Meets MTWR 3-5pm at SOC B59
Instructor: Dr. A. Levichev; r.236 at the Dept.of Math.
tel.353-1487, e-mail (which is more reliable): levit@math.bu.edu
Office Hours: M 5-6pm, Thursday 8.30-9.30pm, and by appointment The Final is scheduled for Wed, 8/9, 3pm. There will be DHW-3,4; no more quizzes, we'll only stay in Chapter 4 (though we did discuss conformal properties, and the notion of the Riemann surface of an analytic function).
This is the list of most important sections: 3,5,7,10,15-17,19,22-28,32, 34,36,38-40. Each problem on the Final will be similar to one of the HW,quiz, or example. In the hw4 answers I apologize for the error in # 1: please divide the original answer by sqrt(2). Today, Wed, I'll be in the office at 2.15. I'll leave w4 solutions on the door (as well as your w4 with my comments).
L-18: 40,(100 discussed, 100 won't be tested) HW 40: 1
TWO MORE DHW-4 problems are 38 # 9 and 40 # 9.
L-17: 38,39. HW 38: 2,3,4abcd
L-16: 35,36.
L-15: 33,34 (and 35 started). DHW-3 assigned (R, 8/3 due). HW 33: 1,2,6
L-14: 28,30-32. HW 31: 1,3
L-13: 26,27 covered. HW 27: 1-5,7.
L-12: some of the HW problems (and # 1 from DHW-2) discussed, 26 started.
L-11: 24,25 covered. HW 24: 2,7-9,16,17; 25: 5-8,14.
L-10: Exercises from 22 discussed (orthogonality of level curves), 23 started. HW 23: 1,2,8.
L-9: 20 covered. HW 22:1,3,6,10.
L-8: More examples considered. HW: Sect.20 (reading). Expect DHW-2 on Thursday (tomorrow), Q-2 on Wed (7/26) covers 11,12,14-20,22-25.
L-7: 17(finished), 18,19 discussed. The notion of a Jacobian matrix J of a mapping f (of one surface onto another; not in the text) recalled. When w = f(z) is differentiable, its J has a specific structure (= CR conditions). HW Sect.19, 1-4.
L-6: Sect.14,15,16 covered; 17 (started). (16 is important but it is very similar to the real calculus; 17 is more specific to complex variables; 11,12,14,15 are less important from the pragmatic (testing !) point of view). HW 16: 1,8,9.
L-5: Sect. 10,11,12 covered. The quiz on Mon covers Sections 1-10. HW: 8-8b, 10: 1,2,4,5,7,13.
L-4: Sect.8,9 covered, 10 started; HW 8: 1-5,7,10
L-3: Sect.6,7 covered; HW 6: 1,2,3ab; 7: 1,2,5. The 1st quiz is scheduled for next Mon.
L-2: questions answered, sections 4,5 covered. HW (from sect.4) ## 1,2,10, 14,17,18.
L-1: Sections 1-3 covered. HW (from Sect.2) ## 1-4,12,13. Optional: 5,8,11
Text: Complex Variables and Applications by J. Brown and R. Churchill, 6th edition.
Chapter 1: Complex Numbers (algebraic properties, moduli and conjugates, polar coordinatesand Euler's formula, roots of complex numbers, regions in the complex plane).
Chapter 2: Analytic Functions (functions of a complex variable, mappings, limits, the point at infinity, continuity, derivatives, Cauchy-Riemann equations, polar coordinates, analytic functions, harmonic functions).
Chapter 3: Elementary Functions (the exponential function, trigonometric functions, hyperbolic functions, the logarithmic function and its branches, identities, complex exponents, inverse trigonometric and hyperbolic functions).
Chapter 8: Mapping by Elementary Functions.
Chapter 9: Conformal Mapping.
Chapter 10: Applications of Conformal Mappings.
Other Sections will be included (if time permits)
Homework problems will be assigned on regular basis. Four designated hws will be collected and graded. There will be four quizzes and the Final (on the last day of classes).
Grading Policy: attendance=one unit; quizzes: one unit each; dhws: 1/2 unit each; Final=4 units. The worst of those 11 units will be dropped, the average of the other ten will determine the grade for the class.