Applied Mathematics: Body and Soul: Volume 1: Derivatives and Geometry in R^3

Description

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 possibilitites 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. Front Matter....Pages I-1 What is Mathematics?....Pages 3-20 The Mathematics Laboratory....Pages 21-24 Introduction to Modeling....Pages 25-31 A Very Short Calculus Course....Pages 33-46 Natural Numbers and Integers....Pages 47-61 Mathematical Induction....Pages 63-70 Rational Numbers....Pages 71-86 Pythagoras and Euclid....Pages 87-102 What is a Function?....Pages 103-117 Polynomial functions....Pages 119-139 Combinations of functions....Pages 141-147 Lipschitz Continuity....Pages 149-164 Sequences and limits....Pages 165-184 The Square Root of Two....Pages 185-194 Real numbers....Pages 195-214 The Bisection Algorithm for f(x) = 0....Pages 215-220 Do Mathematicians Quarrel?....Pages 221-240 The Function y = x r ....Pages 241-244 Fixed Points and Contraction Mappings....Pages 245-263 Analytic Geometry in ℝ 2 ....Pages 265-312 Analytic Geometry in ℝ 3 ....Pages 313-343 Complex Numbers....Pages 345-353 The Derivative....Pages 355-376 Differentiation Rules....Pages 377-391 Newton’s Method....Pages 393-401 Galileo, Newton, Hooke, Malthus and Fourier....Pages 403-416 Back Matter....Pages 417-425