Mathematics for Mechanical Engineers

by Kreith; Frank

• ISBN13: 9780849300561
• ISBN10: 0849300568
• Edition: 1st
• Format: Hardcover
• Copyright: 1999-12-06
• Publisher: CRC Press

Summary

Mathematics for Mechanical Engineers gives mechanical engineers convenient access to the essential problem solving tools that they use each day. It covers applications employed in many different facets of mechanical engineering, from basic through advanced, to ensure that you will easily find answers you need in this handy guide.For the engineer venturing out of familiar territory, the chapters cover fundamentals like physical constants, derivatives, integrals, Fourier transforms, Bessel functions, and Legendre functions. For the experts, it includes thorough sections on the more advanced topics of partial differential equations, approximation methods, and numerical methods, often used in applications. The guide reviews statistics for analyzing engineering data and making inferences, so professionals can extract useful information even with the presence of randomness and uncertainty. The convenient Mathematics for Mechanical Engineers is an indispensable summary of mathematics processes needed by engineers.

Table of Contents

Tables
William F. Ames
Greek Alphabet	1	(1)
International System of Units (SI)	1	(3)
Conversion Constants and Multipliers	4	(2)
Physical Constants	6	(1)
Symbols and Terminology for Physical and Chemical Quantities	7	(3)
Elementary Algebra and Geometry	10	(7)
Table of Derivatives	17	(1)
Integrals	18	(2)
The Fourier Transforms	20	(7)
Bessel Functions	27	(1)
Legendre Functions	28	(1)
Table of Differential Equations	29
Linear Algebra and Matrices
George Cain
Basic Definitions	1	(1)
Algebra of Matrices	2	(1)
Systems of Equations	2	(2)
Vector Spaces	4	(1)
Rank and Nullity	4	(1)
Orthogonality and Length	5	(1)
Determinants	6	(1)
Eigenvalues and Eigenvectors	6
Vector Algebra and Calculus
George Cain
Basic Definitions	1	(1)
Coordinate Systems	2	(1)
Vector Functions	2	(2)
Gradient, Curl, and Divergence	4	(1)
Integration	4	(1)
Integral Thorems	5
Differential Equations
William F. Ames
First-Order Equations	1	(1)
Second-Order Equations	1	(1)
Linear Equations With Constant Coefficients	2	(1)
Generating Function (z Transform)	2
Differential Equations
William F. Ames
Ordinary Differential Equations	1	(4)
Partial Differential Equations	5
Integral Equations
William F. Ames
Classification and Notation	1	(1)
Relation to Differential Equations	1	(1)
Methods of Solution	2
Approximation Methods
William F. Ames
Perturbation	1	(2)
Iterative Methods	3
Integral Transforms
William F. Ames
Laplace Transform	1	(2)
Convolution Integral	3	(1)
Fourier Transform	4	(1)
Fourier Cosine Transform	4
Calculus of Variations
William F. Ames
The Euler Equation	1	(1)
The Variation	1	(2)
Constraints	3
Optimization Methods
George Cain
Linear Programming	1	(1)
Unconstrained Nonlinear Programming	2	(1)
Constrained Nonlinear Programming	2
Engineering Statistics
Y. L. Tong
Introduction	1	(1)
Elementary Probability	1	(2)
Random Sample and Sampling Distributions	3	(1)
Normal Distibution-Related Sampling Distributions	4	(3)
Confidence Intervals	7	(1)
Testing Statistical Hypotheses	8	(2)
A Numerical Example	10	(2)
Concluding Remarks	12
Numerical Methods
William F. Ames
Introduction	1	(1)
Linear Algebra Equations	1	(6)
Nonlinear Equations in One Variable	7	(2)
General Methods for Nonlinear Equations in One Variable	9	(1)
Numerical Solution of Simultaneous Nonlinear Equations	9	(4)
Interpolation and Finite Differences	13	(3)
Numerical Differentiations	16	(3)
Numerical Integration	19	(2)
Numerical Solution of Ordinary Differential Equations	21	(3)
Numerical Solution of Integral Equations	24	(1)
Numerical Methods for Partial Differential Equations	25	(4)
Discrete and Fast Fourier Transforms	29	(1)
Software	30
Experimental Uncertainty Analysis
W.G. Steele
H.W. Coleman
Introduction	1	(1)
Uncertainty of a Measured Variable	2	(2)
Uncertainty of a Result	4	(2)
Using Uncertainty Analysis in Experimentation	6
Chaos
R. L. Kautz
Introduction	1	(1)
Flows, Attractors, adn Liapunov Exponents	1	(3)
Synchronous Motor	4
Fuzzy Sets and Fuzzy Logic
Dan M. Frangopol
Introduction	1	(1)
Fundamental Notions	2
Appendices
A. Properties of Gases and Vapors	A-2
B. Properties of Liquids	B-35
C. Properties of Solids	C-39
D. SI Units	D-75
E. Miscellaneous	E-77