STEM / applied
Numerical analysis · Undergraduate · Math
Learning objectives from the Numerical analysis syllabus, grouped by unit. Click an objective for study materials.
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
Learning objectives
Click an objective for study materials.
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)
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
Multi-Unit Problems
Course-level sets that combine skills across study units (coming soon).
Browse Multi-Unit ProblemsWhat each unit includes
Open a unit below for full materials. Typical resources:
- Study guide
- Exam Strategy
- Common Mistakes
- Worksheets
- Word problems
- Mixed Practice
- Multi-Unit Problems
- Review
- Practice test
- Answer key
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
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