Description
Book SynopsisFrom the reviews: "...one 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
Trade ReviewFrom the reviews: "These books (Introduction to Calculus and Analysis Vol. I/II) are very well written. The mathematics are rigorous but the many examples that are given and the applications that are treated make the books extremely readable and the arguments easy to understand. These books are ideally suited for an undergraduate calculus course. Each chapter is followed by a number of interesting exercises. More difficult parts are marked with an asterisk. There are many illuminating figures...Of interest to students, mathematicians, scientists and engineers. Even more than that." Newsletter on Computational and Applied Mathematics, 1991 "...one 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
Table of ContentsFunctions 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
