MATH 406 ADVANCED CALCULUS FOR ENGINEERS AND SCIENTISTS II

Textbook: Kreyszig, 'Advanced Engineering Mathematics', tenth edition

Office hours: 11.00-1.00 Tuesday, and by appointment.

Midterm: Wednesday February 29th in class.

Final exam: Monday April 30th, 8.00am-9.50am, 162 Willard.

Homework 1: Problem Set 13.1 of Kreyszig: Questions 8, 9, 12, 16, 19, due 25th January.

Homework 2: Due 2nd February:

A)  Problem set 13.2: Questions 1,2

B)  Problem set 13.2: Questions 22, 24

C) Problem set 13.3:  Questions 1,2,3,4,5

D)  Problem set 13.3:  Question 24 part e) only

Homework 3: Due 9th February:

A) Problem set 13.4 questions 2,3,5,7,10 and 11

Hint: Remember to say WHERE the function is analytic. For a function to be analytic, we require that the function is defined. For example f(z) = 1/z is not analytic at z=0. This issue occurs in at least one of these questions. Remember that the Cauchy-Riemann equations also have a polar form, and polar coordinates will definitely be the way to go for some of these questions.

B) Problem set 13.4 questions 13, 16, 18 and 22.

Homework 4: Due 15th February:

A) Problem set 13.6 questions 6, 8, 13

B) Problem set 13.7 questions 5,6,7, 12, 14

C) Problem set 13.7 questions 23, 26

D) Problem set 14.1 questions 23, 24

Homework 5: Due Friday 24th February.

A) Section 14.1 Questions 21, 23, 25, 26. Use ANY applicable integration techniques from class.

B) Section 14.2 Questions 9, 11, 12

C) Section 14.3 Questions 5, 6,7, 17

Hint for 17: You'll need partial fractions and to notice that z^2+1 = (z-i)(z+i)

D) Section 14.4 Questions 1,2,3,8

Here is homework 6 on convergence of series, and radius of convergence for power series:

A) Section 15.1: Questions 16, 18, 20, 24

B) Section 15.2: Questions 6, 7, 8, 11, 12

Hint for B) qn 7: You have to change the indices to write the series in the correct form.

Homework is due in class on Wednesday 21st march.

Homework  7:

A) Chapter 15.1, qn. 19

B) Chapter 15.3 qn. 4 Hint: Use your knowledge of geometric series, and properties of power series to answer this question. The Cauchy product of two power series is the power series whose coefficients are given by termwise multiplication.

C) Chapter 15.4 qns. 3, 6, 19

D) Chapter 16.1 qns 1, 2, 9.

Here is homework 8, due in class on wednesday (april 4th). The topics are : finding all Laurent series, finding zeros, and finding and classifying singularities. Here it is:

Homework 8:

A) Section 16.1 - 19, 20, 21, 22

B) Section 16.2 - 1, 3, 8, 10

C) Section 16.2 - 13, 14, 16, 22

Homework 9: Due Wednesday April 11th

A) Section 16.3 questions 3,  5,  8, 9, 12

B) Section 16.3 questions 16,  23

C) Section 16.4 questions 10, 15

D) (Not in textbook)

a) Find all residues for f =  1/sinz
b) Find the integral of f around any circle centered at 0 (where the radius is not equal to a multiple of pi).
c) [not for credit] Can you write down a simple formula for the integral of f around any closed curve?

Homework 10: Final homework due MONDAY 23rd APRIL

A) section 17.1 questions 4, 22, 24, 26

B) section 17.3 questions 10 and 13

C) Suppose the boundary of a body of homogeneous material is two coaxial cylinders of radii 1m and 2m respectively. Suppose the 'inner cylinder' is kept at a constant temperature of zero degrees centigrade, and the 'outer cylinder' is kept at a constant temparature of 400 degrees centigrade and that the temperature distribution has reached equilibrium. What is the temperature distribution? Sketch some isotherms and heat flow lines on a cross-section of the cylinder.

D) section 16.4 questions 16 and 17