A First Look at Numerical Functional Analysis

by W. W. Sawyer

Introduction
This is an excellent textbook on more theoretical aspects of numerical analysis, yet presented with many practical examples. The problems are enjoyable and interesting. I would recommend it highly. Currently, I am working with Delbert Franz on typesetting a complete solution manual to this book. You can find the most recent version below.

Status
Currently I am working on finishing the solutions for Chapter 6 which introduced the modified Newton-Raphson iterations in general function spaces. Delbert has provided solutions and commentary to the problems in the other chapters.

• The Most Recent Solution Manual
• My original handwritten notes can also be found here
  • Download Problem Solutions (Part 1 of 1).

Chapter 1 (A First Course in Functional Analysis):

• There were no computational problems for this chapter
Chapter 2 (Old Ideas in New Contexts):

• newtons_method_page_11.nb (Newton's method with various starting points ... Mathematica)
  
• newtons_method_page_11.py (Newton's method with various starting points ... Python)
  
Chapter 3 (Iteration and Contraction Mappings):

• There were no computational problems for this chapter
Chapter 4 (Minkowski Spaces):

• page43.m (plots and integrates the funcion g_n(x) = (n^2 x)^n e^{-n^2 x} for various n ... Matlab)
  
• page43.py (integrates the funcion g_n(x) = (n^2 x)^n e^{-n^2 x} for various n ... Python)
  
Chapter 5 (Linear Operators and their Norms):

• There were no computational problems for this chapter
Chapter 6 (Differentiation and Integration):

• chap_6_sec_1_prob_2.py (newtons method for f(x)=sin(x)+0.5 x ... Python)
  
• chap_6_sec_4_prob_2.m (numerical newtons method for a functional equation ... Matlab)
  
• chap_6_sec_4_prob_2.nb (newtons method for a functional equation ... Mathematica)
  
• chap_6_sec_6_page_111.nb (newtons method for the example differential equation ... Mathematica)
  
• chap_6_sec_6_prob_1.m (numerical Newton-Raphson method)
  
• chap_6_sec_6_prob_2.nb (some algebra for this problem)
  
• chap_6_sec_6_prob_2.m (the numerical Newton-Raphson method for this problem)
  
• chap_6_sec_6_prob_3.nb (some algebra for this problem)
  
• chap_6_sec_6_prob_3.m (the numerical Newton-Raphson method for this problem)
  
• chap_6_sec_6_prob_5.nb (the algebraic Newton-Raphson method for this problem)
  
• chap_6_sec_6_prob_6.nb (the algebraic Newton-Raphson method for this problem)
  
Chapter 7 (Further Developments):

• There were no computational problems for this chapter
Chapter 8 (Euclidean Space):

• chap_8_sec_2_prob_1.m (a least squares approximation to an exponential)
  
• chap_8_sec_2_prob_2.m (a least squares approximation to the cosign function)
  
• integrals_on_page_138.nb (calcuation of some integrals with Mathematica)
  
• chap_8_sec_4_prob_1_integrals.nb (Fourier series of x and x^3)
  
• chap_8_sec_4_prob_1_evaluation.m (comparions with the Fourier series of x and x^3)
  
Chapter 9 (Some Tools of the Trade):

• There were no computational problems for this chapter
Chapter 10 (Some Bridgeheads):

• There were no computational problems for this chapter