Math 312. Partial Differential Equations for Engineering. Spring 2013.


Sections:

Books:

Section 001. TR 9:30-10:45. Room: ASM 1070 ECON 1002. Syllabus for Math 312-001 (18479)
Syllabus version from January 16th, 2013.
Richard Haberman
Applied Partial Differential Equations,
5th Edition, Pearson.

Additional material on special functions:
Abramowitz and Stegun,
Handbook on Mathematical Functions
(see external links section for downloads)

Office hours:


TR 12:30-13:45. Room: SMLC 220.

How grades are assigned?

All homeworks: 100 points (only few key problems from the homework will be graded, approximately 8 points for homework).
Two midterm exams: 100 points each (100+100 points).
In class quizzes: 50 points.
Final exam: 200 points.
Total: 550 points.
Lowest boundaries for grades (not higher than):
A = 495, B = 440, C = 380, D = 330.
No late HWs are accepted after graded HW is returned. Even before for a late submission you shall get -1 point from the late HW grade.
HW # Homework problems Due date
Final Cumulative Final Exam on Tuesday, May 7th. (Solution published)
The exam will take place on Tuesday, May 7th, in the usual classroom at 7:30-9:30am. One page (two sides) of formulae is allowed. Calculators are prohibited.
Additional preparation material Part 1, Part 2.
Topics (See training sets and preparation materials for the previous exams):
  • Separation of variables;
  • Heat and wave equations in the rectangular regions;
  • Equations with cylindrical symmetry (Bessel and modified Bessel functions);
  • Equations with spherical symmetry (Legendre polynomials and spherical harmonics);
  • Nonhomogeneous equations (both forcing term and boundary conditions);
  • Poisson's equation;
  • Green's functions for ODEs.
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11 Quiz 07 on Tuesday, April 30th. (At the beginning of the class!) (Solution published) Topic: Legendre polynomials and equations with spherical symmetry.
Quiz 08 on Tuesday, April 30th. (At the end of the class) (Solution published) Topic: Inhomogeneous problem for heat equation.
Quiz 09 on Thursday, May 2nd. (At the beginning of the class!) (Solution published) Topic: Poisson's equation.
Quiz 10 on Thursday, May 2nd. (At the end of the class) (Solution published) Topic: Green's functions.
RH Section 9.3, p. 393: 1, 5(a,b,c), 6(a,b,c), 14(d), 15(a,b), 21.
Final lecture, given on Thursday, May 2nd. Topic: Green's functions for Poisson's equation, infinite domain Fourier, method of characteristics.
May 2nd, 2013, class time.
10 Quiz 06 on Tuesday, April 23rd. (Solution published) Topic: Bessel functions and equations with cylindrical symmetry.
RH Section 7.10, p. 338: 3(c), 8, 9(c);
RH Section 8.2, p. 346: 1(d), 2(c), 6(a);
RH Section 8.3, p. 352: 1 (c), 2;
RH Section 8.4, p. 357: 1 (b);
RH Section 8.5, p. 364: 2 (b);
RH Section 8.6, p. 372: 1 (b,c), 3 (a).
April 30th, 2013, class time.
- Exam 2 on Tuesday, April 16th. (Solution published) Topics covered: RH Sections 5.1-7.9.
One page (one side) of formulae is allowed. Calculators are prohibited.
Solutions of key problems from review. Part 1.
Solutions of key problems from review. Part 2.
Solutions of key problems from review. Part 3 (Also work through RH 7.9.4).
Training (review) for Exam 2:
RH Section 5.6, p. 188: 1(c);
RH Section 5.8, p. 204: 3;
RH Section 5.9, p. 210: 1(b), 3(a);
RH Section 7.3, p. 278: 1(a,c), 2(b), 4(b), 7(c);
RH Section 7.5, p. 291: 7, 8(a);
RH Section 7.7, p. 308: 3(a), 8, 9(b), 10, 12(c);
RH Section 7.8, p. 317: 1(a-e), 2(d);
RH Section 7.9, p. 328: 1(b), 2(a), 3(a), 4(b).
None.
8 Quiz 06 on Thursday, April 11th.Canceled Topic: Bessel functions and equations with cylindrical symmetry.
RH Section 7.8, p. 317: 1(a-d), 2, 7, 8;
RH Section 7.9, p. 328: 1(b), 2(a), 3(a), 4(b);
April 11th, 2013, class time.
7 Quiz 04 on Tuesday, April 2nd. (Solution published) Topic: RH 5.8.3(b).
Quiz 05 on Thursday, April 4th. (Solution published) Topic: RH Section 7.3.
RH Section 7.3, p. 278: 1(a,c), 2(b), 4(b), 7(c);
RH Section 7.5, p. 291: 6, 7, 8(a);
RH Section 7.7, p. 308: 3(a), 8, 9(b), 10, 12(a,c).
April 4th, 2013, class time.
6 Quiz 04 on Thursday, March 28th. Postponed till April 2nd.
RH Section 5.3, p. 161: 5.3.3, 5.3.5(a,b,c), 5.3.6(a,b,c), 5.3.7, 5.3.9(c);
RH Section 5.5, p. 174: 5.5.1(c,g), 5.5.5(a,b);
RH Section 5.5A, p. 183: 5.5A.5 (see example on p. 181);
RH Section 5.6, p. 188: 5.6.1(c);
RH Section 5.7, p. 192: 5.7.1;
RH Section 5.8, p. 204: 5.8.3, 5.8.7(b,c,d,e), 5.8.10(a,c);
RH Section 5.9, p. 210: 5.9.1(b), 5.9.3(a).
March 28th, 2013, class time.
5 Exam 1 on Tuesday, March 5th. (Solution published) Topics: All section covered, up to and including 4.4.
One page (one side) of formulae is allowed. Calculators are prohibited.
Solutions of key problems from review. Part 1.
Solutions of key problems from review. Part 2.
Solutions of key problems from review. Part 3.
Training (review) for Exam 1:
RH Section 1.4, p. 18: 1.4.1(a,c,f);
RH Section 2.3, p. 52: 2.3.3 (b,c), 2.3.8;
RH Section 2.4, p. 65: 2.4.1(a,b,c), 2.4.2.;
RH Section 2.5, p. 81: 2.5.1(a,e), 2.5.3(a), 2.5.8(a), 2.5.9(a);
RH Section 3.2, p. 91: 3.2.2(a,c);
RH Section 3.3, p. 110: 3.3.2(a,d);
RH Section 3.4, p. 120: 3.4.9, 3.4.12;
RH Section 4.4, p. 142: 4.4.3.
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4 Quiz 02 on Tuesday, February 26th. (Solution published) Topic: Fourier series.
Quiz 03 on Thursday, February 28th. (Solution published) Topic: Wave equation.
RH Section 3.3, p. 110: 3.3.2(a,d), 3.3.3(a), 3.3.10, 3.3.13;
RH Section 3.4, p. 120: 3.4.6, 3.4.9, 3.4.12;
RH Section 3.5, p. 126: 3.5.1(c), 3.5.7;
RH Section 4.2, p. 133: 4.2.1(a), 4.2.5;
RH Section 4.4, p. 140: 4.4.1, 4.4.3.
February 28th, 2013, class time.
3 RH Section 2.5, p. 81: 2.5.1(a,e), 2.5.3(a), 2.5.6(a), 2.5.8(a), 2.5.9(a);
RH Section 3.2, p. 91: 3.2.1(d), 3.2.2(a,c).
February 14th, 2013, class time.
2 Quiz 01 on Thursday, February 7th. (Solution published) Topic: Separation of variables for heat equation.
RH Section 2.3, p. 51: 2.3.2(b,d), 2.3.3 (b,c - I require the final integral to be calculated, you can use this table), 2.3.4(a), 2.3.8;
RH Section 2.4, p. 65: 2.4.1(a,b,c), 2.4.2.
February 7th, 2013, class time.
1 RH Section 1.2, p. 10: 1.2.5;
RH Section 1.3, p. 13: 1.3.2;
RH Section 1.4, p. 18: 1.4.1(a,c,f), 1.4.3, 1.4.10.
January 29th, 2013, class time.