INTRODUCTION TO MATHEMATICS 2

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Subtitle	Fundamentals and advances of mathematics for development of economics
Lecturer(s)	MIZUSAWA, ATSUHIKO
Credit(s)	2
Academic Year/Semester	2026 Fall
Day/Period	Thu.2
Campus	Hiyoshi
Class Format	Face-to-face classes (conducted mainly in-person)
Registration Number	74659
Faculty/Graduate School	ECONOMICS
Department/Major	ECONOMICS Type A, B
Year Level	1
Field	FOUNDATION
Grade Type	This item will appear when you log in (Keio ID required).
Course Description	This course prepares students for the in-depth study of economics in their third and fourth years by developing the skills necessary for a deeper understanding of the discipline. Particular emphasis is placed on mathematical and deductive methods.
K-Number	FEC-EC-13173-211-12

Course Administrator	Faculty/Graduate School	FEC	ECONOMICS
Course Administrator	Department/Major	EC	ECONOMICS
Main Course Number	Level	1	First-year level coursework
	Major Classification	3	Foudation Course / Major Subjects Course - Introductory Subject
	Minor Classification	17	Foundational Course - Introduction to Mathematics
	Subject Type	3	Elective subject
Supplemental Course Information	Class Classification	2	Lecture
	Class Format	1	Face-to-face classes (conducted mainly in-person)
	Language of Instruction	1	Japanese
Academic Discipline		12	Analysis, applied mathematics, and related fields

Course Contents/Objectives/Teaching Method/Intended Learning Outcome

Based on the basic knowledge of mathematics prepared in the course "Introduction to Mathematics I", in this course, the students will learn the basics of multivariable functions, focusing on the partial differentiation of two variable functions. Linear algebra plays an important role in the Extreme Value Problem of multivariable functions. The content and order of the lectures may differ slightly from the description of the syllabus.

Course Taught by Faculty Member with Professional Experience

Not applicable

Active Learning MethodsDescription

Not applicable

Preparatory Study

To understand the lectures, students need to prepare and review according to their ability.

Course Plan

Lesson 1

Limits

Lesson 2

Derivatives of one variable functions (1)

Lesson 3

Derivatives of one variable functions (2)

Lesson 4

Partial derivatives (1)

Lesson 5

Partial derivatives (2) : gradient vector fields and tangent spaces

Lesson 6

Partial derivatives (3) : the Chain Rule

Lesson 7

Partial derivatives and Hesse matrices

Lesson 8

Extreme Value Problem (1)

Lesson 9

Extreme Value Problem (2)

Lesson 10

The method of Lagrange multipliers

Lesson 11

Basic properties of matrices

Lesson 12

Determinant

Lesson 13

Inverse matrix

Lesson 14

Solving Systems of Linear Equations (1)

Other

Solving Systems of Linear Equations (2)

Method of Evaluation

Grades will be evaluated based on examinations and class participation (attendance, behavior, class assignments, etc.).

Generative AI Policy for Classes

In this course, emphasis is placed on students’ own thinking and expressive abilities. Therefore, the use of generative AI is, in principle, prohibited. Use of AI is not allowed in the following activities:
- Writing reports or assignments
- Preparing for in-class discussions or presentations
If AI use is discovered, the work may be excluded from evaluation or treated as academic misconduct and subject to disciplinary measures. If you are unsure about what is permitted, please consult the lecturer in advance.

Lab / Skill-development / On-site training	An educational approach in which students deepen their understanding of educational content through first-hand experience and trial-and-error by initiating their own activities at facilities and accommodations both on and off campus.
Fieldwork	An educational approach in which students conduct surveys and observations on their own to collect information both on and off campus.
Presentations	An educational approach in which students deepen their understanding of educational content by preparing materials and delivering presentations in class.
Discussions, Debates	An educational approach in which students deepen their understanding of educational content through sharing and discussing their opinions on designated topics.
Group work	An educational approach in which students are divided into small groups and assigned tasks on issues related to educational content.
Role-playing	An educational approach in which students deepen their understanding of educational content by being assigned specific roles to play, thus allowing them to experience different viewpoints.
Flipped classroom	An educational approach in which students study the course lecture in advance, and questions and discussions relating to that content are then held in class.
Problem-based learning	An educational approach in which students acquire knowledge and skills related to educational content by attempting to tackle specific projects or problems posed to them.

Keio University Syllabus and Timetable