Mathematical Tripos IB Numerical Analysis (Lent 2019)

Lecture notes

• Lecture 1: Interpolation
• Lecture 2: Finite differences and Newton's interpolation formula
• Lecture 3: Orthogonal polynomials
• Lecture 4: Least-squares polynomial fitting and Gaussian quadrature
• Lecture 5: Gaussian quadrature (continued) and Peano kernel theorem
• Lecture 6: Peano kernel theorem (continued) and Euler's method for ODEs
• Lecture 7: Multistep methods for ODEs
• Lecture 8: Convergence of multistep methods
• Lecture 9: Runge-Kutta methods
• Lecture 10: Stiffness and linear stability domains
• Lecture 11: Implementation of ODE methods: error control
• Lecture 12: LU decomposition
• Lecture 13: Pivoting in LU factorization, symmetric matrices and LDL^T factorization
• Lecture 14: LU factorization for sparse matrices; QR factorization
• Lecture 15: QR factorization: Gram-Schmidt algorithm and Givens algorithm
• Lecture 16: QR factorization: Householder reflections; least-squares

Example sheets

• Example sheet 1
• Example sheet 2
• Example sheet 3

Other resources

• Matlab demos
• Lecture notes for the same course by Dr. Stephen Cowley [also inspired by the 2010 edition]
• The definition of numerical analysis by L. N. Trefethen
• Top ten algorithms of the 20th century, by Barry Cipra