By Kenneth Eriksson, Donald Estep, Claes Johnson
Applied arithmetic: physique & Soul is a arithmetic schooling reform venture constructed at Chalmers collage of expertise and contains a sequence of volumes and software program. this system is encouraged via the pc revolution establishing new chances of computational mathematical modeling in arithmetic, technological know-how and engineering. It comprises a synthesis of Mathematical research (Soul), Numerical Computation (Body) and alertness. Volumes I-III current a contemporary model of Calculus and Linear Algebra, together with constructive/numerical ideas and functions meant for undergraduate courses in engineering and technology. additional volumes current subject matters similar to Dynamical platforms, Fluid Dynamics, sturdy Mechanics and Electro-Magnetics on a sophisticated undergraduate/graduate point.
The authors are best researchers in Computational arithmetic who've written quite a few profitable books.
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Extra resources for Applied Mathematics Body and Soul, Volume 2: Integrals and Geometry in Rn
2 The Cauchy-Riemann Equations . . . . . . 4 Conjugate Harmonic Functions . . . . . . 5 Curves in the Complex Plane . . . . . . . 7 Complex Integrals . . . . . 8 Cauchy's Theorem . . . . . 9 Cauchy's Representation Formula . 10 Taylor's Formula . . 11 The Residue Theorem . . . . 2 Convolution.......... 4 Parseval's Formula . . . 5 Discrete Fourier Transforms . 6 Fourier Transforms . . . 8 The Sampling Theorem . . . 1 Introduction................... 2 The Incompressible Navier-Stokes Equations.
The Transpose of a 2-Column Vector The Identity Matrix .. . . The Inverse of a Matrix . . . Rotation in Matrix Form Again! A Mirror in Matrix Form Change of Basis Again! Queen Christina . . 1 Introduction . . . . . . . . . . 3 Scalar Product and Norm . . . 5 The Angle Between Two Vectors .. 6 Vector Product . . . . . . 21. 9 Volume of a Parallelepiped Spanned by Three Vectors . . . . . . 10 The Triple Product a· b xc . . 11 A Formula for the Volume Spanned by Three Vectors .
9 The Cauchy-Riemann Equations and the Derivative. 12 Conjugate Harmonic Functions . . . . . . 14 Curves in the Complex Plane . . . . 15 Conformal Mappings . . . . . . . 17 Inversion. . . . . . . . . . 18 Mobius Transformations . . . . . . 19 w = zl/2, W = e Z , W = log(z) and W = sin(z). 20 Complex Integrals: First Shot . . . . . 32 Contents Volume 3 Complex Integrals: General Case . . . Basic Properties of the Complex Integral. Taylor's Formula: First Shot. .
Applied Mathematics Body and Soul, Volume 2: Integrals and Geometry in Rn by Kenneth Eriksson, Donald Estep, Claes Johnson