Applied Linear Algebra and Numerical Analysis

(Tentative) Course syllabus

Chapters and sections refer to the Mathews and Fink textbook.

• Introduction to MATLAB
• Computer arithmetic and errors (1.3)
• Solution of Nonlinear Equations
  • Fixed Point Iteration (2.1)
  • Bisection Method (2.2)
  • Newton's method and Secant methods (2.4)
• Linear algebra
  • vectors, matrices and related terms (3.1-3.3)
  • vector and matrix norms
  • Gaussian elimination (3.4)
  • Factorization/Decomposition (3.5)
  • Iteration (3.6)
  • Newton's method for nonlinear systems (3.7)
• Interpolation
  • Taylor series (4.1)
  • Lagrange polynomials (4.3)
  • Newton polynomials (4.4)
• Curve fitting and least squares
  • Least squares curve fitting (5.1)
  • Curve fitting with arbitrary basis functions. (5.2)
  • Piecewise polynomial fits (5.3)
• Numerical integration (quadrature)
  • Introduction (7.1)
  • Composite Trapazoidal and Simpson's rules (7.2)
  • Adaptive quadrature (7.4)
• Ordinary differential equations
  • Introduction (9.1)
  • Euler's method (9.2)
  • Taylor series methods (9.4)