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Searching... | QA310 .T35 1999 3RD EDITION | Adult Non-Fiction | Central Closed Stacks | Searching... | Searching... |

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### Summary

### Summary

Pocket Book of Integrals and Mathematical Formulas, a revision of a very successful pocket book, provides a handy desk-top reference for engineers and scientists seeking essential formulas, concepts, and definitions. Topics range from pre-calculus to vector analysis and from Fourier transforms to statistics.

This third edition contains:

A new chapter on business and financial mathematics - providing information on progressions, especially geometric progressions, which is the basis for many formulas related to annuities, growth of funds, and interest payments

Additional topics in statistics - including sample size calculations for testing differences and proportions

Featuring numerical tables of probability distributions, the book also includes

Discussions on formula listings and differential equations

Fourier series

Laplace and z-transforms

Vector analysis

Orthogonal polynomials

Many other handbooks go too far in their attempts, essentially mimicking larger comprehensive texts they try to summarize. The result is a reference less detailed than the full texts and too big to be conveniently portable. Most scientists do not carry them.

Through a careful selection of topics and detail, Pocket Book of Integrals and Mathematical Formulas truly meets the needs of engineers and scientists - a convenient, usable supplementary text providing worked examples where most necessary. Its comprehensive information and convenient arrangement of tables makes it an essential and easy to use reference.

### 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. Exponents | p. 2 |

3. Fractional Exponents | p. 2 |

3. Fractional Exponents | p. 2 |

4. Irrational Exponents | p. 2 |

5. Logarithms | p. 3 |

6. Factorials | p. 3 |

7. Binomial Theorem | p. 4 |

8. Factors and Expansion | p. 4 |

9. Progression | p. 4 |

10. Complex Numbers | p. 5 |

11. Polar Form | p. 6 |

12. Permutations | p. 7 |

13. Combinations | p. 7 |

14. Algebraic Equations | p. 8 |

15. Geometry | p. 9 |

2 Determinants, Matrices, and Linear Systems of Equations | |

1. Determinants | p. 15 |

2. Evaluation by Cofactors | p. 16 |

3. Properties of Determinants | p. 17 |

4. Matrices | p. 18 |

5. Operations | p. 18 |

6. Properties | p. 19 |

7. Transpose | p. 20 |

8. Identity Matrix | p. 20 |

9. Adjoint | p. 21 |

10. Inverse Matrix | p. 21 |

11. Systems of Linear Equations | p. 22 |

12. Matrix Solution | p. 23 |

3 Trigonometry | |

1. Triangles | p. 24 |

2. Trigonometric Functions of an Angle | p. 25 |

3. Trigonometric Indentities | p. 27 |

4. Inverse Trigonometric Functions | p. 29 |

4 Analytic Geometry | |

1. Rectangular Coordinates | p. 31 |

2. Distance between Two Points; Slope | p. 32 |

3. Equations of Straight Lines | p. 33 |

4. Distance from a Point to a Line | p. 35 |

5. Circle | p. 36 |

6. Parabola | p. 36 |

7. Ellipse | p. 39 |

8. Hyperbola | p. 41 |

9. Change of Axes | p. 44 |

10. General Equation of Degree Two | p. 46 |

11. Polar Coordinates (Figure 4.16) | p. 46 |

12. Curves and Equations | p. 49 |

5 Series | |

1. Bernoulli and Euler Numbers | p. 55 |

2. Series of Functions | p. 56 |

3. Error Function | p. 62 |

6 Differential Calculus | |

1. Notation | p. 63 |

2. Slope of a Curve | p. 63 |

3. Angle of Intersection of Two Curves | p. 64 |

4. Radius of Curvature | p. 64 |

5. Relative Maxima and Minima | p. 65 |

6. Points of Inflection of a Curve | p. 66 |

7. Taylor's Formula | p. 67 |

8. Indeterminant Forms | p. 68 |

9. Numerical Methods | p. 68 |

10. Functions of Two Variables | p. 70 |

11. Partial Derivatives | p. 71 |

7 Integral Calculus | |

1. Indefinite Integral | p. 73 |

2. Definite Integral | p. 73 |

3. Properties | p. 74 |

4. Common Applications of the Definite Integral | p. 74 |

5. Cylindrical and Spherical Coordinates | p. 77 |

6. Double Integration | p. 78 |

7. Surface Area and Volume by Double Integration | p. 79 |

8. Centroid | p. 80 |

8 Vector Analysis | |

1. Vectors | p. 82 |

2. Vector Differentiation | p. 83 |

3. Divergence Theorem | p. 85 |

4. Stokes' Theorem | p. 85 |

5. Planar Motion in Polar Coordinates | p. 85 |

9 Special Functions | |

1. Hyperbolic Functions | p. 87 |

2. Gamma Function (Generalized Factorial Function) | p. 88 |

3. Laplace Transforms | p. 89 |

4. Z-Transform | p. 92 |

5. Fourier Series | p. 95 |

6. Functions with Period Other than 2[pi] | p. 96 |

7. Bessel Functions | p. 98 |

8. Legendre Polynomials | p. 100 |

9. Laguerre Polynomials | p. 102 |

10. Hermite Polynomials | p. 103 |

11. Orthogonality | p. 104 |

10 Differential Equations | |

1. First Order-First Degree Equations | p. 105 |

2. Second Order Linear Equations (With Constant Coefficients) | p. 106 |

11 Statistics | |

1. Arithmetic Mean | p. 109 |

2. Median | p. 109 |

3. Mode | p. 109 |

4. Geometric Mean | p. 109 |

5. Harmonic Mean | p. 110 |

6. Variance | p. 110 |

7. Standard Deviation | p. 110 |

8. Coefficient of Variation | p. 111 |

9. Probability | p. 111 |

10. Binomial Distribution | p. 113 |

11. Mean of Binomially Distributed Variable | p. 113 |

12. Normal Distribution | p. 113 |

13. Poisson Distribution | p. 115 |

14. Empirical Distributions | p. 115 |

15. Estimation | p. 116 |

16. Hypotheses Testing | p. 116 |

17. t-Distribution | p. 117 |

18. Hypothesis Testing with t- and Normal Distributions | p. 118 |

19. Chi-Square Distribution | p. 121 |

20. Least Squares Regression | p. 123 |

21. The F-Distribution (Analysis of Variance) | p. 126 |

22. Summary of Probability Distributions | p. 128 |

23. Sample Size Determinations | p. 130 |

12 Financial Mathematics | |

1. Simple Interest | p. 134 |

2. True Interest Formula (Loan Payments) | p. 135 |

3. Loan Payment Schedules | p. 136 |

4. Loan Balance Calculation | p. 137 |

5. Accelerated Loan Payment | p. 138 |

6. Lump Sum Payment | p. 140 |

7. Compound Interest | p. 141 |

8. Time to Double (Your Money) | p. 143 |

9. Present Value of a Single Future Payment | p. 143 |

10. Regular Saving to Accumulate a Specified Amount | p. 144 |

11. Monthly Payments to Achieve a Specified Amount | p. 146 |

12. Periodic Withdrawals From an Interest-Bearing Account | p. 146 |

13. Periodic Withdrawals That Maintain the Principal | p. 149 |

14. Time to Deplete an Interest-Bearing Account with Periodic Withdrawals | p. 150 |

15. Amounts to Withdraw for a Specified Number of Withdrawalsp151 | |

16. Amounts to Withdraw for a Specified Number of Withdrawals II | p. 153 |

17. Present Value of Regular Payments | p. 154 |

18. Annuities | p. 155 |

19. The In-Out Formula | p. 158 |

20. Stocks and Stock Quotations | p. 159 |

21. Bonds | p. 160 |

22. Tax-Free Yield | p. 162 |

23. Stock Options (Puts and Calls) | p. 163 |

24. Market Averages | p. 164 |

25. Mutual Fund Quotations | p. 165 |

26. Dollar Cost Averaging | p. 166 |

27. Moving Average | p. 167 |

Table of Derivatives | p. 169 |

Table of Integrals | p. 176 |

Appendix | p. 250 |

Table A.1 Areas Under the Standard Normal Curve | p. 250 |

Table A.2 Poisson Distribution | p. 251 |

Table A.3 t-Distribution | p. 253 |

Table A.4 X[superscript 2] Distribution | p. 254 |

Table A.5 Variance Ratio | p. 255 |

Table A.6 Monthly Payments per $1000 of Loan Value | p. 257 |

Table A.7 The Growth of $1 at Various Annual Interest Rates and Specified Number of Years | p. 261 |

Table A.8 Doubling Time for Various Annual Interest Rates | p. 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 Rates | p. 265 |

Table A.12 Growth of Annual Deposits of $1,000 at the End of the Year at Specified Annual Interest Rates | p. 266 |

Table A.13 Growth of Annual Deposits of $1,000 at the Beginning of the Year at Specified Annual Interest Rates | p. 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 Monthly | p. 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 Monthly | p. 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 Monthly | p. 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 Monthly | p. 269 |

Index | p. 271 |