Course title
Calculus III

ikegami daisuke
Course description
We will decide the style of class of this course (in person or online) for Fall 2021 depending on the situation of COVID-19.
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. Lastly, you will learn the basics of second-order linear differential equations in both homogeneous and non-homogeneous cases.
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.
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.
3. The students can compute double & triple integrals of various functions and use them to compute the volume of solids.
4. The students can compute line & surface integrals of simple functions and use them to understand Green's Theorem, Stokes' Theorem, and Divergence Theorem.
5. The students can solve simple second-order linear equations in both homogeneous & non-homogeneous cases.
Class schedule

Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. 2d and 3d Cartesian Coordinates
Polar Coordinates
Dot Product
Read 10.3, 12.1-12.3 160分
Work on exercises 220分
2. Dot Product (continued)
Cross Product
Equations of Lines and Planes
Read 12.3-12.5 120分
Work on exercises 260分
3. Parametric Equations and Vector Functions
Derivatives and Integrals of Vector Functions
Velocity and Acceleration
Read 10.1,13.1, 13.2, 13.4 120分
Work on exercises 260分
4. Functions of Several Variables
Limits and Continuity
Partial Derivatives
Read 14.1-14.3 140分
Work on exercises 240分
5. Tangent Planes and Linear Approximations
The Chain Rule
Directional Derivatives and the Gradient Vector
Read 14.4-14.6 140分
Work on exercises 240分
6. Maximum and Minimum Values
Lagrange Multipliers
Read 14.7-14.8 120分
Work on exercises 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 15.1-15.4 180分
Work on exercises 200分
9. Triple Integrals
Triple Integrals in Cylindrical and Spherical Coordinates
Read 15.6-15.8 120分
Work on exercises 260分
10. Vector Fields
Line Integrals
The fundamental Theorem of Line Integrals
Green’s Theorem
Read 16.1-16.4 160分
Work on exercises 220分
11. Curl and Divergence
Parametric Surfaces
Surface Areas and Surface Integrals
Read 16.5-16.7 160分
Work on exercises 220分
12. Stokes’ Theorem
Divergence Theorem
Read 16.8-16.9 140分
Work on exercises 220分
13. Second-Order Linear Equations
Non-homogeneous Linear Equations
Read 17.1-17.2 120分
Work on exercises 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. 10% 5% 15%
2. 20% 10% 30%
3. 5% 20% 25%
4. 5% 20% 25%
5. 0% 5% 5%
Total. 40% 60% -
Evaluation method and criteria
Mid-term exam, presentation on exercises etc. will contribute 40% of your grade.
Final exam will contribute 60% 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
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, separable equations, linear equations, and polar coordinates.
Office hours and How to contact professors for questions
  • Monday, 17:00-18:00 in the lecturer's office. Contact e-mail address:
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
Education related SDGs:the Sustainable Development Goals
Last modified : Sun Mar 21 16:23:22 JST 2021