Title Multidimensional differential and integral calculus : a practical approach / Giorgio Riccardi, Bruno Antonio Cifra, Enrico De Bernardis

Published Cham, Switzerland : Springer Nature Switzerland, [2024]

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Description 1 online resource (xii, 275 pages) : illustrations (some color) Contents Intro -- Preface -- Contents -- 1 Basic Concepts and Parametrisation of Curves -- 1.1 Introductory Concepts -- 1.2 Parametrization of a Curve -- 1.3 Limit on a Curve -- 1.4 Catalogs of Sample Curves -- 1.5 Suggested Readings -- References -- 2 Differential and Geometric Properties of Curves -- 2.1 Differential and Tangent Vector -- 2.2 Curvilinear Abscissa -- 2.3 Normal Unit Vector and Curvature -- 2.4 Suggested Readings -- References -- 3 Curves in Space: The Frenet Frame -- 3.1 Binormal Unit Vector, Torsion -- 3.2 Suggested Readings -- Reference -- 4 Functions of a Vector Variable 4.1 Scalar Functions of Several Scalar Variables -- 4.2 Field of Existence -- 4.3 Limit of a Function of Several Scalar Variables -- 4.4 Suggested Readings -- References -- 5 Continuity and Differentiability of Functions of a Vector Variable -- 5.1 Divergent Limits and Limits at Infinity -- 5.2 Topological Properties of double struck upper R Superscript nmathbbRn -- 5.3 Consequences of the Continuity -- 5.4 Differential of a Function f colon double struck upper R Superscript n Baseline right arrow double struck upper Rf: mathbbRn tomathbbR -- 5.5 Suggested Readings -- References 6 Partial Derivatives -- 6.1 Partial Derivatives -- 6.2 Directional Derivative -- 6.3 ellipsis... Again on the Differential -- 6.4 Successive Partial Derivatives -- 6.5 Suggested Readings -- References -- 7 Sequences of Functions -- 7.1 Pointwise Convergence -- 7.2 Uniform Convergence -- 7.3 Taking Limits Under the Integral -- 7.4 Taking Limits Under the Derivative -- 7.5 Suggested Readings -- Reference -- 8 Series of Functions -- 8.1 Introduction -- 8.2 Power Series -- 8.3 Remarkable Developments -- 8.4 The Binomial Series -- 8.5 Trigonometric Series and Fourier Series 8.6 Differentiability and Integrability of Fourier Series -- 8.7 Complex Form of Fourier Series -- 8.8 Gibbs Phenomenon -- 8.9 Suggested Readings -- References -- 9 Taylor Series for Functions of Several Variables -- 9.1 Taylor Series for a Function f colon double struck upper R Superscript n Baseline right arrow double struck upper Rf: mathbbRn tomathbbR -- 9.2 Suggested Readings -- References -- 10 Applications of the Taylor Series -- 10.1 Calculation of the Extreme and Saddle Points -- 10.2 Approximation of the Solution of a Partial Differential Problem 11 Integration of Functions of Two Variables -- 11.1 Derivative of a Definite Integral with Variable Limits -- 11.2 Double Integrals -- 11.3 Suggested Readings -- References -- 12 Samples of Two-Dimensional Integration and Change of Variables -- 12.1 A Quite Complicated Integral -- 12.2 Change of Coordinates Inside a Double Integral -- 12.3 Suggested Readings -- References -- 13 Two-Dimensional Integration and Area of a Surface -- 13.1 Examples of Calculus of Two-Dimensional Integrals by Means of the Change of Variables -- 13.2 Evaluation of the Surface Area -- 13.3 Suggested Readings Summary This textbook proposes an informal access to the most important issues of multidimensional differential and integral calculus. The traditional style -- characterized by listing definitions, theorems, and proofs -- is replaced by a conversational approach, primarily oriented to applications. The topics covered, developing along the usual path of a textbook for undergraduate courses, are always introduced by thoroughly carried out examples. This drives the reader in building the capacity of properly use the theoretical tools to model and solve practical problems. To situate the contents within a historical perspective, the book is accompanied by a number of links to the biographies of all scientists mentioned as leading actors in the development of the theory Bibliography Includes bibliographical references and index Notes Description based on online resource; title from digital title page (viewed on December 31, 2024) Subject Differential calculus. Differential equations. Calculus, Integral. Cálculo diferencial Cálculo integral Ecuaciones diferenciales Form Electronic book Author Cifra, Bruno Antonio, author De Bernardis, Enrico, author ISBN 9783031703263 303170326X

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