Numerical analysis
Undergraduate · Math
Syllabus focus
Standard syllabus · STEM / applied
Pricing calculator
Choose materials, tutoring, or both — or book a single session as needed. Customize your plan on the subscribe page.
$1,162 · Numerical analysis · 18 tutoring hrs
Study guides, worksheets, reviews, practice tests, and answer keys for 1 class. 18 tutoring hours (1 hr / week · semester). Bundle discount applied vs buying separately. Pay in full via Zelle or Venmo.
Topics typically covered
Standard syllabus
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
STEM / applied
Differential equations and software
- Euler's method and improved Euler for IVPs
- Runge–Kutta methods (RK4) for ODE systems
- Implementation in MATLAB, Python, or similar environments
- Adaptive step-size control (conceptual overview)
- Applications to physical models from science and engineering
Practical computation
- Least squares fitting and normal equations
- QR factorization overview and least-squares solvers
- Eigenvalue computation: power method and inverse iteration
- Error propagation in engineering calculations
- Validation and verification of numerical results
Notes
Topics reflect common numerical analysis syllabi at US colleges and universities. Applied sections emphasize implementation and modeling; theoretical error analysis depth varies by program.