Math 43 Spring 2007
Syllabus
This is a tentative syllabus. In all likelihood, one of the textbook chapters on this syllabus will actually be omitted. This page will be updated irregularly.
|
Date |
Sections |
Description |
|
Wednesday March 28 |
Section 1- 7 |
Complex numbers, their properties, conjugation, exponential form, products and quotients in exponential form |
|
Friday March 30 |
Sections 8-12 |
Roots of complex numbers, examples, regions, functions of a complex variable |
|
Monday April 2 |
Sections 13-15 |
Mappings by the exponential function, limits and theorems on them |
|
Tuesday April 3 x-hour |
Sections 16-17 |
Limits involving infinity, continuity |
|
Wednesday April 4 |
Sections 18-19 |
Derivatives and differentiation formulas |
|
Friday April 6 |
Sections 20-22 |
Cauchy-Riemann equations, sufficient conditions for differentiability, polar coordinates |
|
Monday April 9 Tuesday April 10 is the last day to elect the NRO option |
Sections 23-25 |
Analytic and Harmonic functions |
|
Wednesday April 11 |
Sections 26-28 |
Uniquely determined Analytic functions, reflection principle, exponential function |
|
Friday April 13 |
Sections 29-31 |
Logarithm, identities, branches |
|
Monday April 16 |
Sections 32-34 |
Complex exponents, trigonometric functions, hyperbolic functions |
|
Wednesday April 18 |
Sections 36-38 |
Derivatives and integrals of functions w(t), contours |
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Friday April 20 |
Sections 39-41 |
Contour integrals, examples, upper bounds for moduli of contour integrals |
|
Monday April 23 The takehome Midterm Exam will be distributed on this date. It
will be due on Friday April 27 |
Sections 42-43 |
Antiderivatives, examples, |
|
Wednesday April 25 |
Sections 44-45 |
Cauchy-Goursat Theorem |
|
Friday April 27 |
Section 46 |
Simply and multiply connected domains |
|
Monday April 30 |
Section 47 |
Cauchy Integral Formula |
|
Wednesday May 2 |
Section 48-49 |
Derivatives of Analytic functions, Liouville’s Theorem |
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Friday May 4 |
Section 49-50 |
Fundamental Theorem of Algebra, Maximum Modulus Theorem |
|
Monday May 7 |
Sections 51- 52 |
Series and their convergence |
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Wednesday May 9 |
Sections 53-54 |
|
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Friday May 11 |
Sections 55-56 |
Laurent series and examples, |
|
Monday May 14 Tuesday May 15 is the final day to withdraw from the course
|
Sections 57-58 |
Absolute and uniform convergence of series, continuity of sums of power series |
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Wednesday May 16 |
Section 58-59 |
Integrations and differentiation of power series |
|
Friday May 18 |
Section 60 and very briefly 61 |
Uniqueness of series representations, Multiplication and division of power series |
|
Monday May 21 Tuesday May 22 is the final day to alter grade
limit filed under the Non-Recording Option |
Section 62-63 |
Residues, Cauchy Residue Theorem |
|
Wednesday May 23 |
Section 64-65 |
Using a singular residue, the three types of isolated singular points |
|
Friday May 25 |
Section 71-72 |
Evaluation of improper integrals, examples |
|
Monday May 28 Memorial
Day, First day of the pre-examination break, No class |
|
|
|
Wednesday May 30 The last
day of classes. The takehome Final
Exam will be distributed on Friday June 1 and it will be due on Tuesday
June 5, the last day of the Final Examination period. |
Section 73, briefly discuss conformal maps |
Improper integrals from Fourier Analysis, conformal maps |