2016 Fundamentals of Numerical Analysis

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Academic unit or major
Undergraduate major in Mechanical Engineering
Nagasaki Takao  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 such as numerical error, various methods to solve systems of linear equations, nonlinear equation, interpolation, numerical integration, and spline.
Students will understand basic concepts of numerical analysis, and they will develop practical skills to utilize numerical analysis by making computer programs in exercises.

Student learning outcomes

By the end of this course, students will be able to:
1) Understand principles of basic methods of numerical analysis 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, Spline

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 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 (Conjugate gradient method) Understand rapid convergence compared to point iterative 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.
Class 8 Spline Understand how to generate a smooth curve from discrete points.


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 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 have elementary knowledge on C programming.

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