This course includes application of the following methods: elements of error analysis, real roots of an equation, polynomial approximation by finite difference and least square methods, interpolation, quadrature, numerical solution of ordinary differential equations, and numerical solutions of systems of linear equations. The student should expect to program a computer in addition to using a graphing calculator.

### Prerequisites

MATH& 163 with grade of 2.0 or higher; or instructor permission

Quarters Offered

Winter

Course Outcomes

Upon successful completion of the course, students should be able to demonstrate the following knowledge or skills:

- Write and document effective Matlab scripts involving logical and iterative flow control and file input and output.
- Utilize the vector/matrix paradigm underlying Matlab to write efficient commands to manipulate data and implement numerical solution algorithms.
- Produce effective plots of numerical data using Matlab’s various data visualization functions.
- Explain the consequences of finite precision and the inherent limits of the numerical methods considered.
- Select appropriate numerical methods to apply to various types of problems in engineering and science in consideration of the mathematical operations involved, accuracy requirements, and available computational resources.
- Demonstrate they understand the mathematics concepts underlying the numerical methods considered.
- Demonstrate understanding and implementation of numerical solution algorithms applied to the following classes of problems:
- Finding roots of equations
- Solving systems of algebraic equations
- Curve fitting
- Interpolation
- Numerical differentiation of data and functions
- Numerical integration of data and functions
- Solutions of ordinary differential equations

Course Content Outline

- MATLAB Fundamentals
- Structured Programming in MATLAB (Loops and Logic)
- Measures of Numerical Error
- Root Finding Algorithms (single nonlinear algebraic equations)
- Linear Systems
- Gauss Elimination
- LU Factorization
- Nonlinear Systems of Algebraic Equations
- Curve-Fitting: Least-Squares Regression
- General Linear Least-Squares
- Polynomial Interpolation
- Numerical Integration: Newton-Cotes Methods
- Numerical differentiation
- Ordinary Differential Equations
- System of Ordinary Differential Equations
- Boundary Value Problems

Department Guidelines

PO5 should be assessed: Students will be able to solve problems by gathering, interpreting, combining and/or applying information from multiple sources.