MATH 2601: WEEK 12

Topics for this week are:

• Linear approximation of functions in several variables
• Gradient, Jacobian
• Chain rule
• Newton's iteration in several variables

Text coverage:

    Sec 15.1-15.3 from [S.H.E], Web-note: Note on chain rule with the Jacobian matrix and Newton's method

Online resources:

• Online notes
  • Web note on chain rule with the Jacobian matrix and Newton's method
  • Note on Convergence of Newton's Method in one variable (by E. Carlen)
• Answers to selected problems
• Maple Worksheets
  • Gradients (by J. A. Ziegler)
  • Directional derivatives (by J. A. Ziegler)
  • Linearization (by J. A. Ziegler)
  • Newton's method (by J. A. Ziegler)

Assignment for this week:

• Problems:
  • Section 15.1: 3, 9, 27
  • Section 15.2: 3, 13, 19, 23, 25, 29, 33, 37
  • Section 15.3: 7, 19, 25, 31
  • Problems on Jacobians and Newton iteration
• Computer project: Fractals with Newton iteration If you are really smart, then you can write a program which is flexible enough to deal with arbitrary input polynomials (then you need a subroutine which first turns a complex polynomial into a system of two real equations then it computes the Jacobian of this system)

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