Ebook: Applied Mathematics: Body and Soul: Volume 2: Integrals and Geometry in IRn

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.

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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.

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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.

Content:
Front Matter....Pages I-XLIII
The Integral....Pages 429-451
Properties of the Integral....Pages 453-471
The Logarithm log(x)....Pages 473-477
Numerical Quadrature....Pages 479-489
Trigonometric Functions....Pages 491-503
The Functions exp(z), log(z), sin(z) and cos(z) for z ? ?....Pages 505-516
Techniques of Integration....Pages 517-519
Solving Differential Equations Using the Exponential....Pages 521-530
Improper Integrals....Pages 531-540
Series....Pages 541-545
Scalar Autonomous Initial Value Problems....Pages 547-557
Separable Scalar Initial Value Problems....Pages 559-566
The General Initial Value Problem....Pages 567-573
Calculus Tool Bag I....Pages 575-583
The Spectral Theorem....Pages 585-595
Solving Linear Algebraic Systems....Pages 597-640
Linear Algebra Tool Bag....Pages 641-649
The Matrix Exponential exp(xA)....Pages 651-683
Lagrange and the Principle of Least Action*....Pages 685-690
The Crash Model*....Pages 691-695
Electrical Circuits*....Pages 697-707
String Theory*....Pages 709-720
Piecewise Linear Approximation....Pages 721-728
FEM for Two-Point Boundary Value Problems....Pages 729-733
Back Matter....Pages 735-739
....Pages 741-753