Introduction to Calculus and Analysis: v. 2/1 Chapters 1-4 (Classics in Mathematics)

Introduction to Calculus and Analysis: v. 2/1 Chapters 1-4 (Classics in Mathematics)

By: John Fritz (author), R. Courant (author)Paperback

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From the reviews: " of the best textbooks introducing several generations of mathematicians to higher mathematics...This excellent book is highly recommended both to instructors and students." --Acta Scientiarum Mathematicarum, 1991

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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

Product Details

  • publication date: 14/12/1999
  • ISBN13: 9783540665694
  • Format: Paperback
  • Number Of Pages: 581
  • ID: 9783540665694
  • weight: 890
  • ISBN10: 3540665692

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