# Math 312. Partial Differential Equations for Engineering. Fall 2017.

## Books:

Section 001. TR 11:00-12:15. Room: DSH 233. Syllabus for Math 312-001 (56734)
Syllabus version from August 18th, 2017.
Richard Haberman
Applied Partial Differential Equations,
5th Edition, Pearson.

Additional material on special functions:
Abramowitz and Stegun,
Handbook on Mathematical Functions

## Office hours:

TR 12:45-14:00. 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 have different cost pointwise.
HW # Homework problems Due date
Final Cumulative Final Exam on Tuesday, December 12th.
The exam will take place in the usual classroom at 12:30-14:30pm. One page (two sides) of formulae is allowed. Calculators are prohibited.
Additional preparation material, Also read extra material on Green's functions, as well as solutions for all quizzes.
Solution of canceled quiz on Characteristics
Topics (See training sets and preparation materials for the previous exams and quizzes solutions):
• 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;
• Characteristics. Work through example considered in class (RH p. 532)
and if you need extra probems: RH Section 12.2, p.533: 2, 5 (b,d), 6.
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10 Quiz 09 on Tuesday, December 5th. (Solution published) Topic: Poisson's equation.
Quiz 10 on Thursday, December 7th. (Solution published) Topic: Green's functions for ODEs.
Preparation for Quiz 10: RH Section 9.3, p. 393: 1, 5(a,b,c), 6(a,b,c), 14(d), 15(a,b), 21.
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 5th, 2017, class time.
10 Quiz 07 on Thursday, November 30th. (Solution published) Topic: Legendre polynomials and equations with spherical symmetry.
Quiz 08 on Thursday, November 30th. (Solution published) Topic: Inhomogeneous problems for heat equation (RH Section 8.2-8.3 (!)).
RH Section 7.10, p. 338: 3(c), 8, 9(c);
RH Section 8.2, p. 346: 1(d), 2(c), 6(a).
November 30th, 2017, class time.
8-9 Exam 2 on Tuesday, November 14th. (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.
7 Quiz 05 on Tuesday, November 7th. (Solution published) Topic: RH Section 7.3.
Quiz 06 on Thursday, November 9th. (Solution published) Topic: Bessel functions and equations with cylindrical symmetry.
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);
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 9th, 2017, class time.
6 Quiz 04 on Thursday, October 24th. (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 24th, 2017, class time.
5 Exam 1 on Thursday, October 5th. (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 03 on Thursday, September 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.
September 28th, 2017, class time.
3 Quiz 02 on Thursday, September 21st. (Solution published) Topic: Fourier series.
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 19th, 2017, class time.
2 Quiz 01 on Tuesday, September 12th. (Solution published) Topic: Separation of variables and solution 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 12th, 2017, 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 31st, 2017, class time.