11/13) 5.5-6 Step functions and ODEs HW9 due Thursday November 20 (1-2) Sec. 4.8: 6, 8 (solve using Laplace transforms) (3-4) Sec. 5.3: 9, 10 (5-8) Sec. 5.4: 2, 4, 8, 10 -------------------------------------------------------------------------------- WEEK 13 24(11/18) Review of Laplace transforms 7.1 Autonomous systems 25(11/20) Demonstration of Coupled Oscillations -------------------------------------------------------------------------------- WEEK 14 26(11/25) 7.2 Almost Linear Systems HW10 due Thursday December 4 (1-6) Sec. 7.2: 1, 4, 7, 8, 12, 19 xx(11/27) Thanksgiving -------------------------------------------------------------------------------- -------------------------------------------------------------------------------- Under construction below -------------------------------------------------------------------------------- WEEK 15 27(11/ 2) 7.3-4 Predator-Prey equations and mathematical ecology 28(12/ 4) 7.5-6 Limit cycles and strange attractors -------------------------------------------------------------------------------- WEEK 16 30(12/ 9) review 30(12/11) (Material from weeks 7-15) -------------------------------------------------------------------------------- ----- Final Examination (Tuesday, December 16, 12:30-14:30) -------------------------------------------------------------------------------- Please follow these instructions when preparing your homework: *Staple your papers together. *Draw a line between problems so that they are clearly separated from each other *Do the problems in the order that they are assigned. *Mark each assignment by the number of the week during which it was assigned *Clearly mark each problem by its number+section and page number. *Print your name clearly on the front page, with week number and problem list --------------------------------------------------------------------------------