The main subject of this course is basic concepts of complex analysis and Fourier series. After introducing such basic facts, we explain some typical examples of Fourier series. This course will be followed by Applied Analysis II.
Complex analysis is one of the fundamental tools in mathematics, and is applicable to a wide variety of objects. On the other hand, it is not easy to comprehend without suitable training. To that end, rigorous proofs will be given for most propositions, lemmas and theorems. Moreover, we study typical examples of complex series.
Students are expected to study basic concepts of complex analysis. More precisely, we study Fourier series, Fourier transform, these definitions, properties and method of these calculations. These have important roles in science and technology.
complex number, holomorphic function, Cauchy-Riemann relations, d'Alembert's ratio test, power series, trigonometric series, Fourier series expansion
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
Before coming to class, students should read the course schedule and check what topics will be covered.
Required learning should be completed outside of the classroom for preparation and review purposes.
|Course schedule||Required learning|
|Class 1||Introductory to Complex Analysis, Four arithmetic operations, complex plane, Euler's formula||Details will be provided during each class session|
|Class 2||Power series, trigonometric series||Details will be provided during each class session|
|Class 3||Fourier series expansion||Details will be provided during each class session|
|Class 4||Convergence, Gibbs phenomenon||Details will be provided during each class session|
|Class 5||sine and cosine series expansions||Details will be provided during each class session|
|Class 6||Fourier series expansion of complex form||Details will be provided during each class session|
|Class 7||Fourier series on general interval||Details will be provided during each class session|
|Class 8||Fourier series of multi-variable function, comprehension check-up||Details will be provided during each class session|
to be determined
Students' course scores are based on final exam 50% and midterm exam 50%.
Students are expected to have passed Calculus I/Recitation and Calculus II+ Recitation.