概要:
工業数学の代表的な計算方法を紹介し、具体的な実例を検討する。工業英語を応用する。
授業の進め方・方法:
授業は教科書の該当箇所を参照して、教員が作成した教材で、演習を中心に行う。
授業の理解を高めるために、予習復習が必須である。
学生は分析計算や数値計算ソフトOctaveを用いて、数値計算を行う。
学生はレポートをLaTeXで作成する
注意点:
点付きのレポート点数の平均値
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|
週 |
授業内容 |
週ごとの到達目標 |
| 前期 |
| 1stQ |
| 1週 |
Gamma function basics |
Understanding the factorial, the Euler integral, and the Stirling approximation
Being able to compute the Gamma function for real argument.
|
| 2週 |
Gamma function: Graph and infinite product |
Understanding the Weierstraß product of the Gamma function
Being able to compute the Gamma function for complex argument.
|
| 3週 |
Complex analysis: Cauchy integral theorem |
Understanding the Cauchy integral theorem
Being able to calculate contour integrals
|
| 4週 |
Gamma function: Functional equations |
Understanding the doubling and reflection formula for the psi and Gamma function, as well as the Gauss multiplication formula.
|
| 5週 |
Gamma function: Spouge algorithm |
Being able to calculate the Gamma function with the effective Spouge algorithm
|
| 6週 |
Uniqueness of the Gamma function |
Understanding that the Gamma function is unique, using the Wieland proof.
|
| 7週 |
Encryption: Modular arithmetic |
Understanding modular arithmetic, Fermat's theorem, Euclid's algorithm, and repeated squaring.
Being able to calculate the inverse and powers in modular arithmetic.
|
| 8週 |
Encryption algorithms: Diffie-Hellman and RSA |
Understanding trapdoor functions.
Being able to encrypt via the RSA and to exchange keys via the Diffie-Hellman algorithm.
|
| 2ndQ |
| 9週 |
Encryption algorithms: El-Gamal and elliptic-curve |
Understanding the El-Gamal public encryption method, and the elliptic-curve encryption method.
|
| 10週 |
Linear algebra and differential equations: Finite Element Method: Basics |
Understanding the finite element method.
Being able to transform a differential equation into a linear algebra problem.
|
| 11週 |
Linear algebra and differential equations: Finite Element Method: Numerics |
Being able to solve differential equations with the help of the Finite element method.
|
| 12週 |
Spline interpolation |
Understanding the concept of a spline.
Being able to calculate cubic spline approximations.
|
| 13週 |
Chaos: Fixed points of maps and their stability |
Understanding regular and chaotic behaviour of a simple dynamic system.
|
| 14週 |
Divide and conquer: Fast wavelet transform |
Understanding the divide-and-conquer principle
for the Fast wavelet transform.
|
| 15週 |
Fast wavelet transform and noise suppression |
Being able to suppress data noise by using the Fast wavelet transform
|
| 16週 |
答案返却など
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解答と採点基準の説明
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