Titlebook: Applied Mathematics: Body and Soul; Volume 2: Integrals Kenneth Eriksson,Donald Estep,Claes Johnson Textbook 2004 Springer-Verlag Berlin H

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Calculus

Separable Scalar Initial Value Problems, : ? → ? and . : ? → ?. We thus consider the initial value problem.where . : ? → ? and . : ? → ? are given functions, which we refer to as a . problem, because the right hand side . (.(.), .) separates into the quotient of one function .(.) of x only, and one function .(.(.)) of .(.) only according

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The General Initial Value Problem, [0, 1] → ?. is a given bounded and Lipschitz continuous function, .. ∈ ?. is a given initial value, and . ≥ 1 is the dimension of the system. The reader may assume . = 2 or . = 3, recalling the chapters on analytic geometry in ?. and ?., and extend to the case . > 3 after having read the chapter on

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The Spectral Theorem, assume that the elements .. are real numbers. If . = (.., ... , ..) ∈ ?. is a non-zero vector that satisfies.where λ is a real number, then we say that . ∈ ?.. is an . of . and that λ is a corresponding e. of .. An eigenvector . has the property that . is parallel to . (if λ ≠ 0), or . = 0 (if λ =

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Solving Linear Algebraic Systems,or . ∈ ?.. We recall that if . is non-singular with non-zero determinant, then the solution . ∈ ?. is theoretically given by Cramer’s formula. However if . is large, the computational work in using Cramer’s formula is prohibitively large, so we need to find a more efficient means of computing the so

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chemical engineering students at the prestigious Chalmers U.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 possib

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Entstehung von Unternehmenskrisengh all of the chapters on functions, sequences, limits, real numbers, derivatives and basic differential equation models. So we hope the gentle reader is both excited and ready to embark on this new exploration.

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