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

## Books:

Section 001. MWF 10:00-10:50. Room: DSH 318. Syllabus for Math 312-001 (32449)
Syllabus version from January 18th, 2017.
Richard Haberman
Applied Partial Differential Equations,
5th Edition, Pearson.

Abramowitz and Stegun,
Handbook on Mathematical Functions

## Office hours:

MW 12:00-13:15. 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 Friday, May 12th.
The exam will take place in the usual classroom at 07:30am-09:30pm. 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.
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.
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10 Quiz 09 on Wednesday, April 26th. (Solution published) Topic: Poisson's equation.
Quiz 10 on Monday, May 1st. (Solution published) Topic: Green's functions for ODEs.
Extra Quiz 11 on Wednesday (will replace any missed quiz or quiz with lower grade). (Solution published) Topic: 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.)
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).
RH Section 9.3, p. 393: 1, 5(a,b,c), 6(a,b,c), 14(d), 15(a,b), 21.
April 26th, 2017, class time.
10 Quiz 07 on Wednesday, April 19th. (Solution published) Topic: Legendre polynomials and equations with spherical symmetry.
Quiz 08 on Friday, April 21st. (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).
April 19th, 2017, class time.
8-9 Quiz 06 on Friday, April 7th. (Solution published) Topic: Bessel functions and equations with cylindrical symmetry.
Exam 2 on Wednesday, April 12th. (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 Wednesday, March 29th. (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);
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).
March 29th, 2017, class time.
6 Quiz 04 on Monday, March 6th. (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).
March 6th, 2017, class time.
5 Exam 1 on Monday, February 27th. (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 Wednesday, February 15th. (Solution published) Topic: Fourier series.
Quiz 03 on Friday, February 17th. (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 15th, 2017, 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 6th, 2017, class time.
2 Quiz 01 on Wednesday, February 1st. (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 1st, 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.
January 25h, 2017, class time.