Course title
310031N31
Differential and Integral Calculus 2

 KAMEKO Masaki
Middle-level Diploma Policy (mDP)
Program / Major mDP Goals
Sports Engineering Course DP-1・3・1 自然科学、情報技術に関する基礎的知識を理解し、利用できる。
Purpose of class
The objective is to acquire the minimum mathematical knowledge required for each specialized field.
Course description
Following the required first-year spring semester course “Calculus I” (differential and integral calculus of functions of one variable), this course covers differential and integral calculus of functions of several variables, mainly functions of two variables. The course emphasizes that functions of several variables arise naturally in science and engineering, and introduces their importance and examples of their applications.
Goals and objectives
  1. Students will acquire basic skills for handling functions of several variables before studying their differential and integral calculus.
  2. Students will be able to correctly determine whether the limit of a given function of several variables converges and whether the function is continuous.
  3. Students will be able to compute partial derivatives of given functions of several variables and apply them appropriately.
  4. Students will be able to compute multiple integrals of given functions of several variables and apply them appropriately.
Relationship between 'Goals and Objectives' and 'Course Outcomes'

 quiz mid-term final Total.
1. 5% 5% 10%
2. 5% 5% 10%
3. 15% 20% 15% 50%
4. 15% 15% 30%
Total. 40% 30% 30% -
Evaluation method and criteria
Grades will be evaluated based on quizzes, a midterm examination, and a final examination, in order to assess whether students have acquired computational skills and solution procedures, and how well they understand the theory.
A score of 60 points will be awarded when the submitted answers indicate that the student has understood 60% of the course content. Students who earn 60 points or more will pass the course.
Language
Class schedule

 Class schedule HW assignments (Including preparation and review of the class.) Amount of Time Required
1. Basic handling and graphs of functions of several variables; limits and continuity of functions of several variables. Review 200minutes
2. Definition of partial derivatives and basic rules for partial differentiation; higher-order partial derivatives. Review 200minutes
3. Total differentials of functions of several variables and tangent planes to their graphs; the implicit function theorem; higher-order partial derivatives. Review 200minutes
4. Partial differentiation of composite functions. Review 200minutes
5. Taylor expansions of functions of several variables. Review 200minutes
6. Fundamentals of extremum problems; extrema of implicit functions and constrained extremum problems. Review 200minutes
7. Midterm examination, review of its solutions, and self-assessment. Review 200minutes
8. Problem-solving exercises. Review 200minutes
9. Definition of multiple integrals and their basic properties. Review 200minutes
10. Changing the order of integration variables in iterated integrals. Review 200minutes
11. Change of variables in multiple integrals. Review 200minutes
12. Improper multiple integrals. Review 200minutes
13. Final examination, review of its solutions, and self-assessment. Review 200minutes
14. Problem-solving exercises. Review 200minutes
Total. - - 2800minutes
Feedback on exams, assignments, etc.
ways of feedback specific contents about "Other"
Feedback in the class
Textbooks and reference materials
「例題で学ぶ微分積分学」（森北出版）阿部剛久・井戸川知之・古城知己・本澤直房共著
“Calculus Learned through Examples” (Morikita Publishing), co-authored by Takehisa Abe, Tomoyuki Idogawa, Tomomi Kojo, and Naofusa Honzawa.
Prerequisites
Thorough review of Calculus I.
Office hours and How to contact professors for questions
  • The use of the Learning Support Room is strongly recommended.
Regionally-oriented
Non-regionally-oriented course
Development of social and professional independence
  • Course that cultivates an ability for utilizing knowledge
Active-learning course
N/A
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 : Wed Aug 19 04:01:10 JST 2026