Introduction to calculus and analysis
Author(s)
Bibliographic Information
Introduction to calculus and analysis
(Classics in mathematics)
Springer-Verlag, c1999-c2000
Reprint of the 1989 ed
- v. 1
- v. II/1
- v. II/2
Available at / 55 libraries
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Note
Vol. 1: Reprint. Originally published: New York : Interscience Publishers, 1965
Vol. II: Reprint. Originally published: New York : Interscience Publishers, 1974
Vol. 1: PHYS: xxiii, 661 p. : ill. ; 25 cm
Vol. II/1: PHYS: xxv, 1-556 p. : ill. ; 24 cm
Vol. II/2: PHYS: xxv, 543-954 p. : ill. ; 24 cm
Includes index
Description and Table of Contents
- Volume
-
v. 1 ISBN 9783540650584
Description
Table of Contents
- Volume
-
v. II/1 ISBN 9783540665694
Description
Table of Contents
- Functions of Several Variables and Their Derivatives: Points and Points Sets in the Plane and in Space
- Functions of Several Independent Variables
- Continuity
- The Partial Derivatives of a Function
- The Differential of a Function and Its Geometrical Meaning
- Functions of Functions (Compound Functions) and the Introduction of New Independent Variables
- The mean Value Theorem and Taylor's Theorem for Functions of Several Variables
- Integrals of a Function Depending on a Parameter
- Differentials and Line Integrals
- The Fundamental Theorem on Integrability of Linear Differential Forms
- Appendix.- Vectors, Matrices, Linear Transformations: Operatios with Vectors
- Matrices and Linear Transformations
- Determinants
- Geometrical Interpretation of Determinants
- Vector Notions in Analysis.- Developments and Applications of the Differential Calculus: Implicit Functions
- Curves and Surfaces in Implicit Form
- Systems of Functions, Transformations, and Mappings
- Applications
- Families of Curves, Families of Surfaces, and Their Envelopes
- Alternating Differential Forms
- Maxima and Minima
- Appendix.- Multiple Integrals: Areas in the Plane
- Double Integrals
- Integrals over Regions in three and more Dimensions
- Space Differentiation. Mass and Density
- Reduction of the Multiple Integral to Repeated Single Integrals
- Transformation of Multiple Integrals
- Improper Multiple Integrals
- Geometrical Applications
- Physical Applications
- Multiple Integrals in Curvilinear Coordinates
- Volumes and Surface Areas in Any Number of Dimensions
- Improper Single Integrals as Functions of a Parameter
- The Fourier Integral
- The Eulerian Integrals (Gamma Function)
- Appendix
- Volume
-
v. II/2 ISBN 9783540665700
Description
Table of Contents
- Relations Between Surface and Volume Integrals: Connection Between Line Integrals and Double Integrals in the Plane
- Vector Form of the Divergence Theorem. Stokes's Theorem
- Formula for Integration by Parts in Two Dimensions: Green's Theorem
- The Divergence Theorem Applied to the Transformation of Double Integrals
- Area Differentiation
- Interpretation of the Formulae of Gauss and Stokes by Two-Dimensional Flows
- Orientation of Surfaces
- Integrals of Differential Forms and of Scalars over Surfaces
- Gauss's and Green's Theorems in Space
- Appendix: General Theory of Surfaces and of Surface Integrals.- Differential Equations: The Differential Equations for the Motion of a Particle in Three Dimensions
- The General Linear Differential Equation of the First Order
- Linear Differential Equations of Higher Order
- General Differential Equations of the First Order
- Systems of Differential Equations and Differential Equations of Higher Order
- Integration by the Method of Undermined Coefficients
- The Potential of Attracting Charges and Laplace's Equation
- Further Examples of Partial Differential Equations from Mathematical Physics .- Calculus of Variations: Functions and Their Extreme Values of a Functional
- Generalizations
- Problems Involving Subsidiary Conditions. Lagrange Multipliers.- Functions of a Complex Variable: Complex Functions Represented by Power Series
- Foundations of the General Theory of Functions of a Complex Variable
- The Integration of Analytic Functions
- Cauchy's Formula and Its Applications
- Applications to Complex Integration (Contour Integration)
- Many-Valued Functions and Analytic Extension.- List of Biographical Dates Index
by "Nielsen BookData"