COURSE SYLLABUS Course Number: MATH6030 Course Title: COMPLEX VARIABLES WITH APPLICATIONS I Credit Hours: 3 Prerequisites: MATH 2650 Corequisite: Objectives: The course will introduce students to the fundamental concepts and techniques of Complex Variables. Major goals will be to develop the student's understanding of the theory of Complex Variables and the corresponding ability to apply the theory to solve problems arising in the physical sciences and engineering. Schedule and Outline of Course Content. (Individual instructors may re-arrange the material and use different headings.) Complex Numbers (2 weeks) Polar form, complex exponentials, powers and roots, planar sets, applications to mechanics. Analytic Functions (3 weeks) Functions of a complex variable, limits and continuity, analyticity, the Cauchy Riemann Equations, harmonic functions and steady state temperatures. Elementary Functions (2 weeks) Exponential, trigonometric, and hyperbolic functions. The complex logarithm, complex powers and inverse trigonometric functions. Applications to oscillating systems. Complex Integration (4 weeks) Contours and contour integrals. Independence of the path and the Cauchy Integral Theorem. The Cauchy Integral formula and its consequences. Bounds for analytic functions. Applications to harmonic functions. Series Representations for Analytic Functions (4 weeks) Taylor series and power series. Theory of convergence. Laurent series, zeros and singularities. The point at infinity. Analytic continuation Possible Textbook: Fundamentals of Complex Analysis for Mathematics, Science, and Engineering, second edition, Saff, E. B. and Snider, A. D.(1993); Other texts may be used by individual instructors. II. Grading and Evaluation Procedures: Typically tests, and quizzes, with other methods employed at the discretion of the instructor. III. Policies related to the conduct of the class are set by individual instructors.