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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 嘥
 
Course description
  Calculus provides indispensable tools to analyze various mathematical changes appearing in natural and social phenomena. In this course, we will learn the differentiations and the integrations of various functions of one variable and their properties. We will practice advanced computations in this course rather than in high schools.

Expected Learning
  The goals of this course are
(1) to master basic methods of the differentiations and the integrations of various functions, such as polynomials, rational and irrational functions, trigonometric functions, exponential functions and logarithmic functions,
(2) to understand how to calculate extreme maximal and minimum values of functions, and
(3) to be capable of performing practical computations on determining areas of figures and lengths of curves.
Corresponding criteria in the Diploma Policy: See the Curriculum maps.

Course schedule
  1. Continuity of real numbers and limits of functions
2. Continuity and differentiability
3. Formulae of differentiations, inverse functions and their differentiations
4. Differentiations of inverse trigonometric functions, high derivatives, and Leibniz乫s theorem
5. Rolle's theorem and the mean-value theorem
6. Taylor's theorem, and its applications
7. Review, and midterm examination
8. Local maxima and minima, and limits of indeterminate forms
9. Indefinite integrals
10. Integrations of rational functions, possibly containing trigonometric functions
11. Definite integrals, and their properties
12. Improper integrals
13. Areas of figures and lengths of curves
14. Exercises of various problems on integrals
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
  Mathematics in high schools (in particular, Mathematics I, II, III).
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
  Differentiation, Taylor expansion, Limit of indeterminate form, Integration of rational function, Improper integral

Office hours
 

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