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AuthorEriksson, Kenneth. author
TitleApplied Mathematics: Body and Soul [electronic resource] : Volume 1: Derivatives and Geometry in IR3 / by Kenneth Eriksson, Donald Estep, Claes Johnson
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2004
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Descript XLIII, 428 p. online resource


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 Newtonโ{128}{153}s Method -- 26 Galileo, Newton, Hooke, Malthus and Fourier -- References

Mathematics Chemometrics Matrix theory Algebra Mathematical analysis Analysis (Mathematics) Computer mathematics Physics Applied mathematics Engineering mathematics Mathematics Analysis Linear and Multilinear Algebras Matrix Theory Computational Mathematics and Numerical Analysis Math. Applications in Chemistry Appl.Mathematics/Computational Methods of Engineering Mathematical Methods in Physics


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