### Introduction to Single-Variable Calculus I University of Tsukuba

#### Course Overview

This course along with the subsequent courses "Introduction to Single-Variable Calculus II" and “Advanced Calculus” introduces the basic tools of calculus and develops their technical competence. The primary goal of this course is to understand the concepts and to build up a working ability of various mathematical manipulations such as derivatives and integrals. This is efficiently achieved by visualization, numerical and graphical experimentations and, thus, students are required to be acquainted with Mathematica (or similar ones) during the course for working exercises and homework problems. The present course provides a basic core and practical knowledge required for many courses in both natural and social sciences.

#### Learning Achievement

1. The students are able to understand the concepts of function from the viewpoint of mapping.

2. The students are able to evaluate the limits of functions by using various techniques.

3. The students are able to carry out differentials of elementary functions.

4. The students are able to carry out integrals of elementary functions.

#### Competence

Related to 1. Mathematical logic and calculation skills.

#### Course prerequisites

* The students must have modest background of mathematics (roughly, the level of Math II and B at high school in Japan. Math III or C is not required).

* "Mathematica" is used to solve numerical problems. You are requested to install "Mathematica" in your own PC before the lectures starts.

* Those who already earned the credit of Calculus I (FJ20104) are not allowed to earn the credit of this course.

#### Grading Philosophy

Homework 30 %

Final 70%

#### Course schedule

Functions and Models

Limits and Derivatives 1

Limits and Derivatives 2

Differential Rules 1

Differential Rules 2

Application of Differentiations 1

Application of Differentiations 2

Integrals

Applications of Integrals 1

Applications of Integrals 2

#### Course type

Lectures and Class Exercises

#### Online Course Requirement

#### Instructor

JUNG Mincherl

#### Other information

* You will be strongly requested to work on many exercise problems in the textbook assigned during the lectures.

* All exams are closed book for in-class lecture.

#### Site for Inquiry

Link to the syllabus provided by the university