Introduction to difference equations: with illustrative examples from economics, psychology, and sociology
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York [u.a.]
Wiley [u.a.]
1958
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 260 S. graph. Darst. |
Staff View
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| 245 | 1 | 0 | |a Introduction to difference equations |b with illustrative examples from economics, psychology, and sociology |c Samuel Goldberg |
| 264 | 1 | |a New York [u.a.] |b Wiley [u.a.] |c 1958 | |
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Record in the Search Index
| _version_ | 1804116656369172480 |
|---|---|
| adam_text | Contents
0 Introduction 1
1 The Calculus of Finite Differences 9
1.1 The First Difference Function 9
1.2 Second and Higher Differences 18
1.3 The Operator £ 21
1.4 Some Properties of A and E 24
1.5 Equivalence of Operators 34
1.6 Indefinite Summation: The Operator A 1 41
* 1.7 Analogies between the Difference and Differential Cal¬
culus 46
2 Difference Equations 50
2.1 Basic Definitions 50
2.2 Solutions of a Difference Equation 55
2.3 An Existence and Uniqueness Theorem 60
2.4 The Equation yic+i = Ay^ + B 63
2.5 Sequences 69
2.6 Solutions as Sequences 77
2.7 Simple and Compound Interest 87
2.8 Economic Dynamics 93
2.9 Inventory Analysis 98
2.10 A Probability Model for Learning 103
2.11 Geometric Growth 110
* 2.12 Approximating a Differential Equation by a Difference
Equation 116
3 Linear Difference Equations with Constant Coefficients 1 21
3.1 Some Basic Theorems 121
3.2 Fundamental Sets of Solutions 128
xi
xii CONTENTS
3.3 General Solution of the Homogeneous Equation 134
3.4 Particular Solutions of the Complete Equation 143
3.5 Limiting Behavior of Solutions 148
3.6 Illustrative Examples from the Social Sciences 153
3.7 The General Case of Order n 163
* 3.8 Linear Differential Equations with Constant Coeffi¬
cients 167
4 Selected Topics 169
4.1 Equilibrium and Stability 169
4.2 First-Order Equations and Cobweb Cycles 176
4.3 A Characteristic-Value Problem 184
* 4.4 Generating Functions 189
4.5 Matrix Methods 207
Selected References 246
Answers to Problems 248
Index 255
|
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| discipline | Mathematik |
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| id | DE-604.BV002201028 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T15:41:58Z |
| institution | BVB |
| language | English |
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| physical | XII, 260 S. graph. Darst. |
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| publishDate | 1958 |
| publishDateSearch | 1958 |
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| publisher | Wiley [u.a.] |
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| spelling | Goldberg, Samuel Verfasser aut Introduction to difference equations with illustrative examples from economics, psychology, and sociology Samuel Goldberg New York [u.a.] Wiley [u.a.] 1958 XII, 260 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Differentialgleichung (DE-588)4012249-9 gnd rswk-swf Differenzengleichung (DE-588)4012264-5 gnd rswk-swf 1\p (DE-588)4151278-9 Einführung gnd-content Differenzengleichung (DE-588)4012264-5 s DE-604 Differentialgleichung (DE-588)4012249-9 s 2\p DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001445863&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Goldberg, Samuel Introduction to difference equations with illustrative examples from economics, psychology, and sociology Differentialgleichung (DE-588)4012249-9 gnd Differenzengleichung (DE-588)4012264-5 gnd |
| subject_GND | (DE-588)4012249-9 (DE-588)4012264-5 (DE-588)4151278-9 |
| title | Introduction to difference equations with illustrative examples from economics, psychology, and sociology |
| title_auth | Introduction to difference equations with illustrative examples from economics, psychology, and sociology |
| title_exact_search | Introduction to difference equations with illustrative examples from economics, psychology, and sociology |
| title_full | Introduction to difference equations with illustrative examples from economics, psychology, and sociology Samuel Goldberg |
| title_fullStr | Introduction to difference equations with illustrative examples from economics, psychology, and sociology Samuel Goldberg |
| title_full_unstemmed | Introduction to difference equations with illustrative examples from economics, psychology, and sociology Samuel Goldberg |
| title_short | Introduction to difference equations |
| title_sort | introduction to difference equations with illustrative examples from economics psychology and sociology |
| title_sub | with illustrative examples from economics, psychology, and sociology |
| topic | Differentialgleichung (DE-588)4012249-9 gnd Differenzengleichung (DE-588)4012264-5 gnd |
| topic_facet | Differentialgleichung Differenzengleichung Einführung |
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