MATH 1501: WEEK 7

Topics for this week are:

• Implicit differentiation
• Fixed points by iteration
• Newton's method

Text coverage:     Sections 3.7 - 3.9 of Salas, Hille, and Etgen

Online resources:

• Online notes
  • Notes on fixed point problems. These notes use a java applet to illustrate the solution of fixed point problems by iteration. It includes a thorough analysis of the problem of determining when to stop the iteration, and includes some suggest problems.
  • Some ``related rates'' problems.
  • Notes on convergence of Newton's method.
• Maple worksheets
  • Solving Equations: This worksheet is about continuity--the intermediate value property of continuous functions, etc. Equations are solved using "bisection," regula falsi, and Newton's method. This assignment help you understand the Maple procedures.
  • Solving f(a) = b: The Method of Bisection: The Method of Bisection for finding roots of an equation is not conceptually hard. It has two especially good features: first, it is easily understood, and second, it can provide initial guesses for methods which might converge faster -- such as Newton's Method. We illustrate the method and provide an example to show that a little care must be taken.

---

Last Modified: . School of Mathematics, Georgia Institute of Technology.