Floating-point arithmetic and error analysis. Solution of non-linear equations. Polynomial interpolation. Numerical integration and differentiation. Data fitting. Solution of linear algebraic systems. Initial and boundary value problems of ordinary differential equations.

After completion of the course, the students should be able to:

- Use Taylor Series to approximate functions, evaluate the approximation errors and estimate their upper bounds.
- Understand and program algorithms to locate the approximate roots of equations.
- Understand and program algorithms to numerically solve linear systems of equations.
- Learn how to smooth collected engineering data using the least squares method.
- Use polynomials to interpolate collected precise (Note: Interpolation applies to precise data while the least-squares method applies to data exhibiting a significant degree of error or scatter.) engineering data or approximate function.
- Understand and program algorithms to evaluate the derivative or the integral of a given function, evaluate the approximation error involved and estimate its upper bound.
- Understand and program algorithms to solve engineering ordinary differential equations (ODEs) or partial differential equations (PDEs).
- Understand relationships among methods, algorithms, and computer errors.
- Apply numerical and computer programming tools to solve common engineering problems.