Applied Mathematics: Body and Soul (Volume 1)

Derivatives and Geometry in R3

Kimmo Eriksson, Donald Estep, C. Johnson

426 pages, parution le 29/10/2003

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Résumé

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.

Volume I (Derivatives and Geometry in R³) 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.

Volume II (Integrals and Geomtery in Rⁿ) develops the Riemann integral as the solution to the problem of determining a function given its derivative, and proceeds to generalizations in the form of initial value problems for general systems of ordinary differential equations, including a variety of applications. Linear algebra including numerics is also presented.

Volume III (Calculus in Several Dimensions) presents Calculus in several variables including partial derivatives, multi-dimensional integrals, partial differential equations and finite element methods, together with a variety of applications modeled as systems of partial differential equations. The authors are leading researchers in Computational Mathematics who have written various successful books. Further information on Applied Mathematics: Body and Soul can be found at http://www.phi.chalmers.se/bodysoul/.

Written for:
Undergraduate students in mathematics, physics, chemistry and engineering

Derivatives and Geometry in R³
What is Mathematics?
The Mathematics Laboratory
Introduction to Modeling
A Very Short Calculus Course
Natural Numbers and Integers
Mathematical Introduction
Raional Numbers
Pythagoras and Euclid
What is a Function?
Polynomial Functions
Combination of Functions
Lipschitz Continuity
Sequences and Limits
The Square Root of Two
Real Numbers
The Bisection Algorithm for f(x) = 0
Do Mathematicians Quarrel?
The Function y = x^r
Fixed Points and Construction Mappings
Analytic Geometry in R²
Complex Numbers
The Derivative
Differentiation Rules
Newton's Method
Galileo, Newton, Malthus and Fourier
References
Index

L'auteur - Kimmo Eriksson

is a professor of applied mathematics at Malardalen University in Sweden. He is the author of several mathematical textbooks and popular articles in Swedish, as well as the opera Kurfursten with music by Jonas Sjostrand. He is a member of the Vastmanland Academy (Sweden).

L'auteur - Donald Estep

Estep, Donald Colorado State University, Fort Collins, CO, USA

Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Kimmo Eriksson, Donald Estep, C. Johnson
Parution	29/10/2003
Nb. de pages	426
Format	16 x 24
Couverture	Relié
Poids	820g
Intérieur	Noir et Blanc
EAN13	9783540008903