Numerical methods for engineers
Undergraduate · Math
Syllabus focus
Standard syllabus · STEM / applied
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$1,162 · Numerical methods for engineers · 18 tutoring hrs
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Topics typically covered
Standard syllabus
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)
STEM / applied
Engineering software and projects
- Implementation in MATLAB, Python (NumPy/SciPy), or engineering platforms
- Simulation of physical systems governed by ODEs
- Finite difference solutions for 1D heat and wave equations
- Least squares curve fitting to experimental data
- Verification against analytical benchmarks
Professional practice
- Documentation and reproducibility of numerical studies
- Choosing step sizes and convergence tolerances
- Interpreting numerical results in design contexts
- Introduction to finite element software workflows
- Error budgets in measurement and simulation pipelines
Notes
Topics reflect common numerical methods syllabi for engineering majors at US universities. Content overlaps with numerical analysis but emphasizes implementation and engineering applications over formal proofs.