| Day of | Contents | Sections, 7th ed. | Sections, 8th ed. | |
|---|---|---|---|---|
| 1/29, 1/31 | Complex numbers: definition and basic properties. Complex conjugetes. Modulus and argument of a complex number. Algebraic, polar and exponential form of a complex number. Triangle inequality. De Moivre's formula. Roots of complex numbers. | 1-9 | 1-10 | |
| 2/5, 2/7 | Regions in the complex plane. Functions of a comlex variable. Mappings (graphical presentations of functions). Linear function w=Az+B, power function w=zn, exponential function w=ez. | 10-13, 83-85 | 11-14, 84-86 | |
| 2/12, 2/14 | Limit of a function. Properties of limit. Limits involving infinity. Continuity. | 14-17 | 15-18 | |
| 2/19, 2/21 | Derivative. Differentiation rules. Cauchy-Riemann equations. Sufficient conditions for differentiability. Cauchy-Riemann equations in polar coordinates. Analytic functions and their elementary properties. | 18-24 | 19-25 | |
| 2/26, 2/28 | Logarithmic function w=log z. Branches of logariths. Mulpiple-valued functions. Complex exponents. Trigonometric functions. Review for Midterm I. | 28-33 | 29-34 | |
| 3/4 | Midterm I. | |||
| 3/6 | Complex-valued functions of a real variable. Definite integrals of such functions. | 36-37 | 37-38 | |
| 3/11, 3/13 | Contours and contour integrals. | 38-41 | 39-43 | |
| 3/17-3/22 | Spring Recess | |||
| 3/25, 3/27 | Antiderivatives. Cauchy-Goursat theorem. Simply and multiply connected domains. | 42-44, 46 | 44-46, 48-49 | |
| 3/25, 3/27 | Cauchy integral formula. Derivatives of analytic functions. Liouville's theorem and Fundamental theorem of algebra. | 47-49 | 50-53 | |
| 4/1, 4/3 | Maximum modulus principle. Sequences and series. Convergence. Taylor series. | 50-54 | 54-59 | |
| 4/8 | Review for Midterm II. | |||
| 4/10 | Midterm II, solutions. | |||
| 4/15, 4/17 | Laurent series. Absolute and uniform convergence of power series. Residues. Cauchy's residue theorem. | 55-57, 62-64 | 60-63, 68-67 | |
| 4/22, 4/24 | Three types of isolated singular points: poles, removable singularities and essential singularities. Residues at poles. Zeros and poles of an analitic function. Behavior near isolated singular points. | 65-70 | 72-77 | |
| 4/29, 5/1 | Improper integrals. Indented paths. | 71-73, 75, 78 | 78-80, 82, 85 | |
| 5/6, 5/8 | Review for the Final exam. | |||
| 5/15 | Final exam | |||