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2020　Numerical Analysis

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Academic unit or major
Undergraduate major in Mathematical and Computing Science
Instructor(s)
Nishibata Shinya  Takahashi Jin 
Class Format
Lecture / Exercise    (ZOOM)
Media-enhanced courses
Day/Period(Room No.)
Tue5-6(W834)  Fri5-8(W834)  
Group
-
Course number
MCS.T321
Credits
3
Academic year
2020
Offered quarter
3Q
Syllabus updated
2020/10/2
Lecture notes updated
-
Language used
Japanese
Access Index

Course description and aims

The development of computers in recent years has enabled large-volume numerical calculations, which are used in various science and technology fields. Along with this, a variety of numerical methods have been developed and more and more theoretical studies have been also conducted.
This course provides basic methods of numerical analysis and exercises in computation.

Student learning outcomes

The aim of this course is for students to understand basic mathematical concepts for numerical calculation methods, and learn programing skills for numerical schemes.

Keywords

Numerical analysis, Contraction principle, Newton's method, LU decomposition, Numerical integration, Runge-Kutta method

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 numerical analysis with recitation sessions.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Numerical representation and rounding error Understand the contents covered by the lecture.
Class 2 Numerical scheme to solve nonlinear equation Understand the contents covered by the lecture.
Class 3 Exercises regarding the contents covered up to the 2nd lecture Cultivate more practical understanding by doing exercises.
Class 4 Contraction principle and convergence theorem Understand the contents covered by the lecture.
Class 5 Convergence of Newton's method Understand the contents covered by the lecture.
Class 6 Exercises regarding the contents covered up to the 5th lecture Cultivate more practical understanding by doing exercises.
Class 7 System of nonlinear equations Understand the contents covered by the lecture.
Class 8 Gaussian elimination　to solve system of linear equations Understand the contents covered by the lecture.
Class 9 Exercises regarding the contents covered up to the 8th lecture Cultivate more practical understanding by doing exercises
Class 10 LU decomposition Understand the contents covered by the lecture.
Class 11 Iterative solution technique for linear equations Understand the contents covered by the lecture.
Class 12 Exercises regarding the contents covered up to the 11th lecture Cultivate more practical understanding by doing exercises
Class 13 Trapezoidal rule for numerical integration, Understand the contents covered by the lecture.
Class 14 Simpson's rule Understand the contents covered by the lecture.
Class 15 Exercises regarding the contents covered up to the 14th lecture Cultivate more practical understanding by doing exercises.
Class 16 Interpolation polynomial Understand the contents covered by the lecture.
Class 17 Gaussian integral formula Understand the contents covered by the lecture.
Class 18 Exercises regarding the contents covered up to the 17th lecture Cultivate more practical understanding by doing exercises.
Class 19 Solution of ordinary differential equations by Euler's method Understand the contents covered by the lecture.
Class 20 Solution of ordinary differential equations by Runge-Kutta method Understand the contents covered by the lecture.
Class 21 Exercises regarding the contents covered up to the 20th lecture Cultivate more practical understanding by doing exercises.
Class 22 Convergence of 1 stage process Understand the contents covered by the lecture.

Out-of-Class Study Time (Preparation and Review)

To enhance effective learning, students are encouraged to spend a certain length of time outside of class on preparation and review (including for assignments), as specified by the Tokyo Institute of Technology Rules on Undergraduate Learning (東京工業大学学修規程) and the Tokyo Institute of Technology Rules on Graduate Learning (東京工業大学大学院学修規程), for each class.
They should do so by referring to textbooks and other course material.

Textbook(s)

Tetsuro Yamamoto, Primer of numerical analysis

Reference books, course materials, etc.

None.

Assessment criteria and methods

By scores of examinations and reports.

Related courses

  • LAS.M101 ： Calculus I / Recitation
  • MCS.T211 ： Applied Calculus
  • MCS.T301 ： Vector and Functional analysis
  • MCS.T311 ： Applied Theory on Differential Equations

Prerequisites (i.e., required knowledge, skills, courses, etc.)

None.

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