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Indeholder "Chapter I. Preliminary Remarks on Analytical Geometry and Vector Analysis", "1. Rectangular Co-ordinates and Vectors", "2. The Area of a Triangle, the Volume of a Tetrahedron, the Vector Multiplication of Vectors", "3. Simple Theorems on Determinants of the Second and Third Order", "4.
Virkelig nydelig lærebog for lærenemme og lærevillige matematikstuderende. Grundliggende matematisk analyse med masser af gennemarbejdede eksempler og en klar rød tråd. Selv om Richard Courant skrev den i 30'ernes Tyskland, er den stadig værd at læse.
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Affine Transformations and the Multiplication of Determinants", "Chapter II. Functions of several Variables and their Derivatives", "1. The Concept of Function in the Case of Several Variables", "2. Continuity", "3. The Derivatives of a Function", "4. The Total Differential of a Function and its Geometrical Meaning", "5. Functions of Functions (Compound Functions) and the Introduction of New Independent Variables", "6. The Mean Value Theorem and Taylor's Theorem for Functions of Several Variables", "7. The Application of Vector Methods", "Appendix" "1. The Principle of the Point of Accumulation in Several Dimensions and its Applications", "2. The Concept of Limit for Functions of Several Variables", "3. Homogeneous Functions", "Chapter III. Development and Applications of the Differential Calculus", "1. Implicit Functions", "2. Curves and Surfaces in Implicit Form", "3. Systems of Functions, Transformations, and Mappings", "4. Applications", "5. Families of Curves, Families of Surfaces, and their Envelopes", "6. Maxima and Minima", "Appendix" "1. Sufficient Conditions for Extreme Values", "2. Singular Points of Plane Curves", "3. Singular Points of Surfaces", "4. Connexion between Euler's and Lagrange's Representations of the Motion of a Fluid", "5. Tangential Representation of a Closed Curve", "Chapter IV. Multiple Integrals", "1. Ordinary Integrals as Functions of a Parameter", "2. The Integral of a Continuous Function over a Region of the Plane or of Space", "3. Reduction of the Multiple Integral to Repeated Single Integrals", "4. Transformation of Multiple Integrals", "5. Improper Integrals", "6. Geometrical Applications", "7. Physical Applications", "Appendix" "1. The Existence of the Multiple Integral", "2. General Formula for the Area (or Volume) of a Region bounded by Segments of Straight Lines or Plane Areas (Guldin's Formula). The Polar Planimeter", "3. Volumes and Areas in Space of any Number of Dimensions", "4. Improper Integrals as Functions of a Parameter", "5. The Fourier Integral", "6. The Eulerian Integrals (Gamma Function)", "7. Differentiation and Integration to Fractional Order. Abel's Integral Equation", "8. Note on the Definition of the Area of a Curved Surface", "Chapter V. Integration over Regions in Several Dimensions", "1. Line Integrals", "2. Connexion between Line Integrals and Double Integrals in the Plane. (The Integral Theorems of Gauss, Stokes, and Green)", "3. Interpretation and Applications of the Integral Theorems for the Plane", "4. Surface Integrals", "5. Gauss's Theorem and Green's Theorem in Space", "6. Stokes's Theorem in Space", "7. The Connexion between Differentiation and Integration for Several Variables", "Appendix" "1. Remarks on Gauss's Theorem and Stokes's Theorem", "2. Representation of a Source-free Vector Field as a Curl", "Chapter VI. Differential Equations", "1. The Differential Equations of the Motion of a Particle in Three Dimensions", "2. Examples on the Mechanics of a Particle", "3. Further Examples of Differential Equations", "4. Linear Differential Equations", "5. General Remarks on Differential Equations", "6. The Potential of Attracting Charges", "7. Further Examples of Partial Differential Equations", "Chapter VII. Calculus of Variations", "1. Introduction", "2. Euler's Differential Equation in the Simplest Case", "3. Generalizations", "Chapter VIII. Functions of a Complex Variable", "1. Introduction", "2. Foundations of the Theory of Functions of a Complex Variable", "3. The Integration of Analytic Functions", "4. Cauchy's Formula and its Applications", "5. Applications to Complex Integration (Contour Integration)", "6. Many-valued Functions and Analytic Extension". "Supplement: Real Numbers and the Concept of Limit.", "Miscellaneous Examples", "Summary of Important Theorems and Formulæ", "Answers and Hints", "Index".Virkelig nydelig lærebog for lærenemme og lærevillige matematikstuderende. Grundliggende matematisk analyse med masser af gennemarbejdede eksempler og en klar rød tråd. Selv om Richard Courant skrev den i 30'ernes Tyskland, er den stadig værd at læse.
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Genres
Publication
Blackie (1967), Hardcover
Description
Volume 2 of the classic advanced calculus text Richard Courant's Differential and Integral Calculus is considered an essential text for those working toward a career in physics or other applied math. Volume 2 covers the more advanced concepts of analytical geometry and vector analysis, including multivariable functions, multiple integrals, integration over regions, and much more, with extensive appendices featuring additional instruction and author annotations. The included supplement contains formula and theorem lists, examples, and answers to in-text problems for quick reference.
Subjects
Language
Original language
German
Physical description
682 p.; 22.2 cm
Local notes
Omslag: Ikke angivet
Omslaget viser en saddelkurve u = x^2 + y^2
Indskannet omslag - N650U - 150 dpi
Fra forordet:
'I would impress on readers new to the subject, even more than I did in the preface to Volume I, that they are not expected to read a book like this consecutively.'
Omslaget viser en saddelkurve u = x^2 + y^2
Indskannet omslag - N650U - 150 dpi
Fra forordet:
'I would impress on readers new to the subject, even more than I did in the preface to Volume I, that they are not expected to read a book like this consecutively.'
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Pages
682
DDC/MDS
| 515 |