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

• Lecturer: Ovidiu Costin
• Office: Hill Center 214, phone 732 445 2472;     E-mail
• Office Hours: Tuesdays 7:40PM, Hill Center 214.
• Textbook:  Michael D. Greenberg, Advanced Engineering Mathematics, 2nd ed;
•                      Francis B. Hildebrand, Methods of Applied Mathematics, 2nd ed

## Approximate Syllabus

(AEM) is Textbook 1
(MAM) is Textbook 2
 Date Sections fromText and Section(Assigned problem numbers parts) Lecture Topics covered 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.