AMPA 0340 METHODS OF APPLIED MATHEMATICS II

General Information

Instructor: Dr. Shun Zhang, shun_zhang@brown.edu

Office: 180 George, Room 18

Lecture Time/Location: MWF 12-12:50, B&H 157

Office Hour: Wednesday and Friday 1:00 -1:50 pm in Room 102A, 180 George St.

TEXTBOOK: Elementary Differential Equations and Boundary Value Problems , 9th edition, by W.E. Boyce and R.C. DiPrima

Teaching Assistant

Teaching Assistant: Hong Zhang, hong_zhang@brown.edu

Recitation: 2:00-4:00pm Wednesday, 101 Thayer Street, Room 116B

Office Hour: 1:00-3:00pm Friday, 180 George Street, Room 106

Final Exam

December 19th, 9AM, Wilson 302
Review problems for the final: review problems .
solutions of review problems solution PDF some corrections: Problem III, all cosh sinh should be cos and sin; Problem IV: the ODE for T should be T'+4 lambda T=0; Problem VI, 1, x3=(4,6) is stable, elliptic 3. (0,0) is unstable saddle point
eigenvalue/function problem solutions PDF

Handouts

solutions of midterm PDF

Midterm, 10/26, Friday, in class, Chapter 7
review of chap 7, by Dr. Peter van Heijster PDF
midterm and solutions by by Dr. Peter van Heijster midterm PDF , solution PDF
euler forward matlab program for x'=1-t+4t, x(0)=1 eulerf.m ,
euler backward matlab program for x'=1-t+4t, x(0)=1 eulerb.m .
euler forward matlab program for x'=2x-3t, x(0)=1 eulerforward.m .
improved euler matlab program for x'=2x-3t, x(0)=1 improvedeuler.m . The old version is wrong, the current one should be correct
Course outline & general information PDF
examples of elementary row operations PDF
examples of Gaussian elimination PDF
Handout on using Matlab PDF , and the program pplane8 (which has been developed by John C Polking at Rice university) can be downloaded, by Peter van Heijster. Draw "direction plot", choose "arrows", then click proceed. Draw "phase portrait", click on the graph to get a trajectory, click enough points to draw the phase portrait

Homework

Homework 1: section 7.1 page 359, 1,4,5,6, section 7.2 page 371. 1,4,12,14,20 due 9/21 Friday in class
Homework 2: section 7.3 page 383, 1,2,3,4,6,21,22,24,31,33 due 9/28 Friday in class
Homework 3: section 7.4 page 389, 2(a,b,c) 6,8,9 section 7.5 1,2,3,6,9,11,13,15,17,18,19,20,22,28 due 10/05 Friday in class (2(d) of 7.4 is not required)
Homework 4: section 7.6 1,2,3,17,,21 section 7.7 6 12 15 16 17 due 10/12 Friday in class
Homework 5: section 7.8 1,2,17,18,19,21 section 7.9 1, 2 due 10/19 Friday in class
Homework 6: section 8.1 22,26 section 8.2 1, 3 (matlab programs for 3 of 8.2 is provided above, modify them to do 1 of 8.3. for euler backward, modify eulerb.m since different right hand side need to be handled differently)due to the cancelation of the class on monday, the hw is due on friday
Homework 7: section 9.2 15,23 section 9.3 6,18,26 (use pplane8.m provided above to draw phase portraits) due 11/09 Friday in class
Homework 8: section 10.1 5,6,17, and an extra set of problems for Chap 9. extra hw PDF due 11/15 Friday in class
Homework 9: section 10.2 3,5,13,14,15;section 10.4 7,10;section 10.5: 1,2,5,7 11/30 Friday in class
Homework 10: section 10.7 1(a),5(a);section 10.8: 1(a,b),6(a,b) 12/7 Friday in class