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MATHEMATICAL TOOLS FOR ENGINEERS

# MATHEMATICAL TOOLS FOR ENGINEERS - MATHEMATICAL TOOLS FOR...

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1 MATHEMATICAL TOOLS FOR ENGINEERS 2.1 INTRODUCTION 2.2 FUNCTIONS 2.3 SPATIAL RELATIONSHIPS 2.4 COORDINATE SYSTEMS 2.5 MATRICES AND VECTORS 2.6 CALCULUS 2.7 NUMERICAL METHODS 2.8 LAPLACE TRANSFORMS 2.9 z-TRANSFORMS 2.10 FOURIER SERIES 2.11 TOPICS NOT COVERED (YET) 2.12 REFERENCES/BIBLIOGRAPHY

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2 2.1 INTRODUCTION · This section has been greatly enhanced, and tailored to meet our engineering requirements. · The section outlined here is not intended to teach the elements of mathematics, but it is designed to be a quick reference guide to support the engineer required to use techniques that may not have been used recently. · For those planning to write the first ABET Fundamentals of Engineering exam, the following topics are commonly on the exam. 1. - quadratic equation 2. - straight line equations - slop and perpendicular 3. - conics, circles, ellipses, etc. 4. - matrices, determinants, adjoint, inverse, cofactors, multiplication 5. - limits, L'Hospital's rule, small angle approximation 6. - integration of areas 7. - complex numbers, polar form, conjugate, addition of polar forms 8. - maxima, minima and inflection points 9. - first order differential equations - guessing and separation 10. - second order differential equation - linear, homogeneous, non-homogeneous, second order 11. - triangles, sine, cosine, etc. 12. - integration - by parts and separation 13. - solving equations using inverse matrices, Cramer's rule, substitution 14. - eigenvalues, eigenvectors 15. - dot and cross products, areas of parallelograms, angles and triple product 16. - divergence and curl - solenoidal and conservative fields 17. - centroids 18. - integration of volumes 19. - integration using Laplace transforms 20. - probability - permutations and combinations 21. - mean, standard deviation, mode, etc. 22. - log properties 23. - taylor series 24. - partial fractions 25. - basic coordinate transformations - cartesian, cylindrical, spherical 26. - trig identities 27. - derivative - basics, natural log, small angles approx., chain rule, partial fractions
3 2.1.1 Constants and Other Stuff The constants listed are amount some of the main ones, other values can be derived through calculation using modern calculators or computers. The values are typically given with more than 15 places of accuracy so that they can be used for double precision calculations. 2.1.2 Basic Operations · These operations are generally universal, and are described in sufficient detail for our use. · Basic properties include,

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4 2.1.2.1 - Factorial · A compact representation of a series of increasing multiples. 2.1.3 Exponents and Logarithms · The basic properties of exponents are so important they demand some sort of mention · Logarithms also have a few basic properties of use, · All logarithms observe a basic set of rules for their application,
5 2.1.4 Polynomial Expansions · Binomial expansion for polynomials, 2.2 FUNCTIONS 2.2.1 Discrete and Continuous Probability Distributions · The Binomial distribution is, · The Poisson distribution is,

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MATHEMATICAL TOOLS FOR ENGINEERS - MATHEMATICAL TOOLS FOR...

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