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This title in other editionsIntegrals and Geometry in RNby Claes (chalmers University Of Technology, Gothenberg) Johnson
Synopses & ReviewsPublisher Comments: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 IIII 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 ElectroMagnetics 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 Geometry 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, multidimensional 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/.
Synopsis: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 IIII 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 ElectroMagnetics on an advanced undergraduate/graduate level. The authors are leading researchers in Computational Mathematics who have written various successful books.
Table of Contents27. The Integral. 28. Properties of the Integral. 29. The Logarithm log (x). 30. Numerical Quadrature. 31. The Exponential Function exp(x) = ex. 32. Trigonometric Functions. 33. The Functions exp(z), log(z), sin(z), and cos(z) for z __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 Rn. 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. NBody Systems. 49. The Crash Model. 50. Electrical Circuits. 51. String Theory. 52. Piecewise Linear Approximation. 53. FEM for TwoPoint Boundary Value Problems.
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