- Lecturer
- Brezina Jan
- Place
- Tue1-2(H104)
- Credits
- Lecture2 Exercise0 Experiment0
- Code
- 1021
- Syllabus updated
- 2015/6/8
- Lecture notes updated
- 2015/6/9
- Semester
- Spring Semester / Recommended semester:1
Outline of lecture
In Calculus I we first revise our high-school knowledge on integration and differentiation of functions of one-variable and then expand these ideas for functions of multivariables. This course is focused on learning new notions and ability to work with them, i.e., calculate.
Purpose of lecture
To develop and strengthen the ability to calculate derivatives and integrals. This course gives you the ability to use the tools necessary in other technical courses.
Plan of lecture
1. Maps and functions, exponential function, logarithmic function, trigonometric functions.
2. Hyperbolic functionsｼ景nverse trigonometric functions.
3. Differentiation and integration of elementary functions, indefinite integral of rational functions.
4. Multivariable functions, limit and continuity.
5. Partial differentiation, partial derivatives
6. Derivatives of higher order, order of partial differentiation
7. Derivatives of a composite function (chain rule).
8. Area, volume.
9. Integration of multivariable functions
10. Multiple integral and iterated integral.
11. Changing the order of integration.
12. Change of variables (under the integral sign).
13. Examples using transformation of coordinates.
14. Application of multiple integral (area and volume).
15. Improper integral.
Textbook and reference
The course does not follow any book specifically, there will be English handouts.
You can compare with any English or Japanese textbook on introduction to university calculus you find online or
in the library. The main topics are always the same.
Related and/or prerequisite courses
You should register together with the course "Exercise in Calculus I (Course No. 1231)".
Evaluation
Based on the results of tests, mid-term exam and final exam. Also your work during semester counts. Details to be explained on first lecture (see content of the first class).
Comments from lecturer
The course contains the same amount of mathematical knowledge as its Japanese alternatives, but with the advantage of learning mathematical English. Getting used to mathematical English from the beginning will easy your further studies and future work.
Contact Information
<Contact>
Email : brezinaﾂｼmath.titech.ac.jp
Office : Room 219, Main Bldg., Ookayama Campus
TA information:
Name: Hiroki Murakami
Email: murakami.h.ahﾂｼm.titech.ac.jp
Office: H316
Office Hours
First send me an email to set up a time.
