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integral calculus

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Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005452
EISBN: 978-1-62708-196-2
... Abstract This article is a comprehensive collection of formulas, tables, and theorems associated with integral calculus. It also summarizes the applications of single, double, and triple integrations in various fields. integral calculus definite integrals line integrals surface...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005451
EISBN: 978-1-62708-196-2
... transforms. laplace transformations THE METHODS OF LAPLACE AND FOURIER TRANSFORMATION and the Heaviside operational calculus are essentially aspects of the same method. This method simplifies solutions of such problems as ordinary differential equations with constant coefficients, linear...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005453
EISBN: 978-1-62708-196-2
... Abstract This article describes the models of physical phenomena involving solution of differential equations such as ordinary or partial differential equations. It reviews the basic concepts of differential calculus and tabulates the expansion of functions into power series. A table of linear...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002442
EISBN: 978-1-62708-194-8
... Abstract This article presents an overview of the use of mechanism analysis (kinematics and dynamics) and simulation. It provides indications of the directions in which mechanism simulation is growing and how it is integrated in the evolving computer aided design and computer aided engineering...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005233
EISBN: 978-1-62708-187-0
... to solve the CFD equations are described, including geometry description and discretization. Finally, the application of CFD to a few casting problems is demonstrated. Fundamentals of CFD Computational fluid dynamics has as its objective the numerical solution of fluid-flow equations. The calculus...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002446
EISBN: 978-1-62708-194-8
... of the weighted objective method by minimizing the difference between each individual objective and its respective target value in a least-squares sense ( Ref 8 ). Optimization Algorithms When F is an algebraic function of the design variables, classical methods from elementary calculus can be used...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0009020
EISBN: 978-1-62708-187-0
... CASTINGS possess many inherent advantages that have long been accepted by the design engineer and metal parts user. In terms of component design, casting offers a great amount of flexibility. The casting process permits the formation of streamlined, intricate, integral parts of strength and rigidity...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005426
EISBN: 978-1-62708-196-2
... and process design Background and History Computational fluid dynamics has as its objective the numerical solution of fluid-flow equations. The calculus problem of solving a coupled system of nonlinear partial differential equations (PDEs) for the variables of interest (e.g., velocity, pressure...
Series: ASM Handbook
Volume: 11
Publisher: ASM International
Published: 15 January 2021
DOI: 10.31399/asm.hb.v11.a0006767
EISBN: 978-1-62708-295-2
... of a stress transformation is mainly to find the stresses that can be used in a failure criterion. These would be either the largest magnitude stresses in any direction or the magnitude of stresses on a weak plane. For the former, the extreme stresses can be found by taking Eq 11 and applying the calculus...
Book: Casting
Series: ASM Handbook
Volume: 15
Publisher: ASM International
Published: 01 December 2008
DOI: 10.31399/asm.hb.v15.a0005189
EISBN: 978-1-62708-187-0
... coefficient for 1 wt% standard state F * Integral free energy of solution F Faraday's constant G i Gibbs free energy of component i Δ G Integral molar free energy Δ G ¯ i Partial molar free energy of component i Δ G i o Molar free energy...
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002444
EISBN: 978-1-62708-194-8
... design Computational fluid dynamics has as its objective the numerical solution of fluid-flow equations. The calculus problem of solving a coupled system of nonlinear partial differential equations (PDEs) for the variables of interest (e.g., velocity, pressure, and temperature) is transformed...
Series: ASM Handbook Archive
Volume: 11
Publisher: ASM International
Published: 01 January 2002
DOI: 10.31399/asm.hb.v11.a0003530
EISBN: 978-1-62708-180-1
... on a weak plane. For the former, the extreme stresses can be found by taking Eq 11 and applying the calculus principle d σ X ′ / d θ = 0. That is, principal stresses are normal (perpendicular) stresses on planes for which the shear stresses are zero. The values of principal stresses are given by: (Eq...
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.a0005415
EISBN: 978-1-62708-196-2
... is the Lagrange multiplier. However, the derivatives of the corresponding grand function, for example, Eq 31 in a later section, are identically zero.) Because E is a functional, the derivatives are regarded as functional derivatives in the calculus of variations (any calculus of variations textbook may...
Series: ASM Handbook
Volume: 4B
Publisher: ASM International
Published: 30 September 2014
DOI: 10.31399/asm.hb.v04b.a0005923
EISBN: 978-1-62708-166-5
...), mechanical properties required in the parts processed, and the desired distortion control. This is further required in the type of quench tank or equipment used. Quenching systems are integrated into heat treating lines, and the automated lines normally are used to process many types of parts...
Series: ASM Handbook
Volume: 13C
Publisher: ASM International
Published: 01 January 2006
DOI: 10.31399/asm.hb.v13c.a0004209
EISBN: 978-1-62708-184-9
Series: ASM Handbook
Volume: 22A
Publisher: ASM International
Published: 01 December 2009
DOI: 10.31399/asm.hb.v22a.9781627081962
EISBN: 978-1-62708-196-2
Series: ASM Handbook
Volume: 20
Publisher: ASM International
Published: 01 January 1997
DOI: 10.31399/asm.hb.v20.a0002431
EISBN: 978-1-62708-194-8
... reliability, as shown in Fig. 1 . Fig. 1 Reliability as it relates to statistical distributions of structural integrity and applied loads There are numerous texts on statistics, as well as many references on engineering design. A number of sources have combined these two disciplines...
Series: ASM Handbook
Volume: 4F
Publisher: ASM International
Published: 01 February 2024
DOI: 10.31399/asm.hb.v04F.a0007006
EISBN: 978-1-62708-450-5
... used. Quenching systems are integrated into heat treating lines, and the automated lines are normally used to process many types of parts. It is seldom economically feasible to design a quench tank for only one type of part. One of the major goals of any design is to obtain as much flexibility...