Applied mathematics body and soul, volume 3 : calculus in several dimensions应用数学:身体和灵魂
点此进入淘宝搜索页搜索分類: 图书,进口原版书,科学与技术 Science & Techology ,
作者： K. Eriksson, D. Estep, C. Johnson著
出 版 社：
出版时间： 2003-12-1字数：版次： 1页数： 1213印刷时间： 2003/12/01开本： 16开印次： 1纸张： 胶版纸I S B N ： 9783540008910包装： 精装内容简介
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 possibilitites 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/.
目录
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 R2
68 Gauss’Theorem and Green’s Formula in R3
69 Stokes’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 R2 and R3
77 FEM for Boundary Value Problems in R2 and R3
78 Inverse Problems
79 Optimal Control
80 Differential Equations Tool Bag
81 Applications ToolBag
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
References
Index
