2024 Faculty Courses School of Computing Undergraduate major in Mathematical and Computing Science

Applied Calculus

Academic unit or major: Undergraduate major in Mathematical and Computing Science
Instructor(s): Zin Arai / Shinya Nishibata / Masaaki Umehara / Toshiaki Murofushi / Sakie Suzuki / Shunsuke Tsuchioka
Class Format: Lecture (Face-to-face)
Media-enhanced courses: -
Day of week/Period (Classrooms): 3-4 Tue / 3-4 Fri
Class: -
Course Code: MCS.T211
Number of credits: 200
Course offered: 2024
Offered quarter: 2Q
Syllabus updated: Mar 17, 2025
Language: Japanese

Syllabus

Course overview and goals

We first review the basic concepts in calculus using rigorous arguments such as the epsilon-delta method. Then, we study the basic treatment of series and sequences of functions. The latter part of the lecture covers advanced topics such as differential equations, curves, surfaces, and the fundamentals of vector analysis.

Course description and aims

This lecture aims to clearly understand concepts such as limits and continuity through rigorous epsilon-delta arguments. The lecture also aims to cultivate analytical thinking and computational skills for applying mathematics to real-world problems by studying differential equations and vector analysis.

Keywords

epsilon-delta method, termwise integration, differential equations, vector analysis, integral theorems

Competencies

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

Class flow

The lectures provide the fundamentals of calculus.

Course schedule/Objectives

	Course schedule	Objectives
Class 1	Epsilon delta definition of convergence	Understand the contents covered by the lecture.
Class 2	Continuity of real number	Understand the contents covered by the lecture.
Class 3	Continuity of function	Understand the contents covered by the lecture.
Class 4	Uniform continuity of function	Understand the contents covered by the lecture.
Class 5	Convergence of series	Understand the contents covered by the lecture.
Class 6	Convergence of function series	Understand the contents covered by the lecture.
Class 7	Differentiation and integration of function series	Understand the contents covered by the lecture.
Class 8	General solution and particular solution of differential equation	Understand the contents covered by the lecture.
Class 9	Separation of variables type equation	Understand the contents covered by the lecture.
Class 10	First order linear differential equation	Understand the contents covered by the lecture.
Class 11	Second-order linear differential equation	Understand the contents covered by the lecture.
Class 12	Curves	Understand the contents covered by the lecture.
Class 13	Surfaces	Understand the contents covered by the lecture.
Class 14	Line integral and surface integral	Understand the contents covered by the lecture.
Class 15	Integral theorem	Understand the contents covered by the lecture.

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 afterward (including assignments) for each class.

Textbook(s)

Undecided.

Reference books, course materials, etc.

Not specified in particular.

Evaluation methods and criteria

By scores of examinations and reports.

Related courses

LAS.M101 ： Calculus I / Recitation

Prerequisites

None.