Course title
M20130002
Calculus III

 BUI NGOC TAM
Middle-level Diploma Policy (mDP)
Program / Major mDP Goals
先進国際課程 A-1 A-1 Students shall obtain basic and advanced knowledge and skills in mathematics, natural and computer sciences as well as presentation skills to communicate on their knowledge with scholars from various fields.
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.
Course description
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.
Goals and objectives
  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. Students can compute line ＆ surface integrals of simple functions and use Green’s theorem of compute line integrals.
  5. The students can use Stokes' Theorem, Divergence's Theorem for the computation of surface integrals,
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
Homework, and mid-term exams will contribute 50% of your grade.
The final exam will contribute 50% of your grade.
Those who get at least 60% of the full score will pass this course.
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 and Cross Product
Conic Sections in Polar Coordinates
Equations of Lines and Planes 		Read the lecture notes and work on exercises
(Content is 10.6, 12.1-12.5 in the textbook) 		160minutes
Work on exercises and preparation for Quiz 220minutes
2. 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) 		120minutes
Work on exercises and preparation for Quiz 260minutes
3. Functions of Several Variables
Limits and Continuity 		Read the lecture notes and work on exercises
(Content is 14.1, 14.2 in the textbook) 		120minutes
Work on exercises and preparation for Quiz 260minutes
4. Partial Derivatives
Tangent Planes and Linear Approximations 		Read the lecture notes and work on exercises
(Content is 14.3, 14.4 in the textbook) 		140minutes
Work on exercises and preparation for Quiz 240minutes
5. The Chain Rule
Directional Derivatives and the Gradient Vector 		Read the lecture notes and work on exercises
(Content is 14.5, 14.6 in the textbook) 		140minutes
Work on exercises and preparation for Quiz 240minutes
6. Maximum and Minimum Values
Lagrange Multipliers 		Read the lecture notes and work on exercises
(Content is 14.7, 14.8 in the textbook) 		120minutes
Work on exercises and preparation for Mid-term 260minutes
7. Mid-term exam and discussions on the solutions afterwards Preparation for Mid-term 380minutes
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) 		180minutes
Work on exercises and preparation for Quiz 200minutes
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) 		120minutes
Work on exercises and preparation for Quiz 260minutes
10. Vector Fields
Line Integrals 		Read the lecture notes and work on exercises
(Content is 16.1, 16.2 in the textbook) 		160minutes
Work on exercises and preparation for Quiz 220minutes
11. The fundamental Theorem of Line Integrals
Green’s Theorem 		Read the lecture notes and work on exercises
(Content is 16.3, 16.4 in the textbook) 		160minutes
Work on exercises and preparation for Quiz 220minutes
12. Curl and Divergence
Parametric Surfaces
Surface Areas 		Read the lecture notes and work on exercises
(Content is 16.5, 16.6 in the textbook) 		140minutes
Work on exercises and preparation for Quiz 220minutes
13. Surface Integrals
Stokes’ Theorem
Divergence Theorem 		Read the lecture notes and work on exercises
(Content is 16.7-16.9 in the textbook) 		120minutes
Work on exercises and preparation for Final 260minutes
14. Final exam and discussions on the solutions afterwards Preparation for Final 380minutes
Total. - - 5300minutes
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback outside of the class (ScombZ, mail, etc.) Feedback on exams, assignments, etc., can be done inside of the class/outside of the class via Scombz, email, or Google chat.
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: tambn@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
Last modified : Sat Mar 14 13:28:29 JST 2026