HW #

Homework problems

Due date

Final

Cumulative Final Exam on Friday, May 12th.
The exam will take place in the usual classroom at 07:30am09:30pm. 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.



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.

89

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 5.17.9.
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(ae), 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(ad), 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.



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.

