Calculus with probability: For the life and management sciences
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Reading, Mass.
Addison-Wesley
1973
|
| Series: | Addison-Wesley series in mathematics.
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XIII,648 S. |
Staff View
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| 245 | 1 | 0 | |a Calculus with probability |b For the life and management sciences |c Willard E. Baxter ; Clifford W. Sloyer* |
| 264 | 1 | |a Reading, Mass. |b Addison-Wesley |c 1973 | |
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| 700 | 1 | |a Sloyer, Clifford W. |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1804117429323825152 |
|---|---|
| adam_text | CONTENTS
Chapter 1 Sets
1.1 Introduction I
1.2 Sets and subsets I
1.3 Set operations 4
1.4 Some important sets 8
Chapter 2 Counting Techniques
2.1 Introduction 12
2.2 Number of elements in a set 12
2.3 Use of Venn diagrams 14
2.4 Use of tree diagrams 19
2.5 Partitions 21
2.6 Sequences of operations 23
2.7 Counting samples 26
Chapter 3 The Binomial Theorem
3.1 Introduction 33
3.2 Properties of binomial coefficients 33
3.3 The binomial theorem 35
Chapter 4 Finite Sequences and Series
4.1 Introduction 39
4.2 Functions 39
4.3 Sequences 41
4.4 Arithmetic sequences 43
4.5 Geometric sequences 45
4.6 Arithmetic series 47
4.7 Geometric series 52
4.8 The summation notation 58
ix
x Contents
Chapter 5 Probability on Finite Sample Spaces
5.1 Introduction 64
5.2 The idea of probability 64
5.3 Probability measures 67
5.4 Probability of a complement 70
5.5 Probability of a union 73
5.6 Conditional probability 76
5.7 Independent events 82
5.8 Bernoulli experiments 85
5.9 The expected value of an experiment 89
*5.10 An application of probability to genetics 94
5.11 Bayes theorem 96
*5.12 Random variables 102
*5.13 Expected value 107
Chapter 6 Probability and Calculus
6.1 Introduction 113
6.2 Probability densities and areas 113
Chapter 7 Functions, Equations, and Graphs
7.1 Mathematical models 122
7.2 Straight lines and linear functions 123
7.3 Slope of a straight line 134
7.4 Graphs 139
7.5 An application of graphing 145
Chapter 8 The Definite Integral
8.1 Introduction 151
8.2 The notion of area 151
8.3 General definition of area 160
*8.4 Existence of the definite integral 166
*8.5 Approximation of areas 170
8.6 Properties of the definite integral 174
8.7 Geometric interpretation of the definite integral 186
8.8 Simpson s rule 191
Chapter 9 Probability and Differential Calculus
9.1 Introduction 198
9.2 Density at a point 198
Chapter 10 Continuous Functions and Limits
10.1 Introduction 205
10.2 The idea of a continuous function 205
Contents xi
10.3 Properties of continuous functions 209
10.4 The notion of limit 214
10.5 Limits and infinity 223
Chapter 11 The Derivative
11.1 Introduction 232
11.2 Problems for the differential calculus 232
11.3 The derivative and a geometric interpretation 235
11.4 An application of the derivative in economics 248
11.5 Computation of the derivative 254
11.6 The derivative of a derivative 261
Chapter 12 Optimization
12.1 Introduction 270
12.2 Extreme values of a function 270
12.3 Optimization models 276
Chapter 13 Exponential Functions and Natural Logarithms
13.1 Introduction 286
13.2 Exponential graphs 287
13.3 Exponents 289
13.4 Exponential functions 292
13.5 The number e and the natural logarithm 298
13.6 Properties of logarithms 306
Chapter 14 Inverse Functions and their Derivatives
14.1 Introduction 311
14.2 Inverse functions 311
14.3 Derivatives of inverse functions 321
14.4 Implicit differentiation 327
Chapter 15 Fundamental Theorem of Calculus
15.1 Introduction 333
15.2 The mean value theorem of integral calculus 334
*15.3 On a proof of the mean value theorem 340
15.4 The fundamental theorem 341
*15.5 On the value of e 348
Chapter 16 The Indefinite Integral and an Introduction to Differential Equations
16.1 Introduction 350
16.2 The indefinite integral 350
xii Contents
16.3 The differential 358
16.4 Introduction to differential equations 361
Chapter 17 Mathematical Models in the Life and Management Sciences
17.1 Introduction 371
17.2 Several models in the life and management sciences 376
Chapter 18 Integration Techniques
18.1 Introduction 392
18.2 Substitution methods in integration 392
18.3 Substitution in definite integrals 396
18.4 On the use of integral tables 398
18.5 A need for some trigonometry 401
18.6 Calculus of the trigonometric functions 414
18.7 Integration by parts 421
Chapter 19 Improper Integrals and Normal Density Functions
19.1 Introduction 424
19.2 Improper integrals 424
19.3 A discussion of normal density functions 430
Chapter 20 Linear Differential Equations
20.1 Introduction 443
20.2 Homogeneous linear differential equations with constant coefficients 444
20.3 Nonhomogeneous linear differential equations with constant
coefficients 450
20.4 The method of undetermined coefficients 455
20.5 An application of linear differential equations 463
20.6 Simultaneous differential equations 466
Chapter 21 Taylor Polynomials and the Poisson Process
21.1 Introduction 472
21.2 Taylor polynomials 472
21.3 The error term 483
21.4 The Poisson process 486
Chapter 22 Functions of Several Variables
22.1 Introduction 493
22.2 Functions of two or more variables 494
22.3 Limits and continuity 498
Contents xiii
Chapter 23 Differential Calculus with Several Variables
23.1 Introduction 507
23.2 Partial derivatives 507
23.3 A geometric interpretation of partial derivatives 516
23.4 Higher partial derivatives 521
23.5 Chain rules with several variables 527
Chapter 24 Optimization with Several Variables
24.1 Introduction 533
24.2 Existence of extreme values 534
24.3 Locating extreme values 542
24.4 Some optimization models involving two variables 551
24.5 An optimization model involving three variables 557
24.6 Lagrange multipliers 559
24.7 The method of least squares 564
Chapter 25 Multiple Integrals
25.1 Introduction 572
25.2 Iterated double integrals 572
2,5.3 Geometric interpretation of double integrals 578
25.4 Iterated triple integrals 582
25.5 Improper multiple integrals 583
25.6 Probability and multiple integrals 586
Chapter 26 Introduction to Difference Equations
26.1 Introduction 590
26.2 Techniques and applications of difference equations 590
26.3 The cobweb phenomenon in economics 595
26.4 On the spread of a disease 598
Answers to Odd Numbered Problems 605
Comprehensive Problem Sets 619
Index 645
|
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| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| spelling | Baxter, Willard E. Verfasser aut Calculus with probability For the life and management sciences Willard E. Baxter ; Clifford W. Sloyer* Reading, Mass. Addison-Wesley 1973 XIII,648 S. txt rdacontent n rdamedia nc rdacarrier Addison-Wesley series in mathematics. Calcul infinitésimal Probabilités Calculus Probabilities Sloyer, Clifford W. Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001971041&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Baxter, Willard E. Sloyer, Clifford W. Calculus with probability For the life and management sciences Calcul infinitésimal Probabilités Calculus Probabilities |
| title | Calculus with probability For the life and management sciences |
| title_auth | Calculus with probability For the life and management sciences |
| title_exact_search | Calculus with probability For the life and management sciences |
| title_full | Calculus with probability For the life and management sciences Willard E. Baxter ; Clifford W. Sloyer* |
| title_fullStr | Calculus with probability For the life and management sciences Willard E. Baxter ; Clifford W. Sloyer* |
| title_full_unstemmed | Calculus with probability For the life and management sciences Willard E. Baxter ; Clifford W. Sloyer* |
| title_short | Calculus with probability |
| title_sort | calculus with probability for the life and management sciences |
| title_sub | For the life and management sciences |
| topic | Calcul infinitésimal Probabilités Calculus Probabilities |
| topic_facet | Calcul infinitésimal Probabilités Calculus Probabilities |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001971041&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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