Numerical methods for engineers
Undergraduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Numerical Methods for Engineers — scope drawn from open numerical methods engineering texts and typical US numerical methods syllabi.
Error analysis and root finding
- Sources of error — Sources of error
- Propagation — Propagation
- Taylor series review for error estimates — Taylor series review for error estimates
- Bisection and Newton–Raphson methods — Bisection and Newton–Raphson methods
- Secant methods — Secant methods
- Fixed-point iteration — Fixed-point iteration
- Convergence criteria — Convergence criteria
- Systems of nonlinear equations (Newton's method introduction) — Systems of nonlinear equations (Newton's method introduction)
Linear algebra computations
- Gaussian elimination — Gaussian elimination
- Pivoting strategies — Pivoting strategies
- LU decomposition and matrix inversion — LU decomposition and matrix inversion
- Condition number and ill-conditioning — Condition number and ill-conditioning
- Iterative methods: Jacobi, Gauss–Seidel, and SOR — Iterative methods: Jacobi, Gauss–Seidel, and SOR
- Eigenvalue problems — Eigenvalue problems
- QR overview — QR overview
Numerical calculus
- Numerical differentiation — Numerical differentiation
- Richardson extrapolation — Richardson extrapolation
- Newton–Cotes formulas — Newton–Cotes formulas
- Simpson's rules — Simpson's rules
- Gaussian quadrature (introduction) — Gaussian quadrature (introduction)
- Numerical solution of ODEs — Numerical solution of ODEs
- Runge–Kutta methods — Runge–Kutta methods
- Stiff equations — Stiff equations
- Stability of methods (introduction) — Stability of methods (introduction)
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Error analysis and root finding
Sources of error
Coming soon - Linear algebra computations
Gaussian elimination
Coming soon - Numerical calculus
Numerical differentiation
Coming soon
Notes
Undergraduate Numerical Methods for Engineers — scope drawn from open numerical methods engineering texts and typical US numerical methods syllabi. Topic outline: `content/topics/undergraduate/numerical_methods_eng.json`.