2019 Fundamentals of Numerical Analysis

Font size  SML

Register update notification mail Add to favorite lecture list
Academic unit or major
Undergraduate major in Mechanical Engineering
Nagasaki Takao  Xiao Feng 
Course component(s)
Lecture / Exercise     
Day/Period(Room No.)
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
Access Index

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, numerical integration, and spline, 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 bring laptop PC (Windows PC)
and have elementary knowledge on C programming.

Page Top