Numerical analysis
Undergraduate · Math
Syllabus focus
Topics typically covered
Click a topic for the full text and related unit practice.
Undergraduate Numerical Analysis — scope drawn from open numerical analysis texts (e.g. Heath / Sauer-style OER mirrors) and typical US numerical analysis syllabi.
Floating-point and error analysis
- Floating-point representation — Floating-point representation
- Machine epsilon — Machine epsilon
- Round-off error and truncation error — Round-off error and truncation error
- Stability — Stability
- Condition numbers — Condition numbers
- Ill-conditioned problems — Ill-conditioned problems
- Norms for vectors — Norms for vectors
- Matrices (introduction) — Matrices (introduction)
- Convergence rates for iterative methods — Convergence rates for iterative methods
Root finding and interpolation
- Bisection and fixed-point iteration — Bisection and fixed-point iteration
- Newton's method — Newton's method
- Secant method — Secant method
- Convergence analysis (informal) — Convergence analysis (informal)
- Lagrange and Newton interpolation polynomials — Lagrange and Newton interpolation polynomials
- Runge phenomenon — Runge phenomenon
- Piecewise polynomial interpolation — Piecewise polynomial interpolation
- Splines (linear and cubic) and their continuity conditions — Splines (linear and cubic) and their continuity conditions
Numerical linear algebra and integration
- Gaussian elimination with partial pivoting — Gaussian elimination with partial pivoting
- LU factorization — LU factorization
- Its use in solving Ax = b — Its use in solving Ax = b
- Iterative methods — Iterative methods
- Gauss–Seidel (introduction) — Gauss–Seidel (introduction)
- Numerical differentiation — Numerical differentiation
- Central differences — Central differences
- Numerical integration — Numerical integration
- Simpson's rules — Simpson's rules
Study units
Each unit includes a study guide, worksheets, review, practice test, and answer key. One unit is free; subscribe for the full class.
- Floating-point and error analysis
Floating-point representation
Coming soon - Root finding and interpolation
Bisection and fixed-point iteration
Coming soon - Numerical linear algebra and integration
Gaussian elimination with partial pivoting
Coming soon
Notes
Undergraduate Numerical Analysis — scope drawn from open numerical analysis texts (e.g. Heath / Sauer-style OER mirrors) and typical US numerical analysis syllabi. Topic outline: `content/topics/undergraduate/numerical_analysis.json`.