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Mathematical Analysis II / by Claudio Canuto, Anita Tabacco
Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: Universitext | SpringerLink BücherPublisher: Milano : Springer-Verlag Italia, 2010Description: Online-Ressource (X, 543p, digital)ISBN:- 9788847017849
- 510
- QA1-939
- QA300
Contents:
Summary: Numerical series -- Series of functions and power series -- Fourier series -- Functions between Euclidean spaces -- Differential calculus for scalar functions -- Differential calculus for vector-valued functions -- Applying differential calculus -- Integral calculus in several variables -- Integral calculus on curves and surfaces -- Ordinary differential equations.Summary: The purpose of this textbook is to present an array of topics in Calculus, and conceptually follow our previous effort Mathematical Analysis I.The present material is partly found, in fact, in the syllabus of the typical second lecture course in Calculus as offered in most Italian universities. While the subject matter known as `Calculus 1' is more or less standard, and concerns real functions of real variables, the topics of a course on `Calculus 2'can vary a lot, resulting in a bigger flexibility. For these reasons the Authors tried to cover a wide range of subjects, not forgetting that the number of credits the current programme specifications confers to a second Calculus course is not comparable to the amount of content gathered here. The reminders disseminated in the text make the chapters more independent from one another, allowing the reader to jump back and forth, and thus enhancing the versatility of the book. On the website: http://calvino.polito.it/canuto-tabacco/analisi 2, the interested reader may find the rigorous explanation of the results that are merely stated without proof in the book, together with useful additional material. The Authors have completely omitted the proofs whose technical aspects prevail over the fundamental notions and ideas. The large number of exercises gathered according to the main topics at the end of each chapter should help the student put his improvements to the test. The solution to all exercises is provided, and very often the procedure for solving is outlined.PPN: PPN: 1650743998Package identifier: Produktsigel: ZDB-2-SEB | ZDB-2-SXMS | ZDB-2-SMA
""Title Page ""; ""Copyright Page ""; ""Preface ""; ""Table of Contents ""; ""1 Numerical series ""; ""1.1 Round-up on sequences ""; ""1.2 Numerical series ""; ""1.3 Series with positive terms ""; ""1.4 Alternating series ""; ""1.5 The algebra of series ""; ""1.6 Exercises ""; ""1.6.1 Solutions ""; ""2. Series of functions and power series ""; ""2.1 Sequences of functions ""; ""2.2 Properties of uniformly convergent sequences ""; ""2.2.1 Interchanging limits and integrals ""; ""2.2.2 Interchanging limits and derivatives ""; ""2.3 Series of functions ""; ""2.4 Power series ""
""2.4.1 Algebraic operations """"2.4.2 Differentiation and integration ""; ""2.5 Analytic functions ""; ""2.6 Power series in C ""; ""2.7 Exercises ""; ""2.7.1 Solutions ""; ""3 Fourier series ""; ""3.1 Trigonometric polynomials ""; ""3.2 Fourier Coefficients and Fourier series ""; ""3.3 Exponential form ""; ""3.4 Differentiation ""; ""3.5 Convergence of Fourier series ""; ""3.5.1 Quadratic convergence ""; ""3.5.2 Pointwise comvergence ""; ""3.5.3 Uniform convergence ""; ""3.5.4 Decay of Fourier coefficients ""; ""3.6 Periodic functions with period T > 0 ""; ""3.7 Exercises ""
""3.7.1 Solutions """"4 Functions between Euclidean spaces ""; ""4.1 Vector in Rn ""; ""4.2 Matrices ""; ""Square matrices ""; ""Eigenvalues and eigenvectors ""; ""Symmetric matriices ""; ""4.3 Sets in Rn and their properties ""; ""4.4 Functions: definitions and first examples ""; ""4.5 Continuity and limits ""; ""4.5.1 Properties of limits and continuity ""; ""4.6 Curves in Rm ""; ""Curves in polar, cylindrical and spherical coordinates ""; ""4.7 Surfaces in R3 ""; ""4.8 Exercises ""; ""4.8.1 Solutions ""; ""5 Differential calculus for scalar functions ""
""5.1 First partial dervatives and gradient """"5.2 Differentiability and differentials ""; ""5.2.1 Mean Value Theorem and Lipschitz functions ""; ""5.3 Second partial derivatives and Hessian matrix ""; ""5.4 Higher-oder partial derivatives ""; ""5.5 Taylor expansions; convexity ""; ""5.5.1 Convexity ""; ""5.6 Extremal points of a function; stationary points ""; ""5.6.1 Saddle points ""; ""5.7 Exercises ""; ""5.7.1 Solutions ""; ""6 Differential calculus for vector-valued functions ""; ""6.1 Partial derivatives and Jacobian matrix ""; ""6.2 Fifferentiability and Lipschitz functions ""
""6.3 Basic differential operators """"6.3.1 First-order operators ""; ""6.4 Differentiating composite functions ""; ""6.4.1 Functions defined by integrals ""; ""6.5 Regular curves ""; ""6.5.1 Congruence of curves; orientation ""; ""6.5.2 Length and arc length ""; ""6.5.3 Elements of differential geometry for curves ""; ""6.6 Variable changes ""; ""6.6.1 Special frame systems ""; ""6.7 Regular surfaces ""; ""6.7.1 Changing parametrisation ""; ""6.7.2 Orientable surfaces ""; ""6.7.3 Boundary of a surface; closed surfaces ""; ""6.7.4 Piecewise-regular surfaces ""; ""6.8 Exercises ""
""6.8.1 Solutions ""
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