# Math 312. Partial Differential Equations for Engineering. Spring 2016.

## Books:

Section 003. TR 12:00-13:45. Room: CENT 1030. Syllabus for Math 312-003 (57709)
Syllabus version from August 23rd, 2016.
Richard Haberman
Applied Partial Differential Equations,
5th Edition, Pearson.

Abramowitz and Stegun,
Handbook on Mathematical Functions

## Office hours:

TR 14:00-15:15. Room: SMLC 220.

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 Thursday, December 15th.
The exam will take place on Thursday, December 15th, in the usual classroom at 10:00am-12:00pm. One page (two sides) of formulae is allowed. Calculators are prohibited.
Additional preparation material, Also read extra material on Green's functions published before, as well as solutions for all quizzes.
Topics (See training sets and preparation materials for the previous exams):
• Separation of variables, Laplace equation;
• 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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10 Quiz 09 on Tuesday, December 6th. (Solution published) Topic: Poisson's equation.
Training for a Quiz 10:
RH Section 9.3, p. 393: 1, 5(a,b,c), 6(a,b,c), 14(d), 15(a,b), 21.
Solutions for some problems on Green's functions.
Quiz 10 on Thursday, December 8th. (Solution published) Topic: Green's functions for ODEs.
Final lecture, given on Thursday, December 8th. Topic: Green's functions for Poisson's equation, method of characteristics.
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).
December 6th, 2016, class time.
10 Quiz 07 on Tuesday, November 29nd. (Solution published) Topic: Legendre polynomials and equations with spherical symmetry.
Quiz 08 on Thursday, December 1st. (Solution published) Topic: Inhomogeneous problems for heat equation (RH Section 8.2).
RH Section 7.10, p. 338: 3(c), 8, 9(c);
RH Section 8.2, p. 346: 1(d), 2(c), 6(a).
November 22nd, 2016, class time.
- Exam 2 on Thursday, November 17th. (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 7.7, 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 Tuesday, November 15th. (Solution published) 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).
November 8th, 2016, class time.
7 Quiz 05 on Thursday, November 12th. (Solution published) Topic: RH Section 7.3.
RH Section 7.3, p. 278: 1(a,c), 2(b), 4(b), 7(c);
RH Section 7.7, p. 308: 3(a), 8, 9(b), 10, 12(a,c).
November 1st, 2016, class time.
6 Quiz 04 on Thursday, October 20th. (Solution published) Topic: RH 5.8.3(b).
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).
October 20th, 2016, class time.
5 Exam 1 on Tuesday, October 4th. (Solution published) Topics: All sections 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 Thursday, September 22nd. (Solution published) Topic: Fourier series.
Quiz 03 on Tuesday, September 27th. (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.
September 22nd, 2016, 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).
September 13th, 2016, class time.
2 Quiz 01 on Thursday, September 8th. (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.
September 6th, 2016, 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.
August 30th, 2016, class time.