Standard syllabus
Numerical analysis · Undergraduate · Math
Topics
Floating-point and error analysis
- Floating-point representation and machine epsilon
- Round-off error, truncation error, and stability
- Condition numbers and ill-conditioned problems
- Norms for vectors and matrices (introduction)
- Convergence rates for iterative methods
Root finding and interpolation
- Bisection, fixed-point iteration, and Newton's method
- Secant method and convergence analysis (informal)
- Lagrange and Newton interpolation polynomials
- Runge phenomenon and piecewise polynomial interpolation
- Splines (linear and cubic) and their continuity conditions
Numerical linear algebra and integration
- Gaussian elimination with partial pivoting
- LU factorization and its use in solving Ax = b
- Iterative methods: Jacobi and Gauss–Seidel (introduction)
- Numerical differentiation: forward, backward, and central differences
- Numerical integration: trapezoidal and Simpson's rules; composite formulas
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$1,162 · Numerical analysis · 18 tutoring hrs
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