Exercises in Analysis A I

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.C202

Number of credits

020

Course offered

2024

Offered quarter

1-2Q

Syllabus updated

Mar 17, 2025

Language

Japanese

Syllabus

Course overview and goals

This course is a complementary recitation for "Advanced Calculus I (ZUA.C201)". 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:
-- Understand the construction of irrational numbers
-- Be familiar with limits superior and limits inferior
-- Be able to state and prove propositions about limits of sequences and functions by using "epsilons and deltas".
-- Understand some important properties of continuous functions, such as the intermediate value theorem, and the existence of the maximum/minimum.
-- Be able to calculate polynomial approximations of a given function by using the Taylor expansion or asymptotic expansion.
-- Understand the difference between pointwise and uniform convergences
-- Be familiar with calculus of power series in the disk of convergence
-- Understand the differentiability of multivariable functions as linear approximations
-- Understand the relation between gradient vectors and partial derivatives
-- Be able to calculate partial derivatives of composed functions
-- Understand the principle of the method of Lagrange multiplier

Keywords

Continuity of real numbers, infimum, supremum, limit superior, limit inferior,
Cauchy sequence, continuous function, derivative, Taylor expansion
Uniform convergence, power series, total derivative, partial derivative, Taylor expansion of multivariable functions, inverse function theorem, implicit function theorem, the method of Lagrange multiplier

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

Related courses

• ZUA.C201 ： Advanced Calculus I
• MTH.C201 ： Introduction to Analysis I
• MTH.C202 ： Introduction to Analysis II

Prerequisites

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