Exercises in Analysis A II

Academic unit or major

Mathematics

Instructor(s)

Yoshiyuki Kagei / Shinya Kinoshita

Class Format

Exercise (Face-to-face)

Media-enhanced courses

-

Day of week/Period
(Classrooms)

5-8 Mon

Class

-

Course Code

ZUA.C204

Number of credits

020

Course offered

2024

Offered quarter

3-4Q

Syllabus updated

Mar 17, 2025

Language

Japanese

Syllabus

Course overview and goals

This course is a complementary recitation for "Advanced Calculus I (ZUA.C203)".
We will have problem solving sessions about the materials taught in that course.

Course description and aims

At the end of this course, students are expected to:
-- be able to calculate inner and outer products
-- be able to calculate line integrals of vector fields along curves
-- be familiar with parametrization of curves and surfaces
-- understand the meaning of gradient, divergence, and rotation, and be able to calculate them
-- understand what Green's theorem means and know how to use it
-- understand the tangent vectors and tangent space of surfaces
-- be able to calculate surface integrals of vector fields
-- understand the meaning of divergence theorem and Stokes' theorem
-- be able to calculate differential forms

Keywords

Outer product, vector fields, line integral, gradient, divergence, rotation, Green's theorem on the plane
tangent vector, surface integral, divergence theorem, Stokes theorem,
differential forms, exterior derivative

Competencies

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

Class flow

This course provides recitation sessions for "Advanced Calculus II". There will be occasional quizzes.

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)

None required

Reference books, course materials, etc.

None required

Evaluation methods and criteria

Based on the problem solving situation in the recitation sessions. Details will be provided in the class.

Related courses

• ZUA.C203 ： Advanced Calculus II
• MTH.C203 ： Introduction to Analysis III
• MTH.C204 ： Introduction to Analysis IV
• ZUA.C204 ： Exercises in Analysis A II

Prerequisites

Students are expected to have passed
-- Calculus (I/II), Linear Algebra (I/II), and their recitations.
-- Advanced Calculus I. and Exercises in Analysis A II
It is strongly recommended to take Advanced Calculus(ZUA.C202)