Applied mathematics: body and soul derivatives and geometry in IR3: volume 1

By: Eriksson, KContributor(s): Johnson, Claes | Estep, DonMaterial type: TextTextPublication details: New York: Springer, [c2004]Description: 425 pISBN: 9783642056598LOC classification: QA11.2Online resources: Click here to access online
Contents:
1. What is Mathematics? 2. The Mathematics Laboratory 3. Introduction to Modeling 4. A Very Short Calculus Course 5. Natural Numbers and Integers 6. Mathematical Induction 7. Rational Numbers 8. Pythagoras and Euclid 9. What is a Function? 10. Polynomial functions 11. Combinations of functions 12. Lipschitz Continuity 13. Sequences and limits 14. The Square Root of Two 15. Real numbers 16. The Bisection Algorithm for f(x) = 0 17. Do Mathematicians Quarrel? 18. The Function y = x r 19. Fixed Points and Contraction Mappings 20. Analytic Geometry in ℝ2 21. Analytic Geometry in ℝ3 22. Complex Numbers 23. The Derivative 24. Differentiation Rules 25. Newton’s Method 26. Galileo, Newton, Hooke, Malthus and Fourier
Summary: 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.
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1. What is Mathematics?
2. The Mathematics Laboratory
3. Introduction to Modeling
4. A Very Short Calculus Course
5. Natural Numbers and Integers
6. Mathematical Induction
7. Rational Numbers
8. Pythagoras and Euclid
9. What is a Function?
10. Polynomial functions
11. Combinations of functions
12. Lipschitz Continuity
13. Sequences and limits
14. The Square Root of Two
15. Real numbers
16. The Bisection Algorithm for f(x) = 0
17. Do Mathematicians Quarrel?
18. The Function y = x r
19. Fixed Points and Contraction Mappings
20. Analytic Geometry in ℝ2
21. Analytic Geometry in ℝ3
22. Complex Numbers
23. The Derivative
24. Differentiation Rules
25. Newton’s Method
26. Galileo, Newton, Hooke, Malthus and Fourier

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.

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