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.
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.
epsilon delta method, termwise integration、 differential equations, vector analysis, integral theorems
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | ✔ Practical and/or problem-solving skills |
The lectures provide the fundamentals of calculus.
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。
Not specified in particular.
By scores of examinations and reports.
None.
umehara[at]is.titech.ac.jp