Cover image for Pocket book of integrals and mathematical formulas
Title:
Pocket book of integrals and mathematical formulas
Personal Author:
Edition:
2nd ed.
Publication Information:
Boca Raton, Fla. : CRC Press, 1992
ISBN:
9780849301421

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30000003178591 QA310 T34 1992 k Open Access Book Book
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30000003178609 QA310 T34 1992 k Open Access Book Book
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Summary

Summary

Pocket Book of Integrals and Mathematical Formulas, Second Edition, is a handy, compact reference work containing concise discussions of mathematical concepts and formulas frequently needed by students and professionals in engineering, science, applied math and statistics. One of the book's special features is its comprehensive table of integrals arranged and formatted to facilitate the rapid location of the right form. Tables of derivatives; calculus applications; graphs of important Cartesian and polar curves; and formulas from algebra, geometry, trigonometry, calculus and statistics have also been arranged with convenience in mind.
The book also lists infinite series and includes discussions and formula listings in differential equations and in advanced topics such as Fourier series, Laplace and z-transforms, vector analysis, and orthogonal polynomials. Important physical constants and numerical tables of probability distributions such as normal, Poisson, t, chi square, and F are provided. Pocket Book of Integrals and Mathematical Formulas, Second Edition, is a volume every student or professional working with engineering mathematics should have in their coat pocket.

Pocket Book of Integrals and Mathematical Formulas, Second Edition has been updated and expanded to cover even more calculus applications and additional topics, including Z-transforms, orthogonal polynomials, Bessel functions, and a summary of probability distributions.


Author Notes

Ronald J. Tallarida holds B.S. and M.S. degrees in physics/mathematics and a Ph.D. in pharmacology. His primary appointment is as Professor of Pharmacology at Temple University School of Medicine, Philadelphia; he also serves as Adjunct Professor of Biomedical Engineering (Mathematics) at Drexel University in Philadelphia. Dr. Tallarida received the Lindback Award for Distinguished Teaching in 1964 while in the Drexel mathematics department.


Table of Contents

1 Elementary Algebra and Geometry
1. Fundamental Properties (Real Numbers)p. 1
2. Exponentsp. 2
3. Fractional Exponentsp. 2
3. Fractional Exponentsp. 2
4. Irrational Exponentsp. 2
5. Logarithmsp. 3
6. Factorialsp. 3
7. Binomial Theoremp. 4
8. Factors and Expansionp. 4
9. Progressionp. 4
10. Complex Numbersp. 5
11. Polar Formp. 6
12. Permutationsp. 7
13. Combinationsp. 7
14. Algebraic Equationsp. 8
15. Geometryp. 9
2 Determinants, Matrices, and Linear Systems of Equations
1. Determinantsp. 15
2. Evaluation by Cofactorsp. 16
3. Properties of Determinantsp. 17
4. Matricesp. 18
5. Operationsp. 18
6. Propertiesp. 19
7. Transposep. 20
8. Identity Matrixp. 20
9. Adjointp. 21
10. Inverse Matrixp. 21
11. Systems of Linear Equationsp. 22
12. Matrix Solutionp. 23
3 Trigonometry
1. Trianglesp. 24
2. Trigonometric Functions of an Anglep. 25
3. Trigonometric Indentitiesp. 27
4. Inverse Trigonometric Functionsp. 29
4 Analytic Geometry
1. Rectangular Coordinatesp. 31
2. Distance between Two Points; Slopep. 32
3. Equations of Straight Linesp. 33
4. Distance from a Point to a Linep. 35
5. Circlep. 36
6. Parabolap. 36
7. Ellipsep. 39
8. Hyperbolap. 41
9. Change of Axesp. 44
10. General Equation of Degree Twop. 46
11. Polar Coordinates (Figure 4.16)p. 46
12. Curves and Equationsp. 49
5 Series
1. Bernoulli and Euler Numbersp. 55
2. Series of Functionsp. 56
3. Error Functionp. 62
6 Differential Calculus
1. Notationp. 63
2. Slope of a Curvep. 63
3. Angle of Intersection of Two Curvesp. 64
4. Radius of Curvaturep. 64
5. Relative Maxima and Minimap. 65
6. Points of Inflection of a Curvep. 66
7. Taylor's Formulap. 67
8. Indeterminant Formsp. 68
9. Numerical Methodsp. 68
10. Functions of Two Variablesp. 70
11. Partial Derivativesp. 71
7 Integral Calculus
1. Indefinite Integralp. 73
2. Definite Integralp. 73
3. Propertiesp. 74
4. Common Applications of the Definite Integralp. 74
5. Cylindrical and Spherical Coordinatesp. 77
6. Double Integrationp. 78
7. Surface Area and Volume by Double Integrationp. 79
8. Centroidp. 80
8 Vector Analysis
1. Vectorsp. 82
2. Vector Differentiationp. 83
3. Divergence Theoremp. 85
4. Stokes' Theoremp. 85
5. Planar Motion in Polar Coordinatesp. 85
9 Special Functions
1. Hyperbolic Functionsp. 87
2. Gamma Function (Generalized Factorial Function)p. 88
3. Laplace Transformsp. 89
4. Z-Transformp. 92
5. Fourier Seriesp. 95
6. Functions with Period Other than 2[pi]p. 96
7. Bessel Functionsp. 98
8. Legendre Polynomialsp. 100
9. Laguerre Polynomialsp. 102
10. Hermite Polynomialsp. 103
11. Orthogonalityp. 104
10 Differential Equations
1. First Order-First Degree Equationsp. 105
2. Second Order Linear Equations (With Constant Coefficients)p. 106
11 Statistics
1. Arithmetic Meanp. 109
2. Medianp. 109
3. Modep. 109
4. Geometric Meanp. 109
5. Harmonic Meanp. 110
6. Variancep. 110
7. Standard Deviationp. 110
8. Coefficient of Variationp. 111
9. Probabilityp. 111
10. Binomial Distributionp. 113
11. Mean of Binomially Distributed Variablep. 113
12. Normal Distributionp. 113
13. Poisson Distributionp. 115
14. Empirical Distributionsp. 115
15. Estimationp. 116
16. Hypotheses Testingp. 116
17. t-Distributionp. 117
18. Hypothesis Testing with t- and Normal Distributionsp. 118
19. Chi-Square Distributionp. 121
20. Least Squares Regressionp. 123
21. The F-Distribution (Analysis of Variance)p. 126
22. Summary of Probability Distributionsp. 128
23. Sample Size Determinationsp. 130
12 Financial Mathematics
1. Simple Interestp. 134
2. True Interest Formula (Loan Payments)p. 135
3. Loan Payment Schedulesp. 136
4. Loan Balance Calculationp. 137
5. Accelerated Loan Paymentp. 138
6. Lump Sum Paymentp. 140
7. Compound Interestp. 141
8. Time to Double (Your Money)p. 143
9. Present Value of a Single Future Paymentp. 143
10. Regular Saving to Accumulate a Specified Amountp. 144
11. Monthly Payments to Achieve a Specified Amountp. 146
12. Periodic Withdrawals From an Interest-Bearing Accountp. 146
13. Periodic Withdrawals That Maintain the Principalp. 149
14. Time to Deplete an Interest-Bearing Account with Periodic Withdrawalsp. 150
15. Amounts to Withdraw for a Specified Number of Withdrawalsp151
16. Amounts to Withdraw for a Specified Number of Withdrawals IIp. 153
17. Present Value of Regular Paymentsp. 154
18. Annuitiesp. 155
19. The In-Out Formulap. 158
20. Stocks and Stock Quotationsp. 159
21. Bondsp. 160
22. Tax-Free Yieldp. 162
23. Stock Options (Puts and Calls)p. 163
24. Market Averagesp. 164
25. Mutual Fund Quotationsp. 165
26. Dollar Cost Averagingp. 166
27. Moving Averagep. 167
Table of Derivativesp. 169
Table of Integralsp. 176
Appendixp. 250
Table A.1 Areas Under the Standard Normal Curvep. 250
Table A.2 Poisson Distributionp. 251
Table A.3 t-Distributionp. 253
Table A.4 X[superscript 2] Distributionp. 254
Table A.5 Variance Ratiop. 255
Table A.6 Monthly Payments per $1000 of Loan Valuep. 257
Table A.7 The Growth of $1 at Various Annual Interest Rates and Specified Number of Yearsp. 261
Table A.8 Doubling Time for Various Annual Interest Ratesp. 262
Table A.9 Monthly Savings to Produce $1000 in the Specified Number of Years at the Given Annual Interest Rate (Compounded Monthly)p. 263
Table A.10 Monthly Savings to Produce $1000 in Specified Number of Years at the Given Annual Interest Rate (Compounded Annually)p. 264
Table A.11 Percentage of Funds That May Be Withdrawn Each Year at the Beginning of the Year at Different Annual Interest Ratesp. 265
Table A.12 Growth of Annual Deposits of $1,000 at the End of the Year at Specified Annual Interest Ratesp. 266
Table A.13 Growth of Annual Deposits of $1,000 at the Beginning of the Year at Specified Annual Interest Ratesp. 267
Table A.14 Monthly Amount That Must Be Saved for the Years Indicated in Order to Collect $1,000 Per Month Thereafter at 4% Annual Interest Compounded Monthlyp. 268
Table A.15 Monthly Amount That Must Be Saved for the Years Indicated in Order to Collect $1,000 Per Month Thereafter at 6% Annual Interest Compounded Monthlyp. 268
Table A.16 Monthly Amount That Must Be Saved for the Years Indicated in Order to Collect $1,000 Per Month Thereafter at 8% Annual Interest Compounded Monthlyp. 269
Table A.17 Monthly Amount That Must Be Saved for the Years Indicated in Order to Collect $1,000 Per Month Thereafter at 10% Annual Interest Compounded Monthlyp. 269
Indexp. 271