Numerical Method (TE5278)

Course Description

This course explores critical topics in numerical methods, including error analysis, the Taylor series, root-finding techniques for equations in one variable, and methods for solving linear and nonlinear systems. It also covers curve fitting (regression and interpolation), numerical differentiation and integration, and solving initial value problems for ordinary differential equations. Students will study the underlying algorithms for these methods and implement them using relevant programming languages.

Learning Materials

• Error analysis and Taylor series
• Finding the roots of equations in one variable
• Solving nonlinear systems
• Solving linear systems (slide)
• Curve fitting
  • Regression (slide)
  • Interpolation
• Numerical differentiation (slide)
• Numerical integration
• Initial value problems in ordinary differential equation

References

1. Burden, R.C., Faires J.D., Reynolds, A.C., (2010), Numerical Analysis, (9th Edition), Brooks/Cole Cengage Learning, Boston.
2. Chapra, S.C., and Canale, R.P., (2015), Numerical Methods for Engineers, (7th edition), McGraw-Hill Education.