The Calculus - A Genetic Approach

by Otto Toeplitz

Introduction
This is an excellent extension textbook to use as a supplement in a first or second year calculus class. The problems are especially enjoyable and have the flavor of the type of problems one might find in mathematical competitions. I would recommend it to anyone who desires to develop stronger mathematical maturity beyond introductory calculus classes. Readers can see what others have said about this book here. Originally these notes and solutions were written in PDF (using the mathematical typesetting language LaTeX). I converted the PDF format to a format I thought more people would find easier to read. You can preview and buy a kindle version of the book here.

• exercise_1_1.R (implements the cube root of 7 using Taylor series)
  
• exercise_3_6.R (plots the function -d/(2+d) as a function of d)
  
• exercise_4_1.R (plots the sequence of partial sums for some parts)
  
• exercise_5_1.R (plots the suggested functions)
  
• exercise_11_3.R (iterates the arithmetic-harmonic mean sequence)