Ebook: Applied Mathematics: Body and Soul: Volume 1: Derivatives and Geometry in IR3

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-1
What is Mathematics?....Pages 3-20
The Mathematics Laboratory....Pages 21-24
Introduction to Modeling....Pages 25-31
A Very Short Calculus Course....Pages 33-46
Natural Numbers and Integers....Pages 47-61
Mathematical Induction....Pages 63-70
Rational Numbers....Pages 71-86
Pythagoras and Euclid....Pages 87-102
What is a Function?....Pages 103-117
Polynomial functions....Pages 119-139
Combinations of functions....Pages 141-147
Lipschitz Continuity....Pages 149-164
Sequences and limits....Pages 165-184
The Square Root of Two....Pages 185-194
Real numbers....Pages 195-214
The Bisection Algorithm for f(x) = 0....Pages 215-220
Do Mathematicians Quarrel?....Pages 221-240
Fixed Points and Contraction Mappings....Pages 241-244
Complex Numbers....Pages 245-263
The Derivative....Pages 265-312
Differentiation Rules....Pages 313-343
Newton’s Method....Pages 345-353
Galileo, Newton, Hooke, Malthus and Fourier....Pages 355-376
Back Matter....Pages 377-391
....Pages 393-401