MATH 441/541

Applied Mathematics II

Spring 2009

* Monday, Wednesday, Friday 2:10-3:00 Troy 201 *

Applied Mathematics II

Spring 2009

**Required book:** E. Kreyszig,
*Advanced Engineering Mathematics. 9th Ed.*

**Course outline:**

1. Complex numbers and functions

(a) Complex numbers

(2) Analytic functions

(3) Elementary functions in the complex plane

(4) Cauchy-Riemann equations

2. Complex intergration

(a) Line intergral in the complex plane

(b) Cauchy's integral theorem

(c) Derivatives of complex functions

3. Series

(a) Convergence of sequences and series

(b) Taylor series and Laurent expansions

(c) Residue theorem

4. Conformal mapping

5. Potential theory

* Homework assignments - 40%

* Final exam - 60%

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FINAL EXAM

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1. Homework #1: p.606 #6,10,14, 18 Due Jan.21

2. Homework #2: p.618 #16, 18, 22, 24; p.623 #6,8,10 Due Jan. 21

3. Homework #3: p.623 #18, 20, 23; p.626 #12,16,18 Due Jan. 28

4. Homework #4 p.645 #22, 26; prove example 4 on p.647; Due Feb. 2

5. Homework #5 p.657 #8,10,12. Assigned Feb 2; due Feb.9

6. Homework #6 p.661 #2,4. Assigned Feb 4; due Feb.9

7. Homework #7. p672 #4,6. Assigned Feb.6; due Feb.9

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Week of Feb.9

Feb. 9. HW #8: p.672 #16,18; due Feb.18

Feb.11: no hw

Feb.13. HW #9: Consider Example.3 on p.731 (Joukowski airfoil) and write the code in Matlab (or any other package) to draw the Joukowski airfoil profile as in Fig.381 on p.732.

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Week of Feb.16

Feb. 16. No class

Feb. 18.HW #10 p.737 #6, 10, 12

Feb. 20.HW #11 p.741 # 10,12

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Week of Feb.23

Feb. 23. No class

Feb. 25. HW #12 p.745 #10,18

Feb. 27. No class

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Week of March 2

March 2. HW #13 p.753 #2,4,6; Due March 9

March 4. No HW

March 6. HW #14 p.760 #2,4

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Week of March 9

March 9. No HW

March 11. HW #15 p.771 #4

March 13. HW #16 p.774 #2,6

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Week of March 23

March 23. NO HW

March 25. HW #17 p. 943 #11,12

March 27. HW #18 p. 946 #1

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Week of March 30

March 30. NO HW

April 1. HW #19 p. 844 #4,10

April 3. No HW

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Week of April 6

April 6. NO HW

April 8. NO HW

April 10. NO HW

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Week of April 13

April 13. HW #20 HW

April 15. NO HW

April 17. NO HW

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