Advanced Calculus II

Academic unit or major

Mathematics

Instructor(s)

Yoshiyuki Kagei

Class Format

Lecture (Face-to-face)

Media-enhanced courses

-

Day of week/Period
(Classrooms)

3-4 Mon

Class

-

Course Code

ZUA.C203

Number of credits

200

Course offered

2024

Offered quarter

3-4Q

Syllabus updated

Mar 17, 2025

Language

Japanese

Syllabus

Course overview and goals

In this course we will teach "vector calculus", that is a calculus for scalar fields (single-valued functions) and vector fields (multivalued functions) . Each lecture will be followed by a recitation (a problem-solving session).
The students will learn basic operations of vector fields, such as "divergence" or "rotation". They will also learn "Green's theorem", "divergence theorem" and "Stokes' theorem".

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 is a standard lecture course with recitation sessions. Homework will be assigned every week. 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 final exam and quizzes. Details will be provided in the class.

Related courses

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

Prerequisites

Students are expected to have passed
-- Calculus (I/II), Linear Algebra (I/II), and their recitations.
-- Introduction to Analysis I/II.