Course title
M20130002
Calculus III
Course description
We will conduct classes in a HiFlex manner (i.e., in person class + online classes) in Fall 2021.
This is a continuation of Calculus II. You will learn how to treat differentiation and integration of a function of multiple variables using partial derivatives and double integrals as well as the relationship between partial derivatives and tangent planes and that between double integrals and volumes of solids. Then you will study vector-valued functions and their integrals over lines and surfaces which are closely connected through Green's Theorem and Stokes' Theorem.
Purpose of class
You are expected to obtain skills, knowledge, and understandings of basics of multi-variable calculus, which are widely used in science and engineering.
Goals and objectives

Goals and objectives Course Outcomes
1. The students can use dot product and cross product of vectors to express lines and planes.
A-1
2. The students can compute partial derivatives of various functions using the chain rule and use them to describe tangent lines and to compute maximum and minimum values of a given function.
A-1
3. The students can compute double & triple integrals of various functions and use them to compute the volume of solids.
A-1
4. The students can compute line & surface integrals of simple functions and use them to understand Green's Theorem, Stokes' Theorem, and Divergence Theorem.
A-1
Language
English
Class schedule

Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Guidance
3d Coordinates
Vectors
Dot Product
Conic Sections in Polar Coordinates
Read the lecture notes and work on exercises
(Content is 10.6, 12.1-12.3 in the textbook)
160分
Work on homework 220分
2. Cross Product
Equations of Lines and Planes
Read the lecture notes and work on exercises
(Content is 12.4-12.5 in the textbook)
120分
Work on homework 260分
3. Parametric Equations and Vector Functions
Derivatives and Integrals of Vector Functions
Velocity and Acceleration
Read the lecture notes and work on exercises
(Content is 13.1, 13.2, 13.4 in the textbook)
120分
Work on homework 260分
4. Functions of Several Variables
Limits and Continuity
Partial Derivatives
Read the lecture notes and work on exercises
(Content is 14.1-14.3 in the textbook)
140分
Work on homework 240分
5. Tangent Planes and Linear Approximations
The Chain Rule
Directional Derivatives and the Gradient Vector
Read the lecture notes and work on exercises
(Content is 14.4-14.6 in the textbook)
140分
Work on homework 240分
6. Maximum and Minimum Values
Lagrange Multipliers
Read the lecture notes and work on exercises
(Content is 14.7-14.8 in the textbook)
120分
Work on homework 260分
7. Mid-term exam and discussions on the solutions afterwards Preparation for mid-term 380分
8. Double Integrals
Double Integrals in Polar Coordinates
Applications of Double Integrals
Read the lecture notes and work on exercises
(Content is 15.1-15.4 in the textbook)
180分
Work on homework 200分
9. Triple Integrals
Triple Integrals in Cylindrical and Spherical Coordinates
Read the lecture notes and work on exercises
(Content is 15.6-15.8 in the textbook)
120分
Work on exercises 260分
10. Vector Fields
Line Integrals
The fundamental Theorem of Line Integrals
Green’s Theorem
Read the lecture notes and work on exercises
(Content is 16.1-16.4 in the textbook)
160分
Work on homework 220分
11. Curl and Divergence
Parametric Surfaces
Surface Areas and Surface Integrals
Read the lecture notes and work on exercises
(Content is 16.5-16.7 in the textbook)
160分
Work on homework 220分
12. Stokes’ Theorem
Divergence Theorem
Read the lecture notes and work on exercises
(Content is 16.8-16.9 in the textbook)
140分
Work on homework 220分
13. Reviews Work on exercises 120分
Work on homework 260分
14. Final exam and discussions 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. 12% 3% 15%
2. 30% 5% 35%
3. 20% 10% 30%
4. 8% 12% 20%
Total. 70% 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
ISBN: 978-1285741550
Prerequisites
Content of the syllabus of the courses "Calculus I" and "Calculus II". In particular, the topics such as derivatives of various functions, definite & indefinite integrals, the fundamental theorem of calculus, and polar coordinates.
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 interpersonal 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