Applied Mathematics: Body and Soul (Volume 3)

Calculus in Several Dimensions

Kimmo Eriksson, Donald Estep, C. Johnson

428 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

Vector-Valued Functions of Several Real Variables
Level Curves/Surfaces and the Gradient
Linearization and Stability of Initial Value Problems
Adaptive Solvers for IVPs
Lorenz and the Essence of Chaos*
The Solar System*
Optimization
The Divergence, Rotation and Laplacian
Meteorology and Coriolis Forces*
Curve Integrals
Double Integrals
Surface Integrals
Multiple Integrals
Gauss' Theorem and Green's Formula in R²
Gauss' Theorem and Green's Formula in R³
Stokes' Theorem
Potential Fields
Center of Mass and Archimedes' Principle*
Newton's Nightmare*
Laplacian Models
Chemical Reactions*
Calculus Tool Bag II
Piecewise Linear Polynomials in R² and R³
FEM for Boundary Value Problems in R² and R³
Inverse Problems
Optimal Control
Differential Equations Tool Bag
Applications Tool Bag
Analytic Functions
Fourier Series
Fourier Transforms
Analytic Functions Tool Bag
Fourier Analysis Tool Bag
Incompressible Navier-Stokes: Quick and Easy
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	428
Format	16 x 24
Couverture	Relié
Poids	835g
Intérieur	Noir et Blanc
EAN13	9783540008910