Applied Linear Algebra and Numerical Analysis

Course syllabus

Chapters, sections or pages refer to the Burden and Faires text book.

• Introduction to MATLAB
• Review of Taylor series (1.1)
• Computer arithmetic and errors (1.2)
• Root finding
  • Bisection method (2.1)
  • Fixed point iteration (2.2)
  • Newton's method and Secant method (2.3)
• Linear algebra
  • vectors, matrices, linear independence, column space, rank
  • Gaussian elimination (6.1)
  • Pivoting (6.2)
  • LU decomposition (6.5)
  • Newton's method for nonlinear systems (10.2)
  • vector and matrix norms (7.1)
  • eigenvalues and eigenvectors (7.2)
  • iterative methods (7.3)
• Interpolation, curve fitting, and least squares
  • Lagrange polynomisals (3.1)
  • Newton basis and divided differences (3.2)
  • Relation of Newton form to Taylor series
  • Piecewise polynomial interpolation, splines (3.4)
  • Least squares curve fitting (8.1)
• Numerical integration or quadrature
  • Piecewise polynomial interpolation and composite rules (4.3, 4.4)
  • Adaptive quadrature (4.6)
• Ordinary differential equations
  • The initial value problem (5.1)
  • Euler's method (5.2)
  • Taylor series methods (5.3)
  • Runge Kutta methods (5.4)