2021 Fundamentals of Numerical Analysis

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Academic unit or major
Undergraduate major in Mechanical Engineering
Aoki Takayuki  Onishi Ryo  Xiao Feng 
Class Format
Lecture / Exercise     
Media-enhanced courses
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Course description and aims

Numerical analysis is a technique to solve mathematical problems in practical applications and has been used in many fields of mechanical engineering for research and development. This course explains fundamentals of numerical analysis and how to make computer programs in order to develop practical skills to utilize numerical analysis.

Student learning outcomes

By the end of this course, students will be able to:
1. Understand principles of basic methods of numerical analysis, such as numerical error, various methods to solve systems of linear equations, nonlinear equation, interpolation, and numerical integration, and apply them to practical problems.
2. Make computer programs to solve practical problems.


Numerical analysis, System of linear equations, Nonlinear equation, Interpolation, Numerical integration

Competencies that will be developed

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

Class flow

In the first half of the class, the principle and programming method of the topics are explained. In the latter half, students make computer programs and run them in exercises.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Numerical analysis and error Understand errors in numerical analysis such as discretization and round-off errors.
Class 2 Systems of linear equations (Direct method) Understand Gaussian elimination.
Class 3 Systems of linear equations (Point iterative method) Understand SOR method.
Class 4 Systems of linear equations (Gradient descent method, Conjugate gradient method) Understand Gradient descent method and conjugate gradient method
Class 5 Nonlinear equations Understand bisection method and Newton's method.
Class 6 Interpolation Understand Lagrange polynomial.
Class 7 Numerical integration Understand Gauss-Legendre integration.

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

To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.


None specified.

Reference books, course materials, etc.

Handouts will be provided.

Assessment criteria and methods

Students will be assessed on their understanding of the method and ability to make programs by the final examination anf exercises in every class.

Related courses

  • MEC.K231 : Exercise in Information Processing (Mechanical Engineering)
  • MEC.B332 : Applied Numerical Mathematics

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

Students should bring laptop PC (Windows PC)with Visual Studio 2019
and have elementary knowledge on C programming.

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