### 2019　Applied Calculus

Font size  SML

Academic unit or major
Undergraduate major in Mathematical and Computing Science
Instructor(s)
Umehara Masaaki  Nishibata Shinya  Miura Hideyuki  Murofushi Toshiaki  Suzuki Sakie  Tsuchioka Shunsuke
Course component(s)
Lecture
Day/Period(Room No.)
Tue3-4(W934)  Fri3-4(W934)
Group
-
Course number
MCS.T211
Credits
2
Academic year
2019
Offered quarter
2Q
Syllabus updated
2019/3/18
Lecture notes updated
-
Language used
Japanese
Access Index ### Course description and aims

We discuss the basic method to handle series after studying the basic concepts in calculus by epsilon delta method. We study basic property of function series and calculation method for deep understandings of elemental functions. Then we study quadrature method to derive an explicit formula of solution to first order ordinary differential equation. We also study basic concepts and integral theorems in vector analysis.

### Student learning outcomes

We study basic concepts and methods of calculus to be used for mathematical and computing. We also study elemental theories in ordinary differential equations and vector analysis. Taking this course, students understand the rigorous treatment of actual problems.

### Keywords

epsilon delta method,　termwise integration、 differential equations, vector analysis, integral theorems

### Competencies that will be developed

 ✔ Specialist skills Intercultural skills Communication skills Critical thinking skills ✔ Practical and/or problem-solving skills

### Class flow

The lectures provide the fundamentals of calculus.

### Course schedule/Required learning

Course schedule Required learning
Class 1 Epsilon delta definition of convergence Understand the contents covered by the lecture.
Class 2 Continuity of real number Understand the contents covered by the lecture.
Class 3 Continuity of function Understand the contents covered by the lecture.
Class 4 Uniform continuity of function Understand the contents covered by the lecture.
Class 5 Convergence of series Understand the contents covered by the lecture.
Class 6 Convergence of function series Understand the contents covered by the lecture.
Class 7 Differentiation and integration of function series Understand the contents covered by the lecture.
Class 8 General solution and particular solution of differential equation Understand the contents covered by the lecture.
Class 9 Separation of variables type equation Understand the contents covered by the lecture.
Class 10 First order linear differential equation Understand the contents covered by the lecture.
Class 11 Second-order linear differential equation Understand the contents covered by the lecture.
Class 12 Curves Understand the contents covered by the lecture.
Class 13 Surfaces Understand the contents covered by the lecture.
Class 14 Line integral and surface integral Understand the contents covered by the lecture.
Class 15 Integral theorem Understand the contents covered by the lecture.

Undecided。

### Reference books, course materials, etc.

Not specified in particular.

### Assessment criteria and methods

By scores of examinations and reports.

### Related courses

• LAS.M101 ： Calculus I / Recitation

None.

### Contact information (e-mail and phone)    Notice : Please replace from "[at]" to "@"(half-width character).

umehara[at]is.titech.ac.jp 