Applied Mathematics: Body and Soul, Vol. 2
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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 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/.
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 of Initial Value Problems.- 58. Lorenz and the Essence of Chaos.- 59. Optimization.- 60. The Divergence, Rotation and Laplacian.- 61. Meteorology and Coriolis Forces.- 62. Curve Integrals.- 63. Double Integrals.- 64. Surface Integrals.- 65. Multiple Integrals.- 66. Guass' Theorem and Green's Formula in R2.- 67. Gauss' Theorem and Green's Formula in R3.- 68. Stokes' Theorem.- 69. Potential Fields.- 70. Center of Mass and Archimedes' Principle.- 71. Newton's Nightmare.- 72. Laplacian Models.- 73. Chemical Reactions.- 74. Calculus Tool Bag II.- 75. Piecewise Linears in R2 and R3.- 76. FEM for Boundary Value Problems in R2 and R3.- 77. Inverse Problems.- 78. Differential Equations Tool Bag.- 79. Applications Tool Bag.- 80. Analytic Functions.- 81. Fourier Series.- 82. Fourier Transforms.- 83. Incompressible Navier-Stokes: Quick and Easy.- 84. Fourier Analysis Tool Bag.- 85. Analytic Functions Tool Bag II.- Index
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