Item description for Applied Mathematics Body and Soul, Volume 1: Derivatives and Geometry in R3 by Kenneth Eriksson, Donald J. Estep & Claes Johnson...
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.
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/.
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Est. Packaging Dimensions: Length: 1.25" Width: 6.75" Height: 9.5" Weight: 1.82 lbs.
Release Date Dec 5, 2003
ISBN 354000890X ISBN13 9783540008903
Availability 0 units.
More About Kenneth Eriksson, Donald J. Estep & Claes Johnson
K. Eriksson has an academic affiliation as follows - Chalmers University of Technology, Gothenberg.
Reviews - What do customers think about Applied Mathematics Body and Soul, Volume 1: Derivatives and Geometry in R3?
Calculus + Linear Algebra in One Series Jan 5, 2005
I wish this site would put a text list of the "Table of Contents" for books.
Sorry about the length: this site does not allow postings for each volume in a series!
Volume 1: Derivatives and Geometry in R^3 1. What is Mathematics? 2. The Mathematics Library 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 R^2 21. Analytic Geometry in R^3 22. Complex Numbers 23. The Derivative 24. Differentiation Rules 25. Newton's Method 26. Galileo, Newton, Hooke, Malthus and Fourier
Volume 2: Integrals and Geometry in R^n 27: The Integral 28: Properties of the Integral 29. The Logarithm log(x) 30. Numerical Quadrature 31. The Exponential Function exp(x) = e^x 32. Trigonometric Functions 33. The Functions exp(z), log(z), sin(z) and cos(z) for z e C 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 R^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
Volume 3: Calculus in Several Dimensions 54. Vector-Valued Functions of Several Real Variables 55. Level Curves/Surfaces and the Gradient 56. Linearization and Stability of Initial Value Problems 57. Adaptive Solvers for IVPs 58. Lorenz and the Essence of Chaos 59. The Solar System 60. Optimization 61. The Divergence, Rotation and Laplacian 62. Meteorology and Coriolis Forces 63. Curve Integrals 64. Double Integrals 65. Surface Integrals 66. Multiple Integrals 67. Gauss' Theorem and Green's Formula in R^2 68. Gauss' Theorem and Green's Formula in R^3 69. Stoke's Theorem 70. Potential Fields 71. Center of Mass and Archimedes' Principle 72. Newton's Nightmare 73. Laplacian Models 74. Chemical Reactions 75. Calculus Tool Bag II 76. Piecewise Linear Polynomials in R^2 and R^3 77. FEM for Boundary Value Problems in R^2 and R^3 78. Inverse Problems 79. Optimal Control 80. Differential Equations Tool Bag 81. Applications Tool Bag 82. Analytic Functions 83. Fourier Series 84. Fourier Transforms 85. Analytic Functions Tool Bag 86. Fourier Analysis Tool Bag 87. Incompressible Navier-Stokes: Quick and Easy
This book/series has some problems; however, the attempt to wed Mathematical Analysis, Numerical Computation, and Application AND to also talk about Calculus and Linear Algebra at the same time -- makes these three books worth a look.