<MATH 446>

MATH 446


Course Information

Syllabus

Office hours (may change): W, 11-11:50 am

HW Assignments:

HW 1 (due Friday, January 31st):
p.5 Exercises 1b, 11; p.12 Ex.4, 5c; p.15 Ex.14; p.23 Ex.6, 9; p.30 Ex.3a, 7.

HW 2 (due Friday, February 7th):
p.33 Ex.4, 5, 7a,b,c; p.37 Ex.1ab; 3; p.44 Ex.2, 3b, 7.

EXAM 1 (Monday, February 10th, in class)
Covers Ch.1, Ch.2 up to (and including) the section on Mappings by the Exponential Function.
You are allowed to bring and use during the exam one standard (letter size) sheet of paper with anything written on it (front and back OK). No textbooks, calculators,... are allowed.

HW 3 (due Friday, February 14th):
p.55 Ex.5, 7, 10c; p.62 Ex.4, 8a; p.71 Ex.3b,c, 5, 8.

HW 4 (due Friday, February 21st):
p.77 (Sections 24, 25, Analytic functions, Examples) Ex.1c, 2c, 6, 7; p.81 (Section 26, Harmonic functions) Ex.2, 7; p.87 (Sections 27, 28, Uniquely determined analytic functions, Reflection principle) Ex.2, 5.

HW 5 (due Friday, February 28th):
p.92 (Section 29, The exponential function) Ex.7; p.97 (Sections 30, 31, The logarithmic function, branches and derivatives of logarithms) Ex.5, 8; p.100 (Section 32, Some identities involving logarithms) Ex.6; p.104 (Section 33, Complex exponent) Ex.3; p.108 (Section 34, Trigonometric functions) Ex.12a; p.111 (Section 35, Hyperbolic functions) Ex.6a; p.114 (Section 36, Inverse trigonometric and hyperbolic functions) Ex.2.

HW 6 (due Friday, March 7th):
p.121 (Sections 37, 38, Derivatives of functions, definite integrals of functions) Ex.1b, 2b,c, 4; p.125 (Section 39, Contours) Ex.6; p.135 (Sections 40, 41, 42, Contour integrals, examples) Ex.2, 4, 6; p.140 (Section 43, Upper bounds for moduli of contour integrals) Ex.2, 4.

EXAM 2 (Monday, March 10th, in class)
Covers Ch.2 starting from the section on Limits, Ch.3, Ch.4 up to (and including) the section on Upper Bounds for Moduli of Contour Integrals.
You are allowed to bring and use during the exam one standard (letter size) sheet of paper with anything written on it (front and back OK). No textbooks, calculators,... are allowed.

HW 7 (due Friday, March 14th):
p.149 (Sections 44, 45, Antiderivatives, proof of the theorem) Ex.2b, 5; p.160 (Sections 46, 47, 48, 49, Cauchy-Goursat Theorem, proof, simply and multiply connected domains) Ex.1a,e,f, 2a,b, 4, 6.

HW 8 (due Friday, March 21st):
p.170 (Sections 50, 51, 52, Cauchy integral formula, an extension, consequences) Ex.3, 4, 7, 10; p.178 (Sections 53, 54, Liouville's theorem and the fundamantal theorem of algebra, maximum modulus principle) Ex.1, 3, 4, 5, 8.

HW 9 (due Friday, April 4th):
p.188 (Sections 56, 56, Convergence of sequences, series) Ex.3, 8; p.195 (Sections 57, 58, 59, Taylor series, proof, examples) Ex.2, 8; p.205 (Sections 60, 61, 62, Laurent series, proof, examples) Ex.2, 8; p.219 (Sections 63, 64, 65, 66, Absolute and uniform convergence, continuity, integration and differentiation of power series, uniqueness of series representations) Ex.6, 7; p.225 (Section 67, Multiplication and division of power series) Ex.2, 4.

HW 10 (due Friday, April 11th):
p.239 (Sections 68, 69, 70, 71, Isolated singular points, residues, Cauchy's residue theorem, residue at infinity) Ex.2c,d, 4; p.243 (Section 72, The three rypes of isolated singular points) Ex.2a,b, 4; p.248 (Sections 73, 74, Residues at poles, examples) Ex.2b, 4a, 6c; p.255 (Sections 75, 76, Zeros of analytic functions, zeros and poles) Ex.4b, 5, 8b.

EXAM 3 (Monday, April 14th, in class)
Covers Ch.4 starting from the section on Antiderivatives, Ch.5, Ch.6.
You are allowed to bring and use during the exam one standard (letter size) sheet of paper with anything written on it (front and back OK). No textbooks, calculators,... are allowed.

HW 11 (due Friday, April 18th):
p.267 (Sections 78, 79, Evaluation of improper integrals, example) Ex.2, 4, 6, 8; p.275 (Sections 80, 81, Improper integrals from Fourier analysis, Jordan's lemma) Ex.3, 4, 6, 10; p.286 (Sections 82, 83, 84, Indented paths, an indentetion around a branch point, integration along a branch cut) Ex.4, 6.

HW 12 (due Friday, April 25th):
p.290 (Section 85, Definite integrals involving sines and cosines) Ex.2, 4, 6; p.296 (Sections 86, 87, Argument principle, Rouche's theorem) Ex.2, 5, 8, 9; p.306 (Sections 88, 89, Inverse Laplace transforms, examples) Ex.2, 8, 10.

HW 13 (due Friday, May 2nd):
p.313 (Section 90, Linear transformations) Ex.4; p.317 (Sections 91, 92, The inversion transformation, mappings by the inversion) Ex.4, 13; p.324 (Sections 93, 94, Linear fractional transformations, an implicit form) Ex.2, 8, 12; p.329 (Section 95, Mappings of the upper halfplane) Ex.4; p.334 (Section 96, The sine transformation) Ex.4, 6; p.340 (Section 97, Quadratic and square root mappings) Ex.6; p.346 (Section 98, Square roots of polynomials) Ex.2.

FINAL EXAM (Monday, May 12th, 8:00-11:00 am, in the classroom: 147 AH)
Covers everything covered by Exams 1, 2, 3, and Ch.7, Ch.8 up to (and including) the section on Square Roots of Polynomials, Ch.9.
You are allowed to bring and use during the exam four standard (letter size) sheets of paper with anything written on them (front and back OK). No textbooks, calculators,... are allowed.