Applied Mathematics: Body and Soul

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.

First comprehensive beginners' course for mathematics from an applications-oriented point of view Originally arose from course developed for chemical engineering students at the prestigious Chalmers University of Technology Covers all the undergraduate mathematics in calculus, analysis, and linear algebra Presents completely a new approach to mathematics teaching integrating computation from the very beginning Has been thoroughly class-tested Can be used for students in mathematics, engineering and science Contains many sections on the historical development of computational mathematics, as well as many real applications Accompanying software with examples available via the internet Includes supplementary material: sn.pub/extras

Klappentext

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.

Inhalt
Volume 2.- 27 The Integral.- 28 Properties of the Integral.- 29 The Logarithm log(x).- 30 Numerical Quadrature.- 31 The Exponential Function exp(x) = ex.- 32 Trigonometric Functions.- 33 The Functions exp(z), log(z), sin(z) and cos(z) forz ? ?.- 34 Techniques of Integration.- 35 Solving Differential Equations Using the Exponential.- 36 Improper Integrals.- 37 Series.- 38 Scalar Autonomous Initial Value Problems.- 39 Separable Scalar Initial Value Problems.- 40 The General Initial Value Problem.- 41 Calculus Tool Bag I.- 42 Analytic Geometry in ?n.- 43 The Spectral Theorem.- 44 Solving Linear Algebraic Systems.- 45 Linear Algebra Tool Bag.- 46 The Matrix Exponential exp(xA).- 47 Lagrange and the Principle of Least Action.- 48 N-Body Systems.- 49 The Crash Model.- 50 Electrical Circuits.- 51 String Theory*.- 52 Piecewise Linear Approximation.- 53 FEM for Two-Point Boundary Value Problems.- References.