Course Information
| Instructor | Dr. Changhui Tan |
| Lectures | T Th 2:50pm - 4:05pm, at LeConte 315 |
| Office | LeConte 427 |
| Office Hours | T 11:30am - 12:30pm, or by appointment |
| Textbooks | R.H. Dyer and D.E. Edmunds, From Real to Complex Analysis, Springer International Publishing, 2014. (ISBN: 978-3-319-06208-2) |
| A. Schep, Complex Script, lecture notes. | |
| Syllabus | Click Here |
Course Description
- The official course description for the MATH 703/704 sequence:
- Compactness, completeness, continuous functions. Outer measures, measurable sets, extension theorem and Lebesgue-Stieltjes measure. Integration and convergence theorems. Product measures and Fubini’s theorem. Differentiation theory. Theorems of Egorov and Lusin. \(L^p\) spaces. Analytic functions: Cauchy-Riemann equations, elementary special functions. Conformal mappings. Cauchy’s integral theorem and formula. Classification of singularities, Laurent series, the Argument Principle. Residue theorem, evaluation of integrals and series.
- List of Topics (for MATH 703):
- Metric Spaces:
- Metric spaces, continuous functions.
- Separability, completeness.
- Compactness, the Heine-Borel theorem.
- Connectedness. - Complex Analysis:
- Analytic functions: complex derivatives and Cauchy-Riemann equations, analyticity.
- Special functions: \(\log\left( z\right)\), \(e^z\), trigonometric functions.
- Line integrals, Cauchy's theorem and its consequences: Cauchy integral formula, maximum modulus, power series, Fundamental Theorem of Algebra.
- Classification of zeros and singularities, Laurent series.
- Residue theorem, evaluation of integrals and series.
- Metric Spaces:
Homework Assignments
- Homework assignments will be assigned and collected each week. The tentative due date is on Tuesday in class.
- The homework is not pledged. You are encouraged to discuss the problems. However, each student is responsible for the final preparation of his/her own homework papers.
- Last update: 12/9, Homework 8 is available.
Download Homework Assignments.
Exams
- There will be two 75 minutes in-class midterm exams. The tentative dates are October 3rd and November 14th. There will be a 150 minutes cumulative final exam.
- Exams are under the honor code. Be sure and hand in all the work you do on each problem. Good luck!
- Last update: 11/22, midterm 2 is available.
- Download the Exams.
Grades
- Your grade are distributed as below:
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Homework » 30% Midterms » 20% each Final exam » 30% - You can monitor your grades via Blackboard.
Contact Information
- Contact me at This email address is being protected from spambots. You need JavaScript enabled to view it. if you have any questions.