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Welcome to FAEN 301!

Course Objective:

• Introduce MATLAB as a technical computing environment and mathematical software for engineers and scientists
• Teach important aspects of mathematical modeling using differential equations and associated numerical methods for solutions.
• Enhance students' programming skills using the MATLAB environment to implement numerical method algorithms
• Teach the use of MATLAB as a tool (using built-in functions) for solving mathematical problems that require numerical solutions and introduce the simulation tools of MATLAB

Course Topics:

1. Background for matrix and vector operations;
2. Introduction to numerical methods; Systems of linear equations: Unsolvable and ill-conditioned systems, condition number
3. Solving systems of Linear Equations: Background, Gauss elimination method, Pivoting, Gauss-Jordan method
4. Solving systems of Linear Equations: LU decomposition method, inverse of a matrix, brief MATLAB review
5. Solving systems of Linear Equations: Iterative methods, use of MATLAB built-in functions
6. Matrix eigenvalues and eigenvectors; Power method
7. Curve Fitting and interpolation; interpolation using a single polynomial, Lagrange and Newton’s polynomials, Piecewise interpolation, linear, quadratic, and cubic splines, use of MATLAB built-in functions for curve fitting and interpolation
8. Nonlinear equations; background, estimation of error; Solving nonlinear equations; Fixed-point iteration method, Bisection method, Regula Falsi method, Secant method
9. Multivariate systems of nonlinear equations; Newton’s method, use of MATLAB built-in functions; equations with multiple solutions
10. Numerical differentiation; Differentiation using Lagrange polynomials, use of MATLAB built-in functions for numerical differentiation
11. Numerical differentiation; Richardson’s extrapolation, error in numerical differentiation, numerical partial differentiation
12. Numerical Integration; background, rectangle and midpoint methods, trapezoidal method, Simpson’s methods; use of MATLAB built-in functions for integration, Richardson extrapolation, Romberg integration
13. ODE initial value problems; Runge-Kutta methods, multistep methods, predictor-corrector methods, system of first-order ODEs, higher-order IVP; local truncation error in 2nd-order Runge-Kutta method, step size for desired accuracy, stability, stiff ODEs