Applied Mathematics for Engineers Ib

Academic unit or major

Undergraduate major in Mathematics

Instructor(s)

Takashi Takiguchi

Class Format

Lecture (Face-to-face)

Media-enhanced courses

-

Day of week/Period
(Classrooms)

3-4 Tue

Class

-

Course Code

MTH.U212

Number of credits

100

Course offered

2024

Offered quarter

2Q

Syllabus updated

Mar 17, 2025

Language

Japanese

Syllabus

Course overview and goals

Based on [Applied Mathematics for Engineers Ia] in the first quarter, this course focuses on basic part of complex analysis. First, we explain Cauchy's integral theorem and Cauchy's integral formula after reviewing complex line integrals. Then, we explain the Laurent expansion of meromorphic functions after classifying isolated singularities of complex functions. Finally, we explain the residue theorem and its application to the calculation of definite integrals.

Complex analysis is an absolutely essential mathematical basis of science and engineering. The aim of this lecture is to explain the basic theory and practical way to use of complex analysis by an efficient way.

Course description and aims

・Students are expected to understand Cauchy's integral theorem.
・Students are expected to be familiar with the classificationof isolated singularities of complex functions.
・Students are expected to be able to calculate the Laurent expansion of basic complex functions.
・Students are expected to be able to apply the residue theorem to the calculation of definit integrals.

Keywords

Cauchy's integral theorem, isolated singularities, the Laurent expansion, meromorphic functions, the residue theorem

Competencies

• Specialist skills
• Intercultural skills
• Communication skills
• Critical thinking skills
• Practical and/or problem-solving skills

Class flow

Standard lecture course mixed with recitation.

Course schedule/Objectives

Study advice (preparation and review)

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

H. Shiga, Theory of complex functions to learn in 15 weeks (Japanese), Sugakushobo, 2008

Reference books, course materials, etc.

None in particular

Evaluation methods and criteria

Based on overall evaluation of the results for quizzes, report and final examination. Details will be announced during a lecture.

Related courses

• MTH.U211 ： Applied Mathematics for Engineers Ia
• MTH.U213 ： Applied Mathematics for Engineers Iia
• MTH.U214 ： Applied Mathematics for Engineers Iib

Prerequisites

The prerequisite to take this course is that you have acquired the credits of "Applied Mathematics for Engineers Ia".
Without having acquired the credits of the above course, the credits of this course will not be counted as the necessary number of credits for graduation.

Students are expected to have completed [Calculus I / Recitation], [Calculus II]and [Calculus Recitation II] .
In particular, students are expected to understand partial differentiation, definite integral and multiple integral clearly.