Numerical Methods Concepts
Linear algebra, integration, differentiation, optimisation, ODEs, FFTs and simulation — what the libraries compute.
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Sub-topics (11)
Linear Algebra and Matrix Operations
Solve systems of equations, invert matrices and decompose them with numpy.linalg and scipy.linalg.
Eigenvalues and Eigenvectors
Find $\lambda$ and $v$ with $Av = \lambda v$ — used in vibration, stability and PCA.
Numerical Integration
Approximate definite integrals with the trapezoid rule, Simpson's rule or adaptive quadrature.
Numerical Differentiation
Estimate derivatives from data with finite differences.
Optimization (Numerical)
Find minima, maxima and best-fit parameters with scipy.optimize.
Differential Equations
Simulate systems described by ODEs with solve_ivp.
Fourier Transforms in Python
Compute frequency spectra with numpy.fft / scipy.fft.
Symbolic Mathematics
Manipulate exact formulas — simplify, differentiate, integrate and solve symbolically.
Monte Carlo Methods
Estimate quantities by random sampling — tolerance analysis, risk, integrals.
Random Processes and Simulation
Model noise, queues and stochastic systems; simulate before you build.
Graph Theory and Computational Geometry
Networks (NetworkX) and shapes (Shapely, SciPy spatial) as computational objects.
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