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岎捠丒僉儍儞僷僗儅僢僾
Tokyo University of Agriculture and Technology Division of Mathematical Sciences, Institute of Engineering  
Division of Mathematical Sciences, Institute of Engineering, Tokyo University of Agriculture and Technology

Calculus 嘦
 
Course description
  Calculus provides indispensable tools to analyze various mathematical changes appearing in natural and social phenomena. In this course, we will learn about differentiation and integration of multivariable functions, such as partial differentiations, criteria of local maxima and minima, double and triple integrations, volumes of solids, line integrations and series. Various computations will be practiced with drawing diagrams.

Expected Learning
  The goals of this course are
(1) to master basic methods of the differentiation and integration of two, or multivariable functions, and
(2) to be capable of performing practical computations.
Corresponding criteria in the Diploma Policy: See the Curriculum maps

Course schedule
  1. Limits and continuity of functions of two variables
2. Partial differentiations and total differentiations
3. Higher order partial differentiations, and partial differentiations of composite functions
4. Taylor乫s theorem for functions of two variables
5. Local maxima and minima of functions of two variables
6. Review, and midterm examination
7. Double integrations
8. Changes of variables
9. Triple integrations, and changes of variables by using the system of polar coordinates
10. Improper integrations
11. Volumes of solids and areas of surfaces
12. Line integrations and Green's theorem
13. Series and power series 1
14. Series and power series 2
15. Review, and term examination

(For Faculty of Engineering only)
A common examination will be conducted extra at the last of the term in the adjustment period for all the classes of this course.

Prerequisites
  Knowledge of the course of Calculus I and Exercise will be used in the lecture.
In addition to 60 hours that students spend in the class, students are recommended to prepare for and revise the lectures, spending the standard amount of time as specified by the University and using the lecture handouts as well as the references specified below.

Required Text(s) and Materials
  Textbooks will be introduced in the first lecture, if necessary.

References
  Miyake Toshitsune, 乬Nyuumon-Bibun-Sekibun乭, Baifu-kan (in Jananese)

Assessment/Grading
   
Message from instructor(s)
 
Course keywords
  Multivariable functions, Partial differentiations, Local maxima and minima of functions of two variables, Multiple integrations, Volumes of solids and areas of surfaces, Series

Office hours
 

  Division of Mathematical Sciences, Institute of Engineering, Tokyo University of Agriculture and Technology
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