Course title
微分積分学Ⅰおよび演習   [Calculus Ⅰ]
Course category technology speciality courses  Requirement   Credit 3 
Department   Year 14  Semester 1st 
Course type 1st  Course code 021913
Instructor(s)
嘉藤 桂樹   []
Facility affiliation Graduate School of Engineering Office   Email address

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.

This course is taught by a part-time lecturer. Once the employment of the part-time lecturer is confirmed, this syllabus may be modified. In this case, the official version is the modified syllabus.
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’s theorem
5. Rolle's theorem and the mean-value theorem
6. Taylor's theorem, and its applications
7. Exercises, or 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. Exercise and final examination
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 etc.) will be used in the lecture.
In addition to 60hours 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
R. Dedekind, Was sind und was sollen die Zahlen.(Japanese Trans. Iwanami)
Assessment/Grading
Evaluation will be done according to the Klausuren(Midterm examination 50%. Final examination 50%)
Message from instructor(s)
Course keywords
Differentiation, Taylor expansion, Limit of indeterminate form, Integration of rational function, Improper integral
Office hours
Remarks 1
Remarks 2
Related URL
Lecture Language
Japanese
Language Subject
Last update
1/19/2022 11:05:03 AM