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.
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
|Intercultural skills||Communication skills||Specialist skills||Critical thinking skills||Practical and/or problem-solving skills|
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|
|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.|
Handouts will be provided.
Students will be assessed on their understanding of the method and ability to make programs by exercises in every class.
Students should bring laptop PC (Windows PC）
and have elementary knowledge on C programming.