# MTH203 Numerical Methods (8)

This subject introduces students to a range of frequently used numerical algorithms. Consideration is given to the choice, theory, convergence, stability and implementation of the numerical procedures studied. Topics include error analysis, evaluation of functions, solution of nonlinear equations, difference calculus, curve fitting and data smoothing, numerical integration, numerical solution of differential equations, and systems of linear equations. Students are encouraged to code and test their numerical algorithms using a range of computational environments.

## Availability

Session 2 (60)
Online
Wagga Wagga Campus

Continuing students should consult the SAL for current offering details: MTH203. Where differences exist between the Handbook and the SAL, the SAL should be taken as containing the correct subject offering details.

## Subject Information

HD/FL

One session

##### School

School of Computing and Mathematics

MTH102

## Learning Outcomes

##### Upon successful completion of this subject, students should:
• be able to determine the utility and limitations of numerical solutions;
• be able to estimate the various types of errors inherent in all experimental data and numerical calculations;
• be able to use numerical algorithms in conjunction with a computer to deal with a wide range of problems ranging from the computation of theoretical solutions to the practical analysis of experimental data.

## Syllabus

##### This subject will cover the following topics:
• Error analysis, round off errors, truncation errors, inherent errors, error propagation.
• Evaluation of functions, Taylor series, Chebyshev series, economisation of Taylor series, rational approximations and continued fractions.
• Solution of nonlinear equations, graphical solution, bisection method, chord method, Newton's method, direct iteration, complex roots.
• Difference calculus, extrapolation of data, interpolation of data, experimental data, differentiation of discrete data and detection of errors in data.
• Curve fitting and data smoothing, polynomial curve fitting, least squares curve fitting, smoothing of experimental data.
• Numerical integration, difference methods, trapezoidal rule, Simpson's rule, Gauss quadrature.
• Differential equations, variables separable, homogeneous equations, exact equations, first order linear equations, second order linear equations with constant coefficients.
• Numerical solution of differential equations, Taylor series method, Euler's method, Runge-Kutta methods, predictor-corrector methods.
• Systems of linear equations, Gaussian elimination, Gauss pivotal condensation, Gauss-Seidel iteration.

The information contained in the CSU Handbook was accurate at the date of publication: July 2020. The University reserves the right to vary the information at any time without notice.

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