HW #

Homework problems

Due date

Final

Cumulative Final Exam on Thursday, 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.
Topics (See training sets and preparation materials for the previous exams as well 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.)



11

Quiz 09 on Thursday, May 5th (Solution published). Topic: Poisson's equation.
Quiz 10 (cancelled) (Solution published). Topic: Green's functions for ODEs.
Extra Quiz 11 (cancelled). (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 8.6, 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.

May 6th, 2022, 5pm end of day.

10

Quiz 07 on Thursday, April 28th (Solution published). Topic: Legendre polynomials and equations with spherical symmetry.
Quiz 08 on Tuesday, May 3rd. (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);
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.

May 2nd, 2022, end of day.

89

Exam 2 on Thursday, April 21st (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.

78

Quiz 05 on Tuesday, April 12th (Solution published). Topic: RH Section 7.3.
Quiz 06 on Thursday, April 14th (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(ad), 2, 7, 8;
RH Section 7.9, p. 328: 1(b), 2(a), 3(a), 4(b).

April 12 15th, 2022, end of day.

6

Quiz 04 on Tuesday, April 5th (Solution published). Topic: RH 5.8.3(b).
Lecture for Thursday, March 31st.
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).

April 4th, 2022, end of day.

5

Exam 1 on Tuesday, March 8th (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, March 1st (Solution published). Topic: Fourier series.
Quiz 03 on Friday, March 3rd (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 25th March 2nd, 2022, end of day.

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 17th 18th, 2022, end of day.

2

Quiz 01 on Tuesday, 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, 2022, 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, 2022, class time.

