Applied Mathematics A1
| Numbering Code |
U-ENG29 22050 LJ55 U-ENG29 22050 LJ10 |
Year/Term | 2022 ・ Second semester |
|---|---|---|---|
| Number of Credits | 2 | Course Type | Lecture |
| Target Year | Target Student | ||
| Language | Japanese | Day/Period | Thu.2 |
| Instructor name | SHIBAYAMA MITSURU (Graduate School of Informatics Associate Professor) | ||
| Outline and Purpose of the Course | Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. Students will study the foundation and apply it to compute some integral. | ||
| Course Goals | To understand properties of complex functions with a skill for evaluation of integrals appearing in applied mathematics and physics. | ||
| Schedule and Contents |
1. Complex function 2. Holomorphic functions 3. Elementary functions 4. Integrals in the complex plane 5. Cauchy's integral theorem 6. Power series 7. Taylor series 8. Isolated singularities 9. Laurent series 10. Multivalued functions 11. Analytic continuation 12. Residue 13. Integrals including trigonometric functions 14. Application to improper integral 15. Point at infinity and Riemann sphere |
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| Evaluation Methods and Policy | Evaluation depends mainly on marks of examination, but marks of exercises are taken into account when needed. | ||
| Course Requirements | Calculus, Linear algebra | ||
| Study outside of Class (preparation and review) | Students need to solve exercises. | ||
| References, etc. | Complex Analysis, Lars V. Ahlfors, (McGraw-Hill Education), ISBN:978-0070006577 | ||
| Related URL | |||
