Standard syllabus
Numerical methods for engineers · Undergraduate · Math
Topics
Error analysis and root finding
- Sources of error: truncation, round-off, and propagation
- Taylor series review for error estimates
- Bisection, Newton–Raphson, and secant methods
- Fixed-point iteration and convergence criteria
- Systems of nonlinear equations (Newton's method introduction)
Linear algebra computations
- Gaussian elimination and pivoting strategies
- LU decomposition and matrix inversion
- Condition number and ill-conditioning
- Iterative methods: Jacobi, Gauss–Seidel, and SOR
- Eigenvalue problems: power method and QR overview
Numerical calculus
- Numerical differentiation and Richardson extrapolation
- Newton–Cotes formulas: trapezoidal and Simpson's rules
- Gaussian quadrature (introduction)
- Numerical solution of ODEs: Euler and Runge–Kutta methods
- Stiff equations and stability of methods (introduction)
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$1,162 · Numerical methods for engineers · 18 tutoring hrs
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