Applied Mathematics: Body and Soul [Volume 1]: Derivatives and Geometry in R3 (Repost)

This volume presents basics of Calculus starting with the construction of the natural, rational, real and complex numbers, and proceeding to analytic geometry in two and three space dimensions, Lipschitz continuous functions and derivatives, together with a variety of applications.

This volume is dedicated to derivatives and geometry and gives a modern version of calculus and linear algebra computational methods and a variety of applications starting at a basic undergraduate level.

Applied Mathematics: Body&Soul is a mathematics education reform program including a series of books, together with associated educational material
The Body&Soul series of books presents CC in a synthesis of computational mathematics (Body) and analytical mathematics (Soul) including applications.

AM I-III contains a synthesis of calculus and linear algebra including computational methods and a variety of applications.
AM IV - offers a continuation with aseries of volumes dedicated to specific areas of applications such as Dynamical Systems and Fluid Mechanics

Contents Volume 1
Preface
Acknowledgment
1 What is Mathematics?
2 The Mathematics Laboratory
3 Introduction to Modeling
4 A Very Short Calculus Course
5 Natural Numbers and Integers
6 Mathematical Induction
7 Rational Numbers
8 Pythagoras and Euclid
9 What is a Function?
10 Polynomial functions
11 Combinations of functions
12 Lipschitz Continuity
13 Sequences and limits
14 The Square Root of Two
15 Real numbers
16 The Bisection Algorithm for f(x) = 0
17 Do Mathematicians Quarrel?
18 The Function y=x^r
19 Fixed Points and Contraction Mappings
20 Analytic Geometry in R^2
21 Analytic Geometry in R^3
22 Complex Numbers
23 The Derivative
24 Differentiation Rules
25 Newton's Method
26 Galileo, Newton, Hooke, Malthus and Fourier
References
Index

Volume 2: Integrals and Geometry in Rn:


Volume 3: Calculus in Several Dimensions:


Volume 4: Computational Turbulent Incompressible Flow: