Difference equations: theory and applications
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
New York
Van Nostrand Reinhold u.a.
1990
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| Edition: | 2. ed. |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 448 S. graph. Darst. |
| ISBN: | 0442001363 |
Staff View
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| 100 | 1 | |a Mickens, Ronald E. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Difference equations |b theory and applications |c Ronald E. Mickens |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a New York |b Van Nostrand Reinhold u.a. |c 1990 | |
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Record in the Search Index
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| adam_text | CONTENTS
; Preface/vii
1. THE DIFFERENCE CALCULUSM
1.1. Genesis of Difference EquationsM
1.2. Definitions 6
1.3. Derivation of Difference Equations 9
1.4. Existence and Uniqueness Theorem 12
1.5. Operators A and E 12
1.6. Elementary Difference Operators 16
1.7. Factorial Polynomials 22
1.8. Operator A 1 and the Sum Calculus 33
2. FIRST ORDER DIFFERENCE EQUATIONSU6
2.1. Introduction 46
2.2. General Linear Equation 46
2.3. _v*+1 yk = (n + 1)* 53
2.4. yk+l = /?*yk 56
2.5. Continued Fractions 58
2.6. yk+l kyk = Pk 62
2.7. A General First Order Equation: Geometrical Methods 64
2.8. A General First Order Equation: Expansion Techniques 68
3. LINEAR DIFFERENCE EQUATIONSN88
3.1. Introduction 88
3.2. Linearly Independent Functions 92
3.3. Fundamental Theorems for Homogeneous Equations 95
3.4. Inhomogeneous EquationsM00
3.5. Second Order EquationsM06
3.6. Sturm Liouville Difference EquationsM 14
ix
x CONTENTS
4. LINEAR DIFFERENCE EQUATIONS WITH CONSTANT
COEFFICIENTSM23
4.1. Introduction 123
4.2. Homogeneous EquationsM 23
4.3. Construction of a Difference Equation Having Specified
Solutions 136
4.4. Relationship Between Linear Difference and Differential
EquationsM 39
4.5. Inhomogeneous Equations: Method of Undetermined
Coefficients 141
4.6. Inhomogeneous Equations: Operator Methods 150
4.7. z Transform Method 159
4.8. Systems of Difference EquationsM73
5. LINEAR PARTIAL DIFFERENCE EQUATIONSM77
5.1. Introduction 177
5.2. Symbolic Methods 179
5.3. Lagrange s and Separation of Variables Methods 186
5.4. Laplace s Method 195
5.5. Particular Solutions 198
5.6. Simultaneous Equations with Constant Coefficients 205
6. NONLINEAR DIFFERENCE EQUATIONSX208
6.1. Introduction 208
6.2. Homogeneous Equations 208
6.3. Riccati Equations 209
6.4. Clairaut s Equation 214
6.5. Nonlinear Transformations, Miscellaneous Forms 216
6.6. Partial Difference Equations 223
7. APPLICATIONSN227
7.1. Introduction 227
7.2. Mathematics 228
7.3. Perturbation Techniques 253
CONTENTS xi
7.4. Stability of Fixed Points 263
7.5. The Logistic Equation 272
7.6. Numerical Integration of Differential Equations 290
7.7. Physical Systems 307
7.8. Economics 318
7.9. Warfare 337
7.10. Biological Sciences 348
7.11. Social Sciences 374
7.12. Miscellaneous Applications 388
PROBLEMSN391
APPENDIXX429
NOTES AND REFERENCESV437
BIBLIOGRAPHY 441
INDEXN443
|
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| indexdate | 2024-07-09T16:13:06Z |
| institution | BVB |
| isbn | 0442001363 |
| language | English |
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| physical | XI, 448 S. graph. Darst. |
| publishDate | 1990 |
| publishDateSearch | 1990 |
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| publisher | Van Nostrand Reinhold u.a. |
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| spelling | Mickens, Ronald E. Verfasser aut Difference equations theory and applications Ronald E. Mickens 2. ed. New York Van Nostrand Reinhold u.a. 1990 XI, 448 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Difference equations Differenzengleichung (DE-588)4012264-5 gnd rswk-swf Differenzengleichung (DE-588)4012264-5 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=002755261&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mickens, Ronald E. Difference equations theory and applications Difference equations Differenzengleichung (DE-588)4012264-5 gnd |
| subject_GND | (DE-588)4012264-5 |
| title | Difference equations theory and applications |
| title_auth | Difference equations theory and applications |
| title_exact_search | Difference equations theory and applications |
| title_full | Difference equations theory and applications Ronald E. Mickens |
| title_fullStr | Difference equations theory and applications Ronald E. Mickens |
| title_full_unstemmed | Difference equations theory and applications Ronald E. Mickens |
| title_short | Difference equations |
| title_sort | difference equations theory and applications |
| title_sub | theory and applications |
| topic | Difference equations Differenzengleichung (DE-588)4012264-5 gnd |
| topic_facet | Difference equations Differenzengleichung |
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