TOKYO INSTITUTE OF TECHNOLOGY

Course description and aims

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.

Student learning outcomes

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 that will be developed

Class flow

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

Course schedule/Required learning

Textbook(s)

None required

Reference books, course materials, etc.

None required

Assessment criteria and methods

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 (i.e., required knowledge, skills, courses, etc.)

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)