mathematical formulae quick reference sheet
DESCRIPTION
Mathematical Formulas Quick References for Engineers & Scientists. Prepared by Muhammad Yasir.TRANSCRIPT
MATHEMATICAL FORMULAE
Quick Reference Sheets
Prepared By;
Muhammad Yasir
Mechanical Engineering Department
NED University of Engineering & Technology
Karachi, Pakistan.
Preface
These reference formulae sheets are particularly useful for undergraduate engineering
students, although other undergraduate, graduate students, physicists, scientists and
practitioners can also use. The purpose of these quick references is to quickly recall the
already learned forms & formulas that are difficult to memorize. One important
consideration was to make these sheets concise so that one can easily carry with
him/her. This can also be used as a review guide. But one should remember that these
sheets will not build your concept neither they explain the relevant theory. You should
have learned the relevant theory before you apply these formulas.
Currently I have covered calculus, both differential & integral, basic algebra,
trigonometry, special integrals, Laplace transforms, logarithmic formula, Taylor’s &
Maclaurin’s series formulas & expansions, Fourier series, ordinary differential
equations, system of ordinary differential equation, partial differential equations
method of variables separation, vector differential calculus, vector integral calculus,
numerical solution of equations, numerical integration, numerical solution of ordinary
differential equations & numerical technique for partial differential equations.
In future I plan to cover multiple integrals, multivariable calculus, complex numbers and
some addition to differentiation, partial differential equations & numerical solutions to
partial differential equations.
Sorry for the inconvenience, time constraint did not allow me to digitize the sheets.
They are hand written. I surely will try to digitize all the sheets in future. If anyone is
interested in digitizing these sheets then kindly let me know.
Any criticism, comments, suggestions will be highly appreciated.
Muhammad Yasir
Contents
Vol-1 A: Differentiation, Integration. 1
Vol-1 B: Trignometry, Algebra. 2
Vol-2 A: Special Integrals, Laplace, Logarithmic. 3
Vol-2 B: Series Formulae, Fourier Series. 4
Vol-3 A: Ordinary Differential Equations. 5
Vol-3 B: Ordinary Differential Equations. 6
Vol-4 A: System of Ordinary Differential Equations. 7
Vol-4 B: Partial Differential Equations. 8
Vol-5 A: Vector Calculus. 9
Vol-5 B: Vector Calculus. 10
Vol-6 A: Numerical Solution of Equations, Integration
& Ordinary Differential Equations. 11
Vol-6 B: Numerical Solution of Partial Differential Equations. 12
References 13
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References
� John Dantith, Richard Rennie, The Facts on File Dictionary of Mathematics, 5e,
Market House Books Ltd. 2005.
� Michael Correl, Vector Calculus.
� J. C. A. Wevers, Physics Formularly,2005.
� James Sewart, Calculus, 4e, Books/Cole Publishing Company, 1999.
� George B. Thomas and Ross L. Finney, Calculus and Analytic Geometry, 9e,
Addison Wesley Publishing Company, 1996.
� Erwin Kreyszig, Advanced Engineering Mathematics, 8e, John Wiley & Sons,
2006.
� Denns G. Zill, Michael R. Cullen, Differential Equations with boundary value
problems, PWS Publishing Company, 1993.
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