Applied Mathematics: Body and Soul Volume 1: Derivatives and Geometry in IR3

Applied Mathematics: Body & Soul is a mathematics education reform project developed at Chalmers University of Technology and includes a series of volumes and software. The program is motivated by the computer revolution opening new possibilities of computational mathematical modeling in mathematics, science and engineering. It consists of a synthesis of Mathematical Analysis (Soul), Numerical Computation (Body) and Application. Volumes I-III present a modern version of Calculus and Linear Algebra, including constructive/numerical techniques and applications intended for undergraduate programs in engineering and science. Further volumes present topics such as Dynamical Systems, Fluid Dynamics, Solid Mechanics and Electro-Magnetics on an advanced undergraduate/graduate level.

The authors are leading researchers in Computational Mathematics who have written various successful books.

Volume 1.- 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 = xr.- 19 Fixed Points and Contraction Mappings.- 20 Analytic Geometry in ?2.- 21 Analytic Geometry in ?3.- 22 Complex Numbers.- 23 The Derivative.- 24 Differentiation Rules.- 25 Newton’s Method.- 26 Galileo, Newton, Hooke, Malthus and Fourier.- References.