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Titel:	Lectures on partial differential equations
Von:	Vladimir I. Arnold
Person:	Arnolʹd, V. I. 1937-2010 Verfasser aut
Hauptverfasser:	Arnolʹd, V. I. 1937-2010 (VerfasserIn)
Format:	Buch
Sprache:	Englisch Russisch
Veröffentlicht:	Berlin [u.a.] Springer 2004
Schriftenreihe:	Universitext
Notation:	SK 540
Schlagwörter:	Análise numérica Equações diferenciais parciais Partiële differentiaalvergelijkingen Équations aux dérivées partielles Differential equations, Partial Partielle Differentialgleichung Lehrbuch
Medienzugang:	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010557157&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
Umfang:	X, 157 S. graph. Darst.
ISBN:	3540404481 9783540404484

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adam_text	Contents Preface to the Second Russian Edition ......................... V 1. The General Theory for One First-Order Equation ........ 1 Literature ................................................... 10 2. The General Theory for One First-Order Equation (Continued) ............................................... 11 Literature ................................................... 20 3. Huygens Principle in the Theory of Wave Propagation .... 21 4. The Vibrating String (d Alembert s Method) .............. 27 4.1. The General Solution .................................... 27 4.2. Boundary-Value Problems and the Cauchy Problem ......... 28 4.3. The Cauchy Problem for an Infinite String. d Alembert s Formula ................................................ 29 4.4. The Semi-Infinite String .................................. 31 4.5. The Finite String. Resonance ............................. 31 4.6. The Fourier Method ..................................... 32 5. The Fourier Method (for the Vibrating String) ............ 35 5.1. Solution of the Problem in the Space of Trigonometric Polynomials ............................................ 35 5.2. A Digression ............................................ 36 5.3. Formulas for Solving the Problem of Section 5.1............. 36 5.4. The General Case ....................................... 36 5.5. Fourier Series ........................................... 37 5.6. Convergence of Fourier Series ............................. 37 5.7. Gibbs Phenomenon ..................................... 39 X Contents 6. The Theory of Oscillations. The Variational Principle ...... 41 Literature ................................................... 50 7. The Theory of Oscillations. The Variational Principle (Continued) ............................................... 51 8. Properties of Harmonic Functions ......................... 65 8.1. Consequences of the Mean-Value Theorem .................. 67 8.2. The Mean-Value Theorem in the Multidimensional Case ...... 73 9. The Fundamental Solution for the Laplacian. Potentials ... 77 9.1. Examples and Properties ................................. 78 9.2. A Digression. The Principle of Superposition ................ 79 9.3. Appendix. An Estimate of the Single-Layer Potential ........ 89 10. The Double-Layer Potential ............................... 93 10.1. Properties of the Double-Layer Potential ................... 94 11. Spherical Functions. Maxwell s Theorem. The Removable Singularities Theorem .....................................105 12. Boundary-Value Problems for Laplace s Equation. Theory of Linear Equations and Systems ..........................121 12.1. Four Boundary-Value Problems for Laplace s Equation .......121 12.2. Existence and Uniqueness of Solutions .....................125 12.3. Linear Partial Differential Equations and Their Symbols ......127 A. The Topological Content of Maxwell s Theorem on the Multifield Representation of Spherical Functions ...........135 A.I. The Basic Spaces and Groups .............................136 A. 2. Some Theorems of Real Algebraic Geometry ................137 A.3. From Algebraic Geometry to Spherical Functions ............139 A.4. Explicit Formulas .......................................141 A.5. Maxwell s Theorem and CP2/conj « S4 ....................144 A.6. The History of Maxwell s Theorem ........................145 Literature ...................................................146 B. Problems ..................................................149 B.I. Material from the Seminars ...............................149 B.2. Written Examination Problems ............................156
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spellingShingle	Arnolʹd, V. I. 1937-2010 Lectures on partial differential equations Análise numérica larpcal Equações diferenciais parciais larpcal Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd
subject_GND	(DE-588)4044779-0 (DE-588)4123623-3
title	Lectures on partial differential equations
title_alt	Lekcij ob uravnenijach s častnimi proizvodnimi
title_auth	Lectures on partial differential equations
title_exact_search	Lectures on partial differential equations
title_full	Lectures on partial differential equations Vladimir I. Arnold
title_fullStr	Lectures on partial differential equations Vladimir I. Arnold
title_full_unstemmed	Lectures on partial differential equations Vladimir I. Arnold
title_short	Lectures on partial differential equations
title_sort	lectures on partial differential equations
topic	Análise numérica larpcal Equações diferenciais parciais larpcal Partiële differentiaalvergelijkingen gtt Équations aux dérivées partielles Differential equations, Partial Partielle Differentialgleichung (DE-588)4044779-0 gnd
topic_facet	Análise numérica Equações diferenciais parciais Partiële differentiaalvergelijkingen Équations aux dérivées partielles Differential equations, Partial Partielle Differentialgleichung Lehrbuch
url	http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010557157&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA
work_keys_str_mv	AT arnolʹdvi lekcijoburavnenijachscastnimiproizvodnimi AT arnolʹdvi lecturesonpartialdifferentialequations

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