Here you will find information concerning the *Applied Complex
Variables (3160-1)* class (also known as *Complex Variables for
Engineers*) for the *Fall 2002 Semester*, which meets on
Tuesdays and Thursdays 9:40-10:30 am in OSH 131.

If you have any doubts, problems, concerns, etc., feel free to send a message to the instructor.

**Grades**will be available on Tuesday 17. I will be in my office on Tuesday and Wednesday (preferably during the morning), but after Wednesday I will be gone till the first week of the Spring Semester.

**12/5:**Test 3 was given.**12/3:**Fractional linear transformation and harmonic functions. Sections 70, 82 and 89.**11/26:**Conformal maps and inverse function theorem. Sections 79 and 80.**11/21:**Proper integrals involving sines and cosines. Indented contours. Sections 62 and 63. This concludes the material for Test 3.**11/19:**Improper integrals involving sines and cosines. Section 61.**11/14:**Improper integrals. First examples. Section 60.**11/12:**Residues at poles. Zeroes. Identity principle. Sections 57 and 58.**11/7:**Classification of isolated singularities and residues at poles. Sections 55 and 56.**11/5:**Comments about Test 2. Residue/Integral computations. Section 54.**10/31:**Test 2 was given.**10/29:**Reviewed some material for Test 2. Introduced the notion of residue. Section 53.**10/24:**More properties of series and examples. Sections 50 and 51. This completes the material for Test 2.**10/22:**More examples of Laurent series expansions. Properties of power series. Sections 47 to 49.**10/17:**Taylor and Laurent series. Examples. Sections 43 to 46.**10/15:**More on Cauchy's integral formula. Liouville's Theorem and the maximum modulus. Sections 39 to 42. Test 2 was announced.**10/10:**Cauchy's theorem and formula. Applications. Sections 38 and 39.**10/8:**More examples. Antiderivatives and Cauchy's theorem. Sections 34 to 36.**10/1:**Contours and contour integrals. Examples. Sections 31 to 33.**9/26:**Defined and studied power, exponential, inverse trig and hyperbolic functions. Also, introduced the integral of complex valued functions. Sections 28 to 30.**9/24:**Test 1 was discussed. Then we discussed logarithms. Sections 26 and 27.**9/19:**Test 1 was given.**9/17:**Exponential, trigonometric and hyperbolic functions. Sections 23 to 25.**9/12:**Cauchy-Riemann equations in polar coordinates. Analytic functions. Harmonic functions. Sections 19, 20 and 22.**9/10:**Properties of the (complex) derivative. Cauchy-Riemann equations. Sections 16 to 18.**9/5:**Infinity and related limits. Continuity and complex derivative. Sections 13 to 15. Also, Test 1 was announced.**9/3:**Complex valued functions. Graphics. Limits. Sections 9 to 12.**8/29:**Complex roots. Topological notions in the plane. Sections 7 and 8. We decided to have the problem session on Wednesdays at 5PM.**8/27:**Division. Modulus and argument. Exponential form, products and powers. Sections 4 to 6.**8/22:**Introduction to complex numbers. Sum, difference, multiplication, absolute value, and conjugation. Representation as vectors in the plane. Sections 1 to 3.

**Rules:** all exercises posted in this section are for your
use. None of them will be graded but they are considered required
practice for the exams. Make sure that when you solve the exercises
your solution is clear and complete.

**Chapter 9:***page 289:*1, 2, 3, 6;*page 258 (this is chapter 8!):*1, 3;*page 313:*2, 3, 4.**Chapter 7:***page 208:*1, 2, 4, 6, 8;*page 214:*1, 2, 4, 9, 11;*page 218:*1, 2, 3;*page 226:*1.**Chapter 6:***page 189:*1, 2, 3, 4, 5, 6;*page 197:*1, 3a, 4, 5, 7.**Chapter 5:***page 142:*4,7;*page 149:*2, 3, 5, 6, 10a, 10b;*page 156:*1, 3, 4, 6;*page 172:*1, 2, 5, 7, 10.**Chapter 4:***page 92:*1, 2, 3, 6;*page 102:*1, 2, 3, 5, 6, 13 a and b;*page 119:*1, 2, 4, 5, 7, 8;*page 129:*1, 2, 3, 4, 9;*page 136:*1, 2.**Chapter 3:***page 67:*1, 3, 4, 7, 8b, 12;*page 71:*2, 5, 6, 14a;*page 74:*7, 13;*page 79:*1, 2, 4, 6, 9;*page 84:*1, 2, 6, 9, 13.**Chapter 2:***page 31:*1, 4, 13, 14;*page 42:*1(e), 2, 4, 9, 12;*page 47:*1, 2, 4, 8;*page 54:*1, 2, 3, 10;*page 62:*1, 3, 4, 10.**Chapter 1:***page 5:*1,3;*page 11:*1, 4, 10, 14;*page 17:*1, 4, 13;*page 22:*2, 5, 6, 7;*page 25:*1, 2, 3, 10.

Below you will find different references on the course (syllabus, etc.).

- Some "recommended" exercises to help you prepare for Test 1. (also in PDF and PS formats). Solution (also in PDF and PS formats).
- The syllabus (also in PDF and PS formats). Here you will find the "ultimate" guidelines for the course, textbook, schedule, final exam, etc.
- Short questionnaire (also in PDF and PS formats) that you should print out, complete and return to the instructor.

- Official academic calendar, Fall 2002.
- Student Handbook.
- General Catalog.
- Campus map and building locator.
- University of Utah homepage.
- Mathematics undergraduate colloquium.