8 Vector Analysis 2. Vector Differentiation 89 4. Stokes’ Theorem 5. Planar Motion in Polar Coordinates 90 6. Geostationary Satellite Orbit 90 9 Special Functions 1 Factorial Function) 93 5. Fourier Series 6. Functions with period other than 2t 101 8. Legendre Polynomial 9. Laguerre Polynomials 10. Hermite Polynomials 108 1. Orthogonal 10 Differential Equations 1. First-Order, First-Degree Equ uations 2. Second-Order Linear Equations (with Consta 3. Runge Kutta Method (of Order 4) 11 Statistics 1. Arithmetic Mean
8 Vector Analysis 1. Vectors 86 2. Vector Differentiation 88 3. Divergence Theorem (Gauss) 89 4. Stokes’ Theorem 89 5. Planar Motion in Polar Coordinates 90 6. Geostationary Satellite Orbit 90 9 Special Functions 1. Hyperbolic Functions 92 2. Gamma Function (Generalized Factorial Function) 93 3. Laplace Transforms 94 4. Z-Transform 97 5. Fourier Series 100 6. Functions with Period Other Than 2π 101 7. Bessel Functions 103 8. Legendre Polynomials 105 9. Laguerre Polynomials 107 10. Hermite Polynomials 108 11. Orthogonality 108 10 Differential Equations 1. First-Order, First-Degree Equations 110 2. Second-Order Linear Equations (with Constant Coefficients) 112 3. Runge Kutta Method (of Order 4) 114 11 Statistics 1. Arithmetic Mean 116
2. Median 3. Mode 116 4. Geometric mean 5. Harmonic mean 117 6. Variance 117 7. Standard Deviation 8. Coefficient of variation 9. Probability 10. Binomial distribution 1. Mean of Binomially Distributed 12. Normal distribution 14. Empirical Distributions 15. Estimation 123 17. t-Distribution 18. Hypothesis Testing with t-and Normal Distributions 19. Chi-Square Distribution 20. Least Squares Regression 131 21. Nonlinear Regression Analysis 134 22. The F-Distribution(Analysis of Variance) 23. Summary of Probability Distributio 24. Sample Size Determinations 142 12 Financial mathematics 1. Simple Interest 146 2. True Interest formula (Loan Payments
2. Median 116 3. Mode 116 4. Geometric Mean 116 5. Harmonic Mean 117 6. Variance 117 7. Standard Deviation 117 8. Coefficient of Variation 118 9. Probability 118 10. Binomial Distribution 120 11. Mean of Binomially Distributed Variable 121 12. Normal Distribution 121 13. Poisson Distribution 122 14. Empirical Distributions 123 15. Estimation 123 16. Hypotheses Testing 124 17. t-Distribution 125 18. Hypothesis Testing with t- and Normal Distributions 126 19. Chi-Square Distribution 129 20. Least Squares Regression 131 21. Nonlinear Regression Analysis 134 22. The F-Distribution (Analysis of Variance) 138 23. Summary of Probability Distributions 139 24. Sample Size Determinations 142 12 Financial Mathematics 1. Simple Interest 146 2. True Interest Formula (Loan Payments) 147
3. Loan Payment Schedules 4. Loan balance calculation 5. Accelerated Loan Payment 6. Lump Sum Payment 7. Compound Interest 153 8. Time to Double(Your Money) 9. Present Value of a Single 155 10. Regular Saving to Accumulate a Specified Amount 1. Monthly Payments to Achieve a Specified Amount 12. Periodic withdrawals from an Interest-Bearing Account 13. Periodic Withdrawals That Maintain the Principal 161 14. Time to Deplete an Interest- Bearing account with periodic Withdrawals 15. Amounts to withdraw for a Payments at the End of Each Year 163 16. Amounts to Withdraw for a Specified Number of withdrawals Il: Payments at the Beginning of Each Year 18. Annuities 19. The In-Out Formula 170 0. Stocks and Stock Quotations 21. Bond 22. Tax-Free Yield 23. Stock Options(Puts and Calls) 24. Market Averages
3. Loan Payment Schedules 148 4. Loan Balance Calculation 149 5. Accelerated Loan Payment 150 6. Lump Sum Payment 152 7. Compound Interest 153 8. Time to Double (Your Money) 155 9. Present Value of a Single Future Payment 155 10. Regular Saving to Accumulate a Specified Amount 156 11. Monthly Payments to Achieve a Specified Amount 158 12. Periodic Withdrawals from an Interest-Bearing Account 158 13. Periodic Withdrawals That Maintain the Principal 161 14. Time to Deplete an InterestBearing Account with Periodic Withdrawals 162 15. Amounts to Withdraw for a Specified Number of Withdrawals I: Payments at the End of Each Year 163 16. Amounts to Withdraw for a Specified Number of Withdrawals II: Payments at the Beginning of Each Year 165 17. Present Value of Regular Payments 167 18. Annuities 168 19. The In-Out Formula 170 20. Stocks and Stock Quotations 172 21. Bonds 173 22. Tax-Free Yield 175 23. Stock Options (Puts and Calls) 176 24. Market Averages 177
5. Mutual Fund Quotations 26. Dollar Cost Averaging 27. Moving Average Table of derivatives Table of Integrals Indefinite and Definite Integrals 187 App Index 263
25. Mutual Fund Quotations 177 26. Dollar Cost Averaging 179 27. Moving Average 180 Table of Derivatives 182 Table of Integrals: Indefinite and Definite Integrals 187 Appendix 243 Index 263
Elementary Algebra and Geometry I. Fundamental Properties(Real Numbers) a+b=b+a Commutative Law for Addition (a+b)+c=a+(b+c) Associative Law for a+0=0+a Addition (-a)+a=0 Inverse Law for Addition a(bc)=(ab)c Associative law for (a)1)=(1)a) Identity Law for Multiplication Commutative Law for (b+c)=ab+ Dist Division by zero is not defined
1 1 Elementary Algebra and Geometry 1. Fundamental Properties (Real Numbers) a b b a + = + Commutative Law for Addition ( ) ( ) a b c a b c + + = + + Associative Law for Addition a a + = + 0 0 Identity Law for Addition a a + − = − + = ( ) ( ) 0 a a Inverse Law for Addition a bc ab c ( ) ( ) = Associative Law for Multiplication a a a a a 1 1 1 0 = = ≠ , Inverse Law for Multiplication ( )( ) ( )( ) a a a 1 1 = = Identity Law for Multiplication ab ba = Commutative Law for Multiplication a b c ab ac ( ) + = + Distributive Law Division by zero is not defined