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Mathematical Analysis : An Introduction to Functions of Several Variables / by Mariano Giaquinta, Giuseppe Modica
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: SpringerLink BücherPublisher: Boston, MA : Birkhäuser Boston, 2009Description: Online-Ressource (XII, 348p. 105 illus, digital)ISBN:- 9780817646127
- 515
- QA299.6-433
- QA300
Contents:
Summary: Differential Calculus -- Integral Calculus -- Curves and Differential Forms -- Holomorphic Functions -- Surfaces and Level Sets -- Systems of Ordinary Differential Equations.Summary: This text introduces basic ideas, structures, and results of differential and integral calculus for functions of several variables. The presentation is engaging and motivates the reader with numerous examples, remarks, illustrations, and exercises. Mathematical Analysis: An Introduction to Functions of Several Variables may be used in the classroom setting for advanced undergraduate and graduate students or as a self-study. It is also a valuable reference for researchers in most mathematical disciplines. An appendix highlights mathematicians and scientists who have made important contributions in the development of theories in the subject. Other books recently published by the authors include: Mathematical Analysis: Functions of One Variable, Mathematical Analysis: Approximation and Discrete Processes, and Mathematical Analysis: Linear and Metric Structures and Continuity, all of which provide the reader with a strong foundation in modern-day analysis. Reviews of previous volumes in Mathematical Analysis: The presentation of the theory is clearly arranged, all theorems have rigorous proofs, and every chapter closes with a summing up of the results and exercises with different requirements. . . . This book is excellently suitable for students in mathematics, physics, engineering, computer science and all students of technological and scientific faculties. —Journal of Analysis and its Applications The exposition requires only a sound knowledge of calculus and the functions of one variable. A key feature this lively yet rigorous and systematic treatment is the historical accounts of ideas and methods of the subject. Ideas in mathematics develop in cultural, historical and economical contexts, thus the authors made brief accounts of those aspects and used a large number of beautiful illustrations. —Zentralblatt MATH.PPN: PPN: 1650074786Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
""Preface""; ""Contents""; ""1. Differential Calculus""; ""1.1 Differential Calculus of Scalar Functions""; ""1.2 Differential Calculus for Vector-valued Functions""; ""1.3 Theorems of Differential Calculus""; ""1.4 Invertibility of Maps Rn -> Rn""; ""1.5 Differential Calculus in Banach Spaces""; ""1.6 Exercises""; ""2. Integral Calculus""; ""2.1 Lebesgue�s Integral""; ""2.2 Convergence Theorems""; ""2.3 Mollifiers and Approximations""; ""2.4 Calculus of Integrals""; ""2.5 Measure and Area""; ""2.6 Gauss�Green Formulas""; ""2.7 Exercises""; ""3. Curves and Differential Forms""
""3.1 Differential Forms, Vector Fields, and Work""""3.2 Conservative Fields and Potentials""; ""3.3 Closed Forms and Irrotational Fields""; ""3.4 Stokes�s Formula in the Plane""; ""3.5 Exercises""; ""4. Holomorphic Functions""; ""4.1 Functions from C to C""; ""4.2 The Fundamental Theorem of Calculus on C""; ""4.3 Fundamental Theorems about Holomorphic Functions""; ""4.4 Examples of Holomorphic Functions""; ""4.5 Singularities""; ""4.6 Residues""; ""4.7 Further Consequences of Cauchy�s Formula""; ""4.8 Biholomorphisms""; ""4.9 Exercises""; ""5. Surfaces and Level Sets""
""5.1 Immersed and Embedded Surfaces""""5.2 Implicit Function Theorem""; ""5.3 Some Applications""; ""5.4 Curvature of Curves and Surfaces""; ""5.5 Exercises""; ""6. Systems of Ordinary Differential Equations""; ""6.1 Linear Systems""; ""6.2 Stability""; ""6.3 Poincare�Bendixson Theorem""; ""6.4 Exercises""; ""A. Mathematicians and Other Scientists""; ""B. Bibliographical Notes""; ""C. Index""
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