Essentials of mathematical methods in science and engineering:
Gespeichert in:
| Format: | Elektronisch E-Book |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
Hoboken, N.J.
Wiley
c2008
|
| Schlagworte: | |
| Online-Zugang: | FRO01 TUM01 Volltext |
| Beschreibung: | Includes bibliographical references (p. 787-792) and index 1. Functional Analysis -- 1.1 Concept of Function -- 1.2 Continuity and Limits -- 1.3 Partial Differentiation -- 1.4 Total Differential -- 1.5 Taylor Series -- 1.6 Maxima and Minima of Functions -- 1.7 Extrema of Functions with Conditions -- 1.8 Derivatives and Differentials of Composite Functions -- 1.9 Implicit Function Theorem -- 1.10 Inverse Functions -- 1.11 Integral Calculus and the Definite Integral -- 1.12 Riemann Integral -- 1.13 Improper Integrals -- 1.14 Cauchy Principal Value Integrals -- 1.15 Integrals Involving a Parameter -- 1.16 Limits of Integration Depending on a Parameter -- 1.17 Double Integrals -- 1.18 Properties of Double Integrals -- 1.19 Triple and Multiple Integrals -- Problems -- 2. Vector Analysis -- 2.1 Vector Algebra: Geometric Method -- 2.1.1 Multiplication of Vectors -- 2.2 Vector Algebra: Coordinate Representation -- 2.3 Lines and Planes -- 2.4 Vector Differential Calculus -- 2.4.1 Scalar Fields and Vector Fields -- 2.4.2 Vector Differentiation -- - 2.5 Gradient Operator -- 2.5.1 Meaning of the Gradient -- 2.5.2 Directional Derivative -- 2.6 Divergence and Curl Operators -- 2.6.1 Meaning of Divergence and the Divergence Theorem -- 2.7 Vector Integral Calculus in Two Dimensions -- 2.7.1 Arc Length and Line Integrals -- 2.7.2 Surface Area and Surface Integrals -- 2.7.3 An Alternate Way to Write Line Integrals -- 2.7.4 Green's Theorem -- 2.7.5 Interpretations of Green's Theorem -- 2.7.6 Extension to Multiply Connected Domains -- 2.8 Curl Operator and Stokes's Theorem -- 2.8.1 On the Plane -- 2.8.2 In Space -- 2.8.3 Geometric Interpretation of Curl -- 2.9 Mixed Operations with the Del Operator -- 2.10 Potential Theory -- 2.10.1 Gravitational Field of a Spherically Symmetric Star -- 2.10.2 Work Done by Gravitational Force -- 2.10.3 Path Independence and Exact Differentials -- 2.10.4 Gravity and Conservative Forces -- 2.10.5 Gravitational Potential -- 2.10.6 Gravitational Potential Energy of a System -- 2.10.7 Helmholtz Theorem -- - 2.10.8 Applications of the Helmholtz Theorem -- 2.10.9 Examples from Physics -- Problems -- 3. Generalized Coordinates and Tensors -- 3.1 Transformations Between Cartesian Coordinates -- 3.1.1 Basis Vectors and Direction Cosines -- 3.1.2 Transformation Matrix and the Orthogonality Relation -- 3.1.3 Inverse Transformation Matrix -- 3.2 Cartesian Tensors -- 3.2.1 Algebraic Properties of Tensors -- 3.2.2 Kronecker Delta and the Permutation Symbol -- 3.3 Generalized Coordinates -- 3.3.1 Coordinate Curves and Surfaces -- 3.3.2 Why Upper and Lower Indices -- 3.4 General Tensors -- 3.4.1 Einstein Summation Convention -- 3.4.2 Line Element -- 3.4.3 Metric Tensor -- 3.4.4 How to Raise and Lower Indices -- 3.4.5 Metric Tensor and the Basis Vectors -- 3.4.6 Displacement Vector -- 3.4.7 Transformation of Scalar Functions and Line Integrals -- 3.4.8 Area Element in Generalized Coordinates -- 3.4.9 Area of a Surface -- 3.4.10 Volume Element in Generalized Coordinates -- - 3.4.11 Invariance and Covariance -- 3.5 Differential Operators in Generalized Coordinates -- 3.5.1 Gradient -- 3.5.2 Divergence -- 3.5.3 Curl -- 3.5.4 Laplacian |
| Beschreibung: | 1 Online-Ressource (xxvi, 802 p.) |
| ISBN: | 0470378026 0470378042 9780470378021 9780470378045 |
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| 500 | |a - 3.4.11 Invariance and Covariance -- 3.5 Differential Operators in Generalized Coordinates -- 3.5.1 Gradient -- 3.5.2 Divergence -- 3.5.3 Curl -- 3.5.4 Laplacian | ||
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Datensatz im Suchindex
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| spelling | Essentials of mathematical methods in science and engineering Ş. Selçuk Bayın Hoboken, N.J. Wiley c2008 1 Online-Ressource (xxvi, 802 p.) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references (p. 787-792) and index 1. Functional Analysis -- 1.1 Concept of Function -- 1.2 Continuity and Limits -- 1.3 Partial Differentiation -- 1.4 Total Differential -- 1.5 Taylor Series -- 1.6 Maxima and Minima of Functions -- 1.7 Extrema of Functions with Conditions -- 1.8 Derivatives and Differentials of Composite Functions -- 1.9 Implicit Function Theorem -- 1.10 Inverse Functions -- 1.11 Integral Calculus and the Definite Integral -- 1.12 Riemann Integral -- 1.13 Improper Integrals -- 1.14 Cauchy Principal Value Integrals -- 1.15 Integrals Involving a Parameter -- 1.16 Limits of Integration Depending on a Parameter -- 1.17 Double Integrals -- 1.18 Properties of Double Integrals -- 1.19 Triple and Multiple Integrals -- Problems -- 2. Vector Analysis -- 2.1 Vector Algebra: Geometric Method -- 2.1.1 Multiplication of Vectors -- 2.2 Vector Algebra: Coordinate Representation -- 2.3 Lines and Planes -- 2.4 Vector Differential Calculus -- 2.4.1 Scalar Fields and Vector Fields -- 2.4.2 Vector Differentiation -- - 2.5 Gradient Operator -- 2.5.1 Meaning of the Gradient -- 2.5.2 Directional Derivative -- 2.6 Divergence and Curl Operators -- 2.6.1 Meaning of Divergence and the Divergence Theorem -- 2.7 Vector Integral Calculus in Two Dimensions -- 2.7.1 Arc Length and Line Integrals -- 2.7.2 Surface Area and Surface Integrals -- 2.7.3 An Alternate Way to Write Line Integrals -- 2.7.4 Green's Theorem -- 2.7.5 Interpretations of Green's Theorem -- 2.7.6 Extension to Multiply Connected Domains -- 2.8 Curl Operator and Stokes's Theorem -- 2.8.1 On the Plane -- 2.8.2 In Space -- 2.8.3 Geometric Interpretation of Curl -- 2.9 Mixed Operations with the Del Operator -- 2.10 Potential Theory -- 2.10.1 Gravitational Field of a Spherically Symmetric Star -- 2.10.2 Work Done by Gravitational Force -- 2.10.3 Path Independence and Exact Differentials -- 2.10.4 Gravity and Conservative Forces -- 2.10.5 Gravitational Potential -- 2.10.6 Gravitational Potential Energy of a System -- 2.10.7 Helmholtz Theorem -- - 2.10.8 Applications of the Helmholtz Theorem -- 2.10.9 Examples from Physics -- Problems -- 3. Generalized Coordinates and Tensors -- 3.1 Transformations Between Cartesian Coordinates -- 3.1.1 Basis Vectors and Direction Cosines -- 3.1.2 Transformation Matrix and the Orthogonality Relation -- 3.1.3 Inverse Transformation Matrix -- 3.2 Cartesian Tensors -- 3.2.1 Algebraic Properties of Tensors -- 3.2.2 Kronecker Delta and the Permutation Symbol -- 3.3 Generalized Coordinates -- 3.3.1 Coordinate Curves and Surfaces -- 3.3.2 Why Upper and Lower Indices -- 3.4 General Tensors -- 3.4.1 Einstein Summation Convention -- 3.4.2 Line Element -- 3.4.3 Metric Tensor -- 3.4.4 How to Raise and Lower Indices -- 3.4.5 Metric Tensor and the Basis Vectors -- 3.4.6 Displacement Vector -- 3.4.7 Transformation of Scalar Functions and Line Integrals -- 3.4.8 Area Element in Generalized Coordinates -- 3.4.9 Area of a Surface -- 3.4.10 Volume Element in Generalized Coordinates -- - 3.4.11 Invariance and Covariance -- 3.5 Differential Operators in Generalized Coordinates -- 3.5.1 Gradient -- 3.5.2 Divergence -- 3.5.3 Curl -- 3.5.4 Laplacian SCIENCE / Philosophy & Social Aspects bisacsh Mathematik Naturwissenschaft Science / Mathematics Science / Methodology Engineering mathematics SCIENCE / Philosophy & Social Aspects / bisacsh Technische Mathematik (DE-588)4827059-3 gnd rswk-swf Technische Mathematik (DE-588)4827059-3 s 1\p DE-604 Bayin, Ş. Selçuk Sonstige oth Erscheint auch als Druckausgabe 0-470-34379-6 Erscheint auch als Druckausgabe 978-0-470-34379-1 https://onlinelibrary.wiley.com/doi/book/10.1002/9780470378045 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Essentials of mathematical methods in science and engineering SCIENCE / Philosophy & Social Aspects bisacsh Mathematik Naturwissenschaft Science / Mathematics Science / Methodology Engineering mathematics SCIENCE / Philosophy & Social Aspects / bisacsh Technische Mathematik (DE-588)4827059-3 gnd |
| subject_GND | (DE-588)4827059-3 |
| title | Essentials of mathematical methods in science and engineering |
| title_auth | Essentials of mathematical methods in science and engineering |
| title_exact_search | Essentials of mathematical methods in science and engineering |
| title_full | Essentials of mathematical methods in science and engineering Ş. Selçuk Bayın |
| title_fullStr | Essentials of mathematical methods in science and engineering Ş. Selçuk Bayın |
| title_full_unstemmed | Essentials of mathematical methods in science and engineering Ş. Selçuk Bayın |
| title_short | Essentials of mathematical methods in science and engineering |
| title_sort | essentials of mathematical methods in science and engineering |
| topic | SCIENCE / Philosophy & Social Aspects bisacsh Mathematik Naturwissenschaft Science / Mathematics Science / Methodology Engineering mathematics SCIENCE / Philosophy & Social Aspects / bisacsh Technische Mathematik (DE-588)4827059-3 gnd |
| topic_facet | SCIENCE / Philosophy & Social Aspects Mathematik Naturwissenschaft Science / Mathematics Science / Methodology Engineering mathematics SCIENCE / Philosophy & Social Aspects / bisacsh Technische Mathematik |
| url | https://onlinelibrary.wiley.com/doi/book/10.1002/9780470378045 |
| work_keys_str_mv | AT bayinsselcuk essentialsofmathematicalmethodsinscienceandengineering |