mathematical formulae quick reference sheet

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MATHEMATICAL FORMULAE Quick Reference Sheets Prepared By; Muhammad Yasir Mechanical Engineering Department NED University of Engineering & Technology Karachi, Pakistan.

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Mathematical Formulas Quick References for Engineers & Scientists. Prepared by Muhammad Yasir.

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Page 1: Mathematical Formulae Quick Reference Sheet

MATHEMATICAL FORMULAE

Quick Reference Sheets

Prepared By;

Muhammad Yasir

Mechanical Engineering Department

NED University of Engineering & Technology

Karachi, Pakistan.

Page 2: Mathematical Formulae Quick Reference Sheet

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

[email protected]

Page 3: Mathematical Formulae Quick Reference Sheet

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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