Homepage for 642:528, Methods  Applied Math II Spring 2004
Final exam Friday May 7 12:45 -3:45 PM, Hill 525
                                                                                                                                   
                                                       
Final exam: sample problems

                                                                         
Second midterm: exam and solutions

First midterm: Problems and solutions

General Course Information



  Approximate Syllabus

(AEM) is Textbook 1
(MAM) is Textbook 2
 

Lecture Date Topics covered Sections fromText and Section(Assigned problem numbers parts)
1 01-20 Discussion of complex plane, algebra of complex numbers, functions of a complex variable
21.1-21.2(6,9,11ab) (AEM)
2 01-22
Elementary functions. Polar form of complex numbers
21.3 (7,8)-21.4 (1,2,3,4,5)
3 01-27
More on elementary functions. Multivaluedness and branch cuts. 21.3 (12,13,16abc)   21.4 (11)
4 01-29
More on branch cuts. Regions. Differentiability. C-R equations.
21.5   21.3(18d );   21.4 (11)
5 02-03 More on C-R equations. Analyticity.
21.5(2,5ab)
6 02-05
Analyticity (cont).
21.5(9,10abc,11ab,13)
7 02-10 Introduction to conformal mapping.
22.1-22.2   21.5(10fg,15ad)
8 02-12 Conformal mapping (cont). Bilinear transformations. 22.3   22.2(1,4,5)
9 02-17 Bilinear transformations (cont). Separation of variables. Laplace's equation. Polar coordinates. 22.4-22.6   22.3(10ac,12,14)
10 02-19 Multivalued function, applications. Dirichlet, Neumann boundary conditions. Applications. 22.4(4a) 22.5(3b) 22.6(2a)
11 02-24 More discussions

12 02-26 Review for exam 1.

13 03-02
Exam 1.
Through 22.3 (AEM)
14 03-04
Brief discussion of exam. Introduction to complex integration. Cauchy's theorem.  23.1-23.3  23.2-(3dg) 23.3(4ag,9b)
15 03-09 Fundamental theorem of complex integral calculus. Cauchy's integral formula. 23.4-23.5  23.4(3d) 23.5(1ae,2,4a)
16 03-11 Generalized Cauchy integral formula. Complex power series. Taylor series.
24.1-24.2 24.2(5acfh, 6aceh) 23.5(1ae,2,4a)
17 03-23  Complex Taylor series (cont). Laurent series.
24.3  24.2(8ac, 9ab,10,11be,13a,16acdg)
18 03-25 Taylor and Laurent series (cont).
24.3(4adeh,5ae,6)
19 03-30
Classification of singularities of functions of a complex variable. Residue theorem
24.4-24.5 24.4(2acde,3adg,5acd) 24.5(1a)
20 04-01 More discussions

21 04-06 Applications of residue theorem.
24.5(1d,2d,3j,5c,6b)
22 04-08 Residue theorem and applications (cont). Review for secon exam

23 04-13 Second midterm.
Through 24.3 (AEM)
24 04-15 Brief discussion of exam 2. Introduction to calculus of variations. Lagrange multipliers.
2.2  (MAM) (Ch2, p195 :8,9)
25 04-20 Stationary functions. Euler's equation.
2.2-2.3 Ch2, p195-6 :10,15)
26 04-22 Variational notation. Constraints and  Lagrange multipliers.
2.4-2.9
27 04-27 Hamilton's prnciple. Lagrange's equations
2.10-2.11
28 04-29 Final review.