This text includes the following chapters and appendices: Numbers and Arithmetic Operations, Elementary Algebra, Intermediate Algebra, Fundamentals of Geometry, Fundamentals of Plane Trigonometry, Fundamentals of Calculus, Mathematics of Finance and Economics, Depreciation, Impairment, and Depletion, Introduction to Probability and Statistics, Random Variables, Common Probability Distributions and Tests, Curve Fitting, Regression, and Correlation, Analysis of Variance (ANOVA), Introduction to MATLAB, The Gamma and Beta Functions and Distributions, Introduction to Markov Chains, The Lambda Index, The Black-Scoles Stock Options Model, The Altman Bankruptcy Z-Score. For additional information. please visit the Orchard Publications site.
Author(s): Steven Karris
Edition: 3
Publisher: Orchard Publications
Year: 2007
Language: English
Pages: 629
Mathematics for Business, Science, and Technology......Page 1
Preface......Page 5
Table of Contents......Page 7
1.1 Introduction......Page 16
1.2 Algebraic Equations......Page 17
1.3 Laws of Exponents......Page 20
1.4 Laws of Logarithms......Page 25
1.5 Quadratic Equations......Page 28
1.7 Measures of Central Tendency......Page 30
1.8 Interpolation and Extrapolation......Page 35
1.10 Arithmetic Series......Page 38
1.11 Geometric Series......Page 39
1.12 Harmonic Series......Page 41
1.13 Proportions......Page 42
1.14 Summary......Page 44
1.15 Exercises......Page 48
1.16 Solutions to End-of-Chapter Exercises......Page 50
2.1 Systems of Two Equations......Page 54
2.2 Systems of Three Equations......Page 59
2.3 Matrices and Simultaneous Solution of Equations......Page 60
2.4 Summary......Page 79
2.5 Exercises......Page 83
2.6 Solutions to End-of-Chapter Exercises......Page 85
3.2 Plane Geometry Figures......Page 90
3.3 Solid Geometry Figures......Page 105
3.4 Using Spreadsheets to Find Areas of Irregular Polygons......Page 109
3.5 Summary......Page 112
3.6 Exercises......Page 116
3.7 Solutions to End-of-Chapter Exercises......Page 118
4.1 Introduction......Page 122
4.3 Trigonometric Functions of an Acute Angle......Page 123
4.4 Trigonometric Functions of an Any Angle......Page 124
5.2 Differential Calculus......Page 143
5.3 The Derivative of a Function......Page 145
5.4 Maxima and Minima......Page 153
5.5 Integral Calculus......Page 157
5.7 Definite Integrals......Page 158
5.8 Summary......Page 163
5.9 Exercises......Page 165
5.10 Solutions to End-of-Chapter Exercises......Page 166
6.1 Common Terms......Page 169
6.2 Interest......Page 174
6.3 Sinking Funds......Page 192
6.4 Annuities......Page 197
6.5 Amortization......Page 202
6.6 Perpetuities......Page 204
6.7 Valuation of Bonds......Page 207
6.8 Spreadsheet Financial Functions......Page 213
6.9 The MATLAB Financial Toolbox......Page 229
6.10 Comparison of Alternate Proposals......Page 236
6.11 Kelvin’s Law......Page 239
6.12 Summary......Page 243
6.13 Exercises......Page 246
6.14 Solutions to End-of-Chapter Exercises......Page 249
7.1 Depreciation Defined......Page 257
7.2 Impairments......Page 274
7.3 Depletion......Page 275
7.4 Valuation of a Depleting Asset......Page 276
7.5 Summary......Page 281
7.6 Exercises......Page 283
7.7 Solutions to End-of-Chapter Exercises......Page 284
8.2 Probability and Random Experiments......Page 290
8.3 Relative Frequency......Page 291
8.4 Combinations and Permutations......Page 293
8.5 Joint and Conditional Probabilities......Page 296
8.6 Bayes’ Rule......Page 300
8.7 Summary......Page 302
8.8 Exercises......Page 304
8.9 Solutions to End-of-Chapter Exercises......Page 305
9.1 Definition of Random Variables......Page 307
9.3 Cumulative Distribution Function......Page 308
9.4 Probability Density Function......Page 315
9.5 Two Random Variables......Page 317
9.6 Statistical Averages......Page 318
9.7 Summary......Page 326
9.8 Exercises......Page 329
9.9 Solutions to End-of-Chapter Exercises......Page 330
10.1 Properties of Binomial Coefficients......Page 333
10.2 The Binomial (Bernoulli) Distribution......Page 334
10.3 The Uniform Distribution......Page 338
10.4 The Exponential Distribution......Page 342
10.5 The Normal (Gaussian) Distribution......Page 344
10.6 Percentiles......Page 364
10.7 The Student’s t-Distribution......Page 368
10.8 The Chi-Square Distribution......Page 372
10.9 The F Distribution......Page 375
10.11 Law of Large Numbers......Page 378
10.12 The Poisson Distribution......Page 379
10.13 The Multinomial Distribution......Page 384
10.14 The Hypergeometric Distribution......Page 385
10.16 The Rayleigh Distribution......Page 388
10.17 Other Probability Distributions......Page 391
10.18 Critical Values of the Binomial Distribution......Page 394
10.19 Sampling Distribution of Means......Page 395
10.20 Z -Score......Page 396
10.21 Tests of Hypotheses and Levels of Significance......Page 397
10.22 Tests of Significance......Page 404
10.23 Summary......Page 412
10.24 Exercises......Page 421
10.25 Solutions to End-of-Chapter Exercises......Page 423
11.1 Curve Fitting......Page 428
11.2 Linear Regression......Page 429
11.3 Parabolic Regression......Page 434
11.4 Covariance......Page 437
11.5 Correlation Coefficient......Page 439
11.6 Summary......Page 444
11.7 Exercises......Page 447
11.8 Solutions to End-of-Chapter Exercises......Page 449
12.2 One-way ANOVA......Page 453
12.3.1 Two-factor without Replication ANOVA......Page 460
12.3.2 Two-factor with Replication ANOVA......Page 466
12.4 Summary......Page 477
12.5 Exercises......Page 481
12.6 Solutions to End-of-Chapter Exercises......Page 483
A.2 Positive and Negative Numbers......Page 490
A.3 Addition and Subtraction......Page 491
A.4 Multiplication and Division......Page 496
A.5 Integer, Fractional, and Mixed Numbers......Page 499
A.6 Reciprocals of Numbers......Page 500
A.7 Arithmetic Operations with Fractional Numbers......Page 502
A.8 Exponents......Page 511
A.9 Scientific Notation......Page 514
A.10 Operations with Numbers in Scientific Notation......Page 516
A.11 Square and Cubic Roots......Page 519
A.12 Common and Natural Logarithms......Page 521
A.13 Decibel......Page 522
A.14 Percentages......Page 523
A.15 International System of Units (SI)......Page 524
A.16 Graphs......Page 529
A.17 Summary......Page 533
A.18 Exercises......Page 539
A.19 Solutions to End-of-Appendix Exercises......Page 540
B.2 Command Window......Page 542
B.3 Roots of Polynomials......Page 544
B.4 Polynomial Construction from Known Roots......Page 545
B.5 Evaluation of a Polynomial at Specified Values......Page 546
B.6 Rational Polynomials......Page 549
B.7 Using MATLAB to Make Plots......Page 551
B.9 Multiplication, Division, and Exponentiation......Page 559
B.10 Script and Function Files......Page 567
B.11 Display Formats......Page 572
C.1 The Gamma Function......Page 574
D.1 Stochastic Processes......Page 595
E.2 The Lambda Index Defined......Page 611
E.3 Spreadsheet Construction......Page 612
F.1 Stock Options......Page 615
F.2 The Black-Scholes Model Equations......Page 616
F.3 Spreadsheet for the Black-Scholes Model......Page 617
G.1 The Financial Ratios......Page 620
G.3 Spreadsheet for The Altman Z-Score......Page 621
References and Suggestions for Further Study......Page 624
Index......Page 625
