Course title
Calculus II
Course description
We will conduct online teaching in Spring 2021.
This is a continuation of Calculus I followed by Calculus III. You will learn how to use integration to compute areas of regions, volumes of solids, and lengths of arcs. Then you will study how to model a real-world problem using differential equations through many examples as well as how to solve basic 1st-order linear differential equations such as separable equations with its applications to problems in nature. Lastly, you will learn the basics of infinite series to represent a function using Taylor and Maclaulin series as well as how to approximate a function using Taylor polynomials.
Purpose of class
Together with Calculus I, 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 can compute integrals of various functions using integration by parts, trigonometric integrals, and trigonometric substitution.
A-1
2. The students can compute areas between curves, volumes of solids, arc length, and area of a surface of revolution using integration.
A-1
3. The students can solve basic differential equations such as separable equations and linear equations.
A-1
4. The students can argue to see whether a given infinite series is convergent or not using integral tests, comparison tests, ratio tests, and root tests.
A-1
5. The students can use Taylor and Maclaurin series to represent a given function and you can use Taylor polynomials to approxiate a value of a given function.
A-1
Language
English
Class schedule

Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Review of integration
Areas between curves
Volumes
Review the content of the lecture (5.2-5.5, 6.1-6.3 in the textbook) 180分
Work on homework problems 200分
2. Integration by parts
Trigonometric integrals
Review the content of the lecture (7.1-7.2 in the textbook) 120分
Work on homework problems 260分
3. Trigonometric substitution
Integration of rational functions
Review the content of the lecture (7.3-7.4 in the textbook) 120分
Work on homework problems 260分
4. Strategy for integration
Improper integrals
Review the content of the lecture (7.5, 7.8 in the textbook) 120分
Work on homework problems 260分
5. Arc length
Area of a surface of revolution
Review the content of the lecture (8.1-8.2 in the textbook) 120分
Work on homework problems 260分
6. Modeling with differential equations
Separable equations
Review the content of the lecture (9.1, 9.3 in the textbook) 120分
Work on homework problems 260分
7. Mid-term presentation and discussions on the solutions afterwards Preparation for the mid-term presentation 380分
8. Linear equations
Second-order linear equations
Review the content of the lecture (9.5, 17.1 in the textbook) 120分
Work on homework problems 260分
9. Parametrized curves
Polar coordinates, area length in polar coordinates
Review the content of the lecture (10.1-10.4 in the textbook) 120分
Work on homework problems 260分
10. Sequences
Series and the integral test
Review the content of the lecture (11.1-11.3 in the textbook) 120分
Work on homework problems 260分
11. Comparison tests
Alternating series, absolute convergence, ratio and root tests
Review the content of the lecture (11.4-11.6 in the textbook) 120分
Work on homework problems 260分
12. Strategy for testing series
Power series, representations of functions as power series
Review the content of the lecture (11.7-11.9 in the textbook) 100分
Work on homework problems 260分
13. Taylor and Maclaurin series
Applications of Taylor polynomials
Review the content of the lecture (11.10-11.11 in the textbook) 120分
Work on homework problems 260分
14. Final exam and discussions on the solutions afterwards Preparation for the final exam 380分
Total. - - 5300分
Relationship between 'Goals and Objectives' and 'Course Outcomes'

Homework Mid-term presentation Final exam Total.
1. 20% 4% 5% 29%
2. 15% 4% 5% 24%
3. 10% 4% 3% 17%
4. 10% 3% 10% 23%
5. 7% 7%
Total. 55% 15% 30% -
Evaluation method and criteria
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 "Calculus I". In particular, the topics such as derivatives of various functions, the product and quotient rules, the chain rule, areas and distances, definite & indefinite integrals, net change theorem, the substitution rule, and the fundamental theorem of calculus.
Office hours and How to contact professors for questions
• By appointment. 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 applicable
N/A N/A
Education related SDGs:the Sustainable Development Goals • 4.QUALITY EDUCATION