645:571 Computational Mathematics I / 640:357 Introduction to Computational Mathematics - Fall 2020

Course Outline:
  1. Introduction
    1. Applications
    2. Internal Representation of Numbers
    3. Errors
  2. Interpolation
    1. Newton Form
    2. LagrangeForm
    3. Error Formula for Polynomial Interpolation
    4. Hermite Interpolation
    5. Piecewise Polynomial Interpolation
  3. Roots of Equations
    1. Bisection Method
    2. Method of False Position
    3. Secant Method
    4. Newton's Method
    5. Fixed-Point Iteration
    6. Systems of Nonlinear Equations
    7. Unconstrained Optimization
      1. The Method of Steepest Descent (Gradient Method)
      2. Conjugate Gradient Method
      3. DFP Method
      4. BFGS Method
  4. Numerical Integration
    1. The Definite Integral and the Fundamental Theorem of Calculus
    2. Midpoint Rule
    3. Trapezoidal Rule
    4. Simpson's Rule
    5. Richardson Extrapolation
    6. Romberg Integration
    7. Gaussian Quadrature
    8. Improper Integrals
    9. Multiple Integrals
  5. Numerical Differentiation