Applied Mathematics: Body and Soul (Volume 2)

Integrals and Geometry in Rn

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

Integrals and Geometry in Rⁿ
The Integral
Properties of the Integral
The Logarithm log(x)
Numerical Quadrature
The Exponential Function exp(x) = e^x
Trigonometric Functions
The Functions exp(z), log(z), sin(z) and cos(z) for z E C
Techniques of Integration
Solving Differential Equations Using the Exponential
Improper Integrals
Series
Scalar Autonomous Initial Value Problems
Separable Scalar Initial Value Problems
The General Initial Value Problem
Calculus Tool Bag I
Analytic Geometry in Rⁿ
The Spectral Theorem
Solving Linear Algebraic Systems
Linear Algebra Tool Bag
The Matrix Exponential exp(xA)
Lagrange and the Principle of Least Action*
N-Body Systems*
The Crash Model*
Electrical Circuits*
String Theory*
Piecewise Linear Approximation
FEM for Two-Point Boundary Value Problems
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	9783540008897