Course title
M20050001
Calculus I
Course description
This is an introductory course on calculus followed by Calculus II and Calculus III. You will study the basics of derivatives and integrals through tangent lines and areas of regions as well as the basic connection between derivatives and integrals through the fundamental theorem of calculus. You will also learn how to compute derivatives and integrals of various functions such as polynomials, trigonometric functions, exponentials and logarithms as well as the chain rule, the substitution rule, and integration by parts while how to use differentiation to compute maximum and minimum values of a function, and to investigate the shape of the graph of a function. People with enough background and understanding of the mathematics at the IB higher level do not need to take this course.
Purpose of class
Together with Calculus II, you are expected to obtain skills, knowledge, and understandings of basics of one-variable calculus, which are widely used in science and engineering.
Goals and objectives

Goals and objectives Course Outcomes
1. The students understand the notions of continuity and differentiability of a function and can check if concrete functions are continuous / differentiable or not with clear reasoning.
A-1
2. The students can compute limits and derivatives of basic functions using the product & quotient rules, and the chain rule.
A-1
3. The students can use the theory of derivatives to compute maximum and minimum values and to describe the shape of concrete functions.
A-1
4. The students understand the notions of definite & indefinite integrals as well as the connection between derivatives and integrals, and can compute the integrals of basic functions.
A-1
Language
English
Class schedule

Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Trigonometric functions
Exponential functions
Inverse functions and logarithms
Read Chapter 1 in the textbook 180分
Work on exercises 200分
2. The limit of a function
Calculating limits
Read 2.1-2.3 in the textbook 120分
Work on exercises 260分
3. Continuity
Derivatives and rates of changes
Read 2.5-2.7 in the textbook 120分
Work on exercises 260分
4. The Derivative as a function
Derivatives of polynomials and exponential functions
The product and quotient rules
Read 2.8, 3.1-3.2 in the textbook 120分
Work on exercises 260分
5. Derivatives of the trigonometric functions
The chain rule
Implicit differentiation
Read 3.3-3.5 in the textbook 120分
Work on exercises 260分
6. Derivatives of logarithmic functions
Linear approximation
Read 3.6-3.10 in the textbook 160分
Work on exercises 220分
7. Mid-term exam and discussion on the solutions afterwards Preparation for mid-term 380分
8. Maximum and minimum values
The mean value theorem
Derivatives and the shape of a graph
Read 4.1-4.3 in the textbook 120分
Work on exercises 260分
9. Indeterminate forms and L’Hospital’s rule
Summary of curve sketching
Read 4.3-4.5 in the textbook 120分
Work on exercises 260分
10. Optimization problems
Antiderivatives
Read 4.7 and 4.9 in the textbook 120分
Work on exercises 260分
11. Areas and distances
The definite integral
Read 5.1-5.2 in the textbook 120分
Work on exercises 260分
12. The fundamental theorem of calculus Read 5.3 in the textbook 100分
Work on exercises 260分
13. Indefinite integrals and the net change theorem
The substitution rule
Read 5.4-5.5 in the textbook 120分
Work on exercises 260分
14. Final exam and discussion on the solutions afterwards Preparation for final 380分
Total. - - 5300分
Relationship between 'Goals and Objectives' and 'Course Outcomes'

Mid-term etc. Final Total.
1. 10% 5% 15%
2. 20% 15% 35%
3. 5% 20% 25%
4. 5% 20% 25%
Total. 40% 60% -
Evaluation method and criteria
Mid-term exam, presentation on exercises etc. will contribute 40% of your grade.
Those who get at least 60% of the full score will pass this course.
Textbooks and reference materials
Calculus: Early Transcendentals, 8th edition, James Stewart
Prerequisites
Content of the syllabus of the course "Pre-calculus". In particular, the topics such as Quadratic Equations and Complex Numbers, Functions and Graphs, Sequences and Series, Exponentials and Logarithms, Quadratic Equations, Binomials, The Unit Circle and Radian Measure, Trigonometry, Vectors in 2 and 3 Dimensions.
Office hours and How to contact professors for questions
• Monday, 17:00-18:00 in the lecturer's office. Contact e-mail address: ikegami@shibaura-it.ac.jp
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
• Course that cultivates an ability for utilizing knowledge
• Course that cultivates a basic problem-solving skills
Active-learning course
About half of the classes are interactive
Course by professor with work experience
Work experience Work experience and relevance to the course content if applicatable
N/A N/A
Education related SDGs:the Sustainable Development Goals