Course 17 | Core
Numerical Methods for Mechanical Engineers
Use computation for roots, interpolation, curve fitting, integration, ODEs, error, convergence, and engineering calculation checks.
Course snapshot
- Purpose
- Numerical methods supports dynamics, heat transfer, controls, FEM, CFD, optimization, and modern engineering simulation with checked computation.
- Next in the guided sequence
- Used in Career Directions
How to study this course
- Define the mathematical problem
- Choose a numerical method
- Implement carefully
- Test on a known case
- Check error, convergence, stability, and units
How this course is designed
Every method, with its error
A numerical answer without an error estimate is unfinished. Each module pairs a method with the way to bound or estimate its error, the habit that separates engineering from guesswork.
Methods in the right order
The course moves from error and roots through linear systems and curve fitting to integration, differentiation, and differential equations, each building on the last toward the solvers behind FEM and CFD.
Worked numbers throughout
Every module includes two fully worked examples with verified arithmetic, tested against a known result so you see the method converge and the error shrink.
The 10 modules
01 | Module
Modeling, Error, and Taylor Series
True and relative error, roundoff and truncation, and the Taylor series.
02 | Module
Roots of Equations: Bracketing Methods
Bisection, false position, and the guaranteed error bound.
03 | Module
Roots of Equations: Open Methods
Newton-Raphson, the secant method, and quadratic convergence.
04 | Module
Systems of Linear Equations
Gauss elimination, back substitution, and LU decomposition.
05 | Module
Iterative Methods and Conditioning
Gauss-Seidel iteration, diagonal dominance, and the condition number.
06 | Module
Curve Fitting: Least-Squares Regression
The least-squares line, the coefficient of determination, and linearization.
07 | Module
Interpolation and Splines
Newton divided differences, the Lagrange form, and splines.
08 | Module
Numerical Integration
The trapezoidal rule, Simpson's rules, and integration error.
09 | Module
Numerical Differentiation
Finite differences, the order of accuracy, and Richardson extrapolation.
10 | Module
Numerical Solution of ODEs
Euler's method, Heun and Runge-Kutta, and local versus global error.