What you will learn
- Master root-finding algorithms (bisection, Newton-Raphson, secant methods)
- Learn numerical differentiation/integration techniques
- Solve systems of linear equations using iterative methods
- Implement numerical solutions to ODEs/PDEs
- Analyze truncation errors and algorithm stability
- Apply methods using MATLAB/Python in engineering contexts
Program Overview
Numerical Foundations
⏱️ 3-4 weeks
- Floating-point arithmetic and error analysis
- Condition numbers and algorithm stability
- Taylor series approximations
- Convergence criteria
Equation Solving
⏱️ 4-5 weeks
- Nonlinear equation solvers
- Linear system methods (Gauss-Seidel, Jacobi)
- Eigenvalue numerical computation
- Sparse matrix techniques
Calculus Applications
⏱️ 5-6 weeks
- Numerical differentiation (finite differences)
- Integration (trapezoidal, Simpson’s, Romberg)
- Monte Carlo methods
- Fourier transforms
Differential Equations
⏱️ 5-7 weeks
- ODE solutions (Euler, Runge-Kutta)
- Boundary value problems
- Finite difference methods for PDEs
- Heat/fluid flow applications
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Job Outlook
- Critical for:
- Mechanical/Aerospace Engineers (75K130K)
- Computational Scientists (90K160K)
- Quantitative Analysts (100K200K+)
- Finite Element Analysts (85K140K)
- Industry Demand:
- 68% of engineering roles require numerical methods (2023 survey)
- Key skill for CAE, CFD, and FEA positions
Specification: Numerical Methods for Engineers
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