| Syllabus |
Vanderbilt Math Club |
Putnam Competition |
LaTeX |
| Date | Material covered | HW problems and assignments | Remarks |
| January 9 | Preliminaries | S: I.2.3, I.11.4, I.13.1.
SS: 1.1.7, 1.1.8, 1.1.16, 1.1.21, 1.2.5, 1.2.10, 1.2.17, 1.3.7, 1.5.5. |
Due January 16th |
| January 11 |
Polar form
De Moivre's formula Stereographic projection |
S: II.6.1, II.6.3, II.8.1.
SS:2.1.3, 2.1.7, 2.1.8, 2.1.9, 2.1.10, 2.3.10, 2.3.14, 2.3.15. |
Due January 23rd |
| January 16 |
Differentiation
Cauchy-Riemann Equations |
||
| January 18 |
Holomorphic functions
Harmonic functions |
||
| January 23 |
Exponentiation
Hyperbolic functions |
||
| January 25 |
Logarithms
Inverses of holomorphic functions |
||
| January 30 | Power series | ||
| February 1 | Radius of convergence | ||
| February 6 | The Cauchy-Hadamard theorem | S: IV.5.1, IV.8.3, IV.13.4.
SS: 2.5.3, 2.5.6, 3.1.3, 3.1.9, 3.2.5, 3.2.17, 3.2.18, 3.3.1, 3.3.4, 3.5.1, 3.5.11. |
Due February 13th |
| February 8 | Differentiation of power series | ||
| February 13 | Exam | ||
| February 15 | Linear fractional transformations | S: V.7.1, V.7.2, V.12.3, V.16.2, III.5.1, III.6.1, III.6.3.
SS: 5.1.7, 5.1.9, 5.3.3, 7.3.2, 7.3.7. |
Due February 22nd |
| February 20 | Linear fractional transformations II | ||
| February 22 |
Complex integration
Fundamental theorems of calculus |
||
| February 27 | Cauchy's theorem | S: III.9.1, III.9.4, VI.7.2, VI.8.2.
SS:7.4.1, 7.4.7, 4.1.7, 4.2.6, 4.2.14, 4.3.7. |
Due March 13th |
| March 1 | Cauchy integrals I | ||
| March 13 | Cauchy integrals II | ||
| March 15 |
Liouville's theorem
Fundamental theorem of algebra |
S: VI.8.2, VI.12.1, VII.4.2, VII.5.1, VII.7.1, VII.8.3.
SS:4.4.16, 4.5.3, 4.5.8. |
Due March 22nd |
| March 20 | Exam | ||
| March 22 |
Zeros of holomorphic functions
Maximum modulus principle |
S: VII.8.2, VII.11.1, VII.13.1, VII.14.1, VII.16.1, VII.17.1.
SS: 4.6.5, 4.6.17, 4.6.19. |
Due March 29th |
| March 27 | Laurent series | ||
| March 29 |
Isolated singularities
Residues |
||
| April 3 | Cauchy's theorem III | ||
| April 5 |
Runge's approximation theorem
The residue theorem |
||
| April 10 | Examples | ||
| April 12 | Exam | ||
| April 17 | Examples | ||
| April 19 | Review | S: VIII.2.1, VIII.4.1, VIII.7.2, VIII.7.3, VIII.7.5, VIII.8.3, VIII.12.2, IX.5.3, X.8.1, X.8.2, X.8.3, X.10.2, X.10.3 | |
| Thursday, May 3: 3:00pm | Final Exam |