Elementary Numerical Analysis

In this course, we will cover the fundamentals of floating-point arithmetic and then discuss common basic numerical methods for solving nonlinear equations, interpolating functions, and approximating integrals. Students will learn how to implement an algorithm to solve a numerical analysis problem.

Features of floating-point arithmetic: relative precision and the IEEE format.

  Solving Nonlinear Equations f(x) = 0

• Intermediate Value Theorem, Dichotomy
• Contracting Fixed-Point Method. Convergence Rate.
• Newton's method and the secant method. Convergence rate.

 Polynomial interpolation.

• Existence and Uniqueness of the Interpolation Polynomial
• interpolation error, generalized finite increments theorem
• Runge phenomenon
• Lagrange polynomial, Newton polynomial, and divided differences
• Application to Numerical Differentiation
• Hermite interpolation

  Digital Integration.

• Newton-Cotes methods (midpoint, trapezoidal, Simpson, etc.)
• order of a quadrature method. Estimation of
• Monte Carlo method
• Gauss's method: optimal order, Gauss-Legendre example

The first-year analysis courses (HAX103X and HAX201X) and some basic concepts of linear algebra (HAX102X) are sufficient to take this course unit.

Recommended prerequisites: L1 Math

Hourly volumes*:

            CM: 12

            TD: 9

            TP: 9

            Lot: