Calculus II

Course title

M2009000

Calculus II

Course description

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 Maclaurin 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 approximate a value of a given function.	A-1

Relationship between 'Goals and Objectives' and 'Course Outcomes'

	Mid-term exam	Final exam	Total.
1.	15%	10%	25%
2.	15%	10%	25%
3.	15%	10%	25%
4.		15%	15%
5.		10%	10%
Total.	45%	55%	-

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)	120分
1.	Review of integration Areas between curves Volumes	Preparation before the lecture	260分
2.	Integration by parts Trigonometric integrals	Review the content of the lecture (7.1-7.2 in the textbook)	120分
2.	Integration by parts Trigonometric integrals	Preparation before the lecture	260分
3.	Trigonometric substitution Integration of rational functions	Review the content of the lecture (7.3-7.4 in the textbook)	120分
3.		Preparation before the lecture	260分
4.	Strategy for integration Improper integrals	Review the content of the lecture (7.5, 7.8 in the textbook)	120分
4.	Strategy for integration Improper integrals	Preparation before the lecture	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
5.	Arc length Area of a surface of revolution	Preparation before the lecture	260分
6.	Modeling with differential equations Separable equations Linear equations	Review the content of the lecture (9.1, 9.3, 9.5 in the textbook)	120分
6.		Preparation before the lecture	260分
7.	Mid-term exam and discussions on the solutions afterwards	Preparation for & review of the mid-term exam	380分
8.	Sequences Series and the integral test	Review the content of the lecture (11.1-11.3 in the textbook)	120分
8.	Sequences Series and the integral test	Preparation before the lecture.	260分
9.	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
9.		Preparation before the lecture	260分
10.	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)	120分
10.		Preparation before the lecture	260分
11.	Taylor and Maclaurin series	Review the content of the lecture (11.10 in the textbook)	120分
11.	Taylor and Maclaurin series	Preparation before the lecture	260分
12.	Applications of Taylor polynomials	Review the content of the lecture (11.11 in the textbook)	120分
12.	Applications of Taylor polynomials	Preparation before the lecture	260分
13.	Review	Work on exercises	120分
13.	Review	Preparation before the lecture	260分
14.	Final exam and discussions on the solutions afterwards	Preparation for & Review of the final exam	380分
Total.	-	-	5320分

Goals and objectives (Other Courses)

A:Fundamental Mechanical Engineering	B:Advanced Mechanical Engineering	C:Environment and Materials Engineering	D:Chemistry and Biotechnology	E:Electrical Engineering and Robotics	G:Advanced Electronic Engineering	F:Information and Communications Engineering	L:Computer Science and Engineering	H:Urban Infrastructure and Environment

Language

English

Evaluation method and criteria

Mid-term exam will contribute 45% of your grade.
Final exam will contribute 55% of your grade.
Those who get at least 60% of the full score will pass this course.

Feedback on exams, assignments, etc.

ways of feedback	specific contents about "Other"
Feedback in the class

Textbooks and reference materials

Calculus: Early Transcendentals, 9th 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.

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

Last modified : Tue Feb 18 04:10:15 JST 2025