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The Big Book of Real Analysis [[electronic resource] ] : From Numbers to Measures / / by Syafiq Johar
The Big Book of Real Analysis [[electronic resource] ] : From Numbers to Measures / / by Syafiq Johar
Autore Johar Syafiq
Edizione [1st ed. 2023.]
Pubbl/distr/stampa Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023
Descrizione fisica 1 online resource (950 pages)
Disciplina 510
Soggetto topico Mathematics
Mathematical analysis
Sequences (Mathematics)
Differential equations
Measure theory
Functions of real variables
Càlcul
Anàlisi matemàtica
Successions (Matemàtica)
Analysis
Sequences, Series, Summability
Differential Equations
Measure and Integration
Real Functions
Soggetto genere / forma Llibres electrònics
ISBN 3-031-30832-8
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Preface -- 1. Logic and Sets -- 2. Integers -- 3. Construction of the Real Numbers -- 4. The Real Numbers -- 5. Real Sequences -- 6. Some Applications of Real Sequences -- 7. Real Series -- 8. Additional Topics in Real Series -- 9. Functions and Limits -- 10. Continuity -- 11. Function Sequences and Series -- 12. Power Series -- 13. Differentiation -- 14. Some Applications of Differentiation -- 15. Riemann and Darboux Integration -- 16. The Fundamental Theorem of Calculus -- 17. Taylor and MacLaurin Series -- 18. Introduction to Measure Theory -- 19. Lebesgue Integration -- 20. Double Integrals -- Solutions to the Exercises -- Bibliography -- Index.
Record Nr. UNINA-9910799485303321
Johar Syafiq  
Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Calculus and Linear Algebra : Fundamentals and Applications / / Aldo G. S. Ventre
Calculus and Linear Algebra : Fundamentals and Applications / / Aldo G. S. Ventre
Autore Ventre Aldo G. S.
Edizione [1st ed. 2023.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , 2023
Descrizione fisica 1 online resource (530 pages)
Disciplina 512.5
Soggetto topico Algebras, Linear
Calculus
Geometric analysis
Càlcul
Àlgebra lineal
Soggetto genere / forma Llibres electrònics
ISBN 9783031205491
9783031205484
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Language Sets -- Numbers and propositions -- Relations -- Euclidean geometry -- Functions -- The real line -- Real-valued functions of a real variable. The line.
Record Nr. UNINA-9910659487403321
Ventre Aldo G. S.  
Cham, Switzerland : , : Springer, , 2023
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Calculus and linear algebra in recipes : terms, phrases and numerous examples in short learning units / / Christian Karpfinger
Calculus and linear algebra in recipes : terms, phrases and numerous examples in short learning units / / Christian Karpfinger
Autore Karpfinger Christian
Pubbl/distr/stampa Berlin, Germany : , : Springer, , [2022]
Descrizione fisica 1 online resource (1015 pages)
Disciplina 512.5
Soggetto topico Algebras, Linear
Calculus
Differential equations
Àlgebra lineal
Càlcul
Equacions diferencials
Soggetto genere / forma Llibres electrònics
ISBN 9783662654583
9783662654576
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Foreword to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- 1 Speech, Symbols and Sets -- 1.1 Speech Patterns and Symbols in Mathematics -- 1.1.1 Junctors -- 1.1.2 Quantifiers -- 1.2 Summation and Product Symbol -- 1.3 Powers and Roots -- 1.4 Symbols of Set Theory -- 1.5 Exercises -- 2 The Natural Numbers, Integers and Rational Numbers -- 2.1 The Natural Numbers -- 2.2 The Integers -- 2.3 The Rational Numbers -- 2.4 Exercises -- 3 The Real Numbers -- 3.1 Basics -- 3.2 Real Intervals -- 3.3 The Absolute Value of a Real Number -- 3.4 n-th Roots -- 3.5 Solving Equations and Inequalities -- 3.6 Maximum, Minimum, Supremum and Infimum -- 3.7 Exercises -- 4 Machine Numbers -- 4.1 b-adic Representation of Real Numbers -- 4.2 Floating Point Numbers -- 4.2.1 Machine Numbers -- 4.2.2 Machine Epsilon, Rounding and Floating Point Arithmetic -- 4.2.3 Loss of Significance -- 4.3 Exercises -- 5 Polynomials -- 5.1 Polynomials: Multiplication and Division -- 5.2 Factorization of Polynomials -- 5.3 Evaluating Polynomials -- 5.4 Partial Fraction Decomposition -- 5.5 Exercises -- 6 Trigonometric Functions -- 6.1 Sine and Cosine -- 6.2 Tangent and Cotangent -- 6.3 The Inverse Functions of the Trigonometric Functions -- 6.4 Exercises -- 7 Complex Numbers: Cartesian Coordinates -- 7.1 Construction of C -- 7.2 The Imaginary Unit and Other Terms -- 7.3 The Fundamental Theorem of Algebra -- 7.4 Exercises -- 8 Complex Numbers: Polar Coordinates -- 8.1 The Polar Representation -- 8.2 Applications of the Polar Representation -- 8.3 Exercises -- 9 Linear Systems of Equations -- 9.1 The Gaussian Elimination Method -- 9.2 The Rank of a Matrix -- 9.3 Homogeneous Linear Systems of Equations -- 9.4 Exercises -- 10 Calculating with Matrices -- 10.1 Definition of Matrices and Some Special Matrices.
10.2 Arithmetic Operations -- 10.3 Inverting Matrices -- 10.4 Calculation Rules -- 10.5 Exercises -- 11 LR-Decomposition of a Matrix -- 11.1 Motivation -- 11.2 The LR-Decomposition: Simplified Variant -- 11.3 The LR-Decomposition: General Variant -- 11.4 The LR-Decomposition-with Column Pivot Search -- 11.5 Exercises -- 12 The Determinant -- 12.1 Definition of the Determinant -- 12.2 Calculation of the Determinant -- 12.3 Applications of the Determinant -- 12.4 Exercises -- 13 Vector Spaces -- 13.1 Definition and Important Examples -- 13.2 Subspaces -- 13.3 Exercises -- 14 Generating Systems and Linear (In)Dependence -- 14.1 Linear Combinations -- 14.2 The Span of X -- 14.3 Linear (In)Dependence -- 14.4 Exercises -- 15 Bases of Vector Spaces -- 15.1 Bases -- 15.2 Applications to Matrices and Systems of Linear Equations -- 15.3 Exercises -- 16 Orthogonality I -- 16.1 Scalar Products -- 16.2 Length, Distance, Angle and Orthogonality -- 16.3 Orthonormal Bases -- 16.4 Orthogonal Decomposition and Linear Combination with Respect to an ONB -- 16.5 Orthogonal Matrices -- 16.6 Exercises -- 17 Orthogonality II -- 17.1 The Orthonormalization Method of Gram and Schmidt -- 17.2 The Vector Product and the (Scalar) Triple Product -- 17.3 The Orthogonal Projection -- 17.4 Exercises -- 18 The Linear Equalization Problem -- 18.1 The Linear Equalization Problem and Its Solution -- 18.2 The Orthogonal Projection -- 18.3 Solution of an Over-Determined Linear System of Equations -- 18.4 The Method of Least Squares -- 18.5 Exercises -- 19 The QR-Decomposition of a Matrix -- 19.1 Full and Reduced QR-Decomposition -- 19.2 Construction of the QR-Decomposition -- 19.3 Applications of the QR-Decomposition -- 19.3.1 Solving a System of Linear Equations -- 19.3.2 Solving the Linear Equalization Problem -- 19.4 Exercises -- 20 Sequences -- 20.1 Terms.
20.2 Convergence and Divergence of Sequences -- 20.3 Exercises -- 21 Calculation of Limits of Sequences -- 21.1 Determining Limits of Explicit Sequences -- 21.2 Determining Limits of Recursive Sequences -- 21.3 Exercises -- 22 Series -- 22.1 Definition and Examples -- 22.2 Convergence Criteria -- 22.3 Exercises -- 23 Mappings -- 23.1 Terms and Examples -- 23.2 Composition, Injective, Surjective, Bijective -- 23.3 The Inverse Mapping -- 23.4 Bounded and Monotone Functions -- 23.5 Exercises -- 24 Power Series -- 24.1 The Domain of Convergence of Real Power Series -- 24.2 The Domain of Convergence of Complex Power Series -- 24.3 The Exponential and the Logarithmic Function -- 24.4 The Hyperbolic Functions -- 24.5 Exercises -- 25 Limits and Continuity -- 25.1 Limits of Functions -- 25.2 Asymptotes of Functions -- 25.3 Continuity -- 25.4 Important Theorems about Continuous Functions -- 25.5 The Bisection Method -- 25.6 Exercises -- 26 Differentiation -- 26.1 The Derivative and the Derivative Function -- 26.2 Derivation Rules -- 26.3 Numerical Differentiation -- 26.4 Exercises -- 27 Applications of Differential Calculus I -- 27.1 Monotonicity -- 27.2 Local and Global Extrema -- 27.3 Determination of Extrema and Extremal Points -- 27.4 Convexity -- 27.5 The Rule of L'Hospital -- 27.6 Exercises -- 28 Applications of Differential Calculus II -- 28.1 The Newton Method -- 28.2 Taylor Expansion -- 28.3 Remainder Estimates -- 28.4 Determination of Taylor Series -- 28.5 Exercises -- 29 Polynomial and Spline Interpolation -- 29.1 Polynomial Interpolation -- 29.2 Construction of Cubic Splines -- 29.3 Exercises -- 30 Integration I -- 30.1 The Definite Integral -- 30.2 The Indefinite Integral -- 30.3 Exercises -- 31 Integration II -- 31.1 Integration of Rational Functions -- 31.2 Rational Functions in Sine and Cosine -- 31.3 Numerical Integration.
31.4 Volumes and Surfaces of Solids of Revolution -- 31.5 Exercises -- 32 Improper Integrals -- 32.1 Calculation of Improper Integrals -- 32.2 The Comparison Test for Improper Integrals -- 32.3 Exercises -- 33 Separable and Linear Differential Equations of First Order -- 33.1 First Differential Equations -- 33.2 Separable Differential Equations -- 33.2.1 The Procedure for Solving a Separable Differential Equation -- 33.2.2 Initial Value Problems -- 33.3 The Linear Differential Equation of First Order -- 33.4 Exercises -- 34 Linear Differential Equations with Constant Coefficients -- 34.1 Homogeneous Linear Differential Equations with Constant Coefficients -- 34.2 Inhomogeneous Linear Differential Equations with Constant Coefficients -- 34.2.1 Variation of Parameters -- 34.2.2 Approach of the Right-Hand Side Type -- 34.3 Exercises -- 35 Some Special Types of Differential Equations -- 35.1 The Homogeneous Differential Equation -- 35.2 The Euler Differential Equation -- 35.3 Bernoulli's Differential Equation -- 35.4 The Riccati Differential Equation -- 35.5 The Power Series Approach -- 35.6 Exercises -- 36 Numerics of Ordinary Differential Equations I -- 36.1 First Procedure -- 36.2 Runge-Kutta Method -- 36.3 Multistep Methods -- 36.4 Exercises -- 37 Linear Mappings and Transformation Matrices -- 37.1 Definitions and Examples -- 37.2 Image, Kernel and the Dimensional Formula -- 37.3 Coordinate Vectors -- 37.4 Transformation Matrices -- 37.5 Exercises -- 38 Base Transformation -- 38.1 The Tansformation Matrix of the Composition of Linear Mappings -- 38.2 Base Transformation -- 38.3 The Two Methods for Determining Transformation Matrices -- 38.4 Exercises -- 39 Diagonalization: Eigenvalues and Eigenvectors -- 39.1 Eigenvalues and Eigenvectors of Matrices -- 39.2 Diagonalizing Matrices -- 39.3 The Characteristic Polynomial of a Matrix.
39.4 Diagonalization of Real Symmetric Matrices -- 39.5 Exercises -- 40 Numerical Calculation of Eigenvalues and Eigenvectors -- 40.1 Gerschgorin Circles -- 40.2 Vector Iteration -- 40.3 The Jacobian Method -- 40.4 The QR-Method -- 40.5 Exercises -- 41 Quadrics -- 41.1 Terms and First Examples -- 41.2 Transformation to Normal Form -- 41.3 Exercises -- 42 Schur Decomposition and Singular Value Decomposition -- 42.1 The Schur Decomposition -- 42.2 Calculation of the Schur Decomposition -- 42.3 Singular Value Decomposition -- 42.4 Determination of the Singular Value Decomposition -- 42.5 Exercises -- 43 The Jordan Normal Form I -- 43.1 Existence of the Jordan Normal Form -- 43.2 Generalized Eigenspaces -- 43.3 Exercises -- 44 The Jordan Normal Form II -- 44.1 Construction of a Jordan Base -- 44.2 Number and Size of Jordan Boxes -- 44.3 Exercises -- 45 Definiteness and Matrix Norms -- 45.1 Definiteness of Matrices -- 45.2 Matrix Norms -- 45.2.1 Norms -- 45.2.2 Induced Matrix Norm -- 45.3 Exercises -- 46 Functions of Several Variables -- 46.1 The Functions and Their Representations -- 46.2 Some Topological Terms -- 46.3 Consequences, Limits, Continuity -- 46.4 Exercises -- 47 Partial Differentiation: Gradient, Hessian Matrix, Jacobian Matrix -- 47.1 The Gradient -- 47.2 The Hessian Matrix -- 47.3 The Jacobian Matrix -- 47.4 Exercises -- 48 Applications of Partial Derivatives -- 48.1 The (Multidimensional) Newton Method -- 48.2 Taylor Development -- 48.2.1 The Zeroth, First and Second Taylor Polynomial -- 48.2.2 The General Taylor polynomial -- 48.3 Exercises -- 49 Extreme Value Determination -- 49.1 Local and Global Extrema -- 49.2 Determination of Extrema and Extremal Points -- 49.3 Exercises -- 50 Extreme Value Determination Under Constraints -- 50.1 Extrema Under Constraints -- 50.2 The Substitution Method -- 50.3 The Method of Lagrange Multipliers.
50.4 Extrema Under Multiple Constraints.
Record Nr. UNINA-9910629289203321
Karpfinger Christian  
Berlin, Germany : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Calculus and linear algebra in recipes : terms, phrases and numerous examples in short learning units / / Christian Karpfinger
Calculus and linear algebra in recipes : terms, phrases and numerous examples in short learning units / / Christian Karpfinger
Autore Karpfinger Christian
Pubbl/distr/stampa Berlin, Germany : , : Springer, , [2022]
Descrizione fisica 1 online resource (1015 pages)
Disciplina 512.5
Soggetto topico Algebras, Linear
Calculus
Differential equations
Àlgebra lineal
Càlcul
Equacions diferencials
Soggetto genere / forma Llibres electrònics
ISBN 9783662654583
9783662654576
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Foreword to the Third Edition -- Preface to the Second Edition -- Preface to the First Edition -- Contents -- 1 Speech, Symbols and Sets -- 1.1 Speech Patterns and Symbols in Mathematics -- 1.1.1 Junctors -- 1.1.2 Quantifiers -- 1.2 Summation and Product Symbol -- 1.3 Powers and Roots -- 1.4 Symbols of Set Theory -- 1.5 Exercises -- 2 The Natural Numbers, Integers and Rational Numbers -- 2.1 The Natural Numbers -- 2.2 The Integers -- 2.3 The Rational Numbers -- 2.4 Exercises -- 3 The Real Numbers -- 3.1 Basics -- 3.2 Real Intervals -- 3.3 The Absolute Value of a Real Number -- 3.4 n-th Roots -- 3.5 Solving Equations and Inequalities -- 3.6 Maximum, Minimum, Supremum and Infimum -- 3.7 Exercises -- 4 Machine Numbers -- 4.1 b-adic Representation of Real Numbers -- 4.2 Floating Point Numbers -- 4.2.1 Machine Numbers -- 4.2.2 Machine Epsilon, Rounding and Floating Point Arithmetic -- 4.2.3 Loss of Significance -- 4.3 Exercises -- 5 Polynomials -- 5.1 Polynomials: Multiplication and Division -- 5.2 Factorization of Polynomials -- 5.3 Evaluating Polynomials -- 5.4 Partial Fraction Decomposition -- 5.5 Exercises -- 6 Trigonometric Functions -- 6.1 Sine and Cosine -- 6.2 Tangent and Cotangent -- 6.3 The Inverse Functions of the Trigonometric Functions -- 6.4 Exercises -- 7 Complex Numbers: Cartesian Coordinates -- 7.1 Construction of C -- 7.2 The Imaginary Unit and Other Terms -- 7.3 The Fundamental Theorem of Algebra -- 7.4 Exercises -- 8 Complex Numbers: Polar Coordinates -- 8.1 The Polar Representation -- 8.2 Applications of the Polar Representation -- 8.3 Exercises -- 9 Linear Systems of Equations -- 9.1 The Gaussian Elimination Method -- 9.2 The Rank of a Matrix -- 9.3 Homogeneous Linear Systems of Equations -- 9.4 Exercises -- 10 Calculating with Matrices -- 10.1 Definition of Matrices and Some Special Matrices.
10.2 Arithmetic Operations -- 10.3 Inverting Matrices -- 10.4 Calculation Rules -- 10.5 Exercises -- 11 LR-Decomposition of a Matrix -- 11.1 Motivation -- 11.2 The LR-Decomposition: Simplified Variant -- 11.3 The LR-Decomposition: General Variant -- 11.4 The LR-Decomposition-with Column Pivot Search -- 11.5 Exercises -- 12 The Determinant -- 12.1 Definition of the Determinant -- 12.2 Calculation of the Determinant -- 12.3 Applications of the Determinant -- 12.4 Exercises -- 13 Vector Spaces -- 13.1 Definition and Important Examples -- 13.2 Subspaces -- 13.3 Exercises -- 14 Generating Systems and Linear (In)Dependence -- 14.1 Linear Combinations -- 14.2 The Span of X -- 14.3 Linear (In)Dependence -- 14.4 Exercises -- 15 Bases of Vector Spaces -- 15.1 Bases -- 15.2 Applications to Matrices and Systems of Linear Equations -- 15.3 Exercises -- 16 Orthogonality I -- 16.1 Scalar Products -- 16.2 Length, Distance, Angle and Orthogonality -- 16.3 Orthonormal Bases -- 16.4 Orthogonal Decomposition and Linear Combination with Respect to an ONB -- 16.5 Orthogonal Matrices -- 16.6 Exercises -- 17 Orthogonality II -- 17.1 The Orthonormalization Method of Gram and Schmidt -- 17.2 The Vector Product and the (Scalar) Triple Product -- 17.3 The Orthogonal Projection -- 17.4 Exercises -- 18 The Linear Equalization Problem -- 18.1 The Linear Equalization Problem and Its Solution -- 18.2 The Orthogonal Projection -- 18.3 Solution of an Over-Determined Linear System of Equations -- 18.4 The Method of Least Squares -- 18.5 Exercises -- 19 The QR-Decomposition of a Matrix -- 19.1 Full and Reduced QR-Decomposition -- 19.2 Construction of the QR-Decomposition -- 19.3 Applications of the QR-Decomposition -- 19.3.1 Solving a System of Linear Equations -- 19.3.2 Solving the Linear Equalization Problem -- 19.4 Exercises -- 20 Sequences -- 20.1 Terms.
20.2 Convergence and Divergence of Sequences -- 20.3 Exercises -- 21 Calculation of Limits of Sequences -- 21.1 Determining Limits of Explicit Sequences -- 21.2 Determining Limits of Recursive Sequences -- 21.3 Exercises -- 22 Series -- 22.1 Definition and Examples -- 22.2 Convergence Criteria -- 22.3 Exercises -- 23 Mappings -- 23.1 Terms and Examples -- 23.2 Composition, Injective, Surjective, Bijective -- 23.3 The Inverse Mapping -- 23.4 Bounded and Monotone Functions -- 23.5 Exercises -- 24 Power Series -- 24.1 The Domain of Convergence of Real Power Series -- 24.2 The Domain of Convergence of Complex Power Series -- 24.3 The Exponential and the Logarithmic Function -- 24.4 The Hyperbolic Functions -- 24.5 Exercises -- 25 Limits and Continuity -- 25.1 Limits of Functions -- 25.2 Asymptotes of Functions -- 25.3 Continuity -- 25.4 Important Theorems about Continuous Functions -- 25.5 The Bisection Method -- 25.6 Exercises -- 26 Differentiation -- 26.1 The Derivative and the Derivative Function -- 26.2 Derivation Rules -- 26.3 Numerical Differentiation -- 26.4 Exercises -- 27 Applications of Differential Calculus I -- 27.1 Monotonicity -- 27.2 Local and Global Extrema -- 27.3 Determination of Extrema and Extremal Points -- 27.4 Convexity -- 27.5 The Rule of L'Hospital -- 27.6 Exercises -- 28 Applications of Differential Calculus II -- 28.1 The Newton Method -- 28.2 Taylor Expansion -- 28.3 Remainder Estimates -- 28.4 Determination of Taylor Series -- 28.5 Exercises -- 29 Polynomial and Spline Interpolation -- 29.1 Polynomial Interpolation -- 29.2 Construction of Cubic Splines -- 29.3 Exercises -- 30 Integration I -- 30.1 The Definite Integral -- 30.2 The Indefinite Integral -- 30.3 Exercises -- 31 Integration II -- 31.1 Integration of Rational Functions -- 31.2 Rational Functions in Sine and Cosine -- 31.3 Numerical Integration.
31.4 Volumes and Surfaces of Solids of Revolution -- 31.5 Exercises -- 32 Improper Integrals -- 32.1 Calculation of Improper Integrals -- 32.2 The Comparison Test for Improper Integrals -- 32.3 Exercises -- 33 Separable and Linear Differential Equations of First Order -- 33.1 First Differential Equations -- 33.2 Separable Differential Equations -- 33.2.1 The Procedure for Solving a Separable Differential Equation -- 33.2.2 Initial Value Problems -- 33.3 The Linear Differential Equation of First Order -- 33.4 Exercises -- 34 Linear Differential Equations with Constant Coefficients -- 34.1 Homogeneous Linear Differential Equations with Constant Coefficients -- 34.2 Inhomogeneous Linear Differential Equations with Constant Coefficients -- 34.2.1 Variation of Parameters -- 34.2.2 Approach of the Right-Hand Side Type -- 34.3 Exercises -- 35 Some Special Types of Differential Equations -- 35.1 The Homogeneous Differential Equation -- 35.2 The Euler Differential Equation -- 35.3 Bernoulli's Differential Equation -- 35.4 The Riccati Differential Equation -- 35.5 The Power Series Approach -- 35.6 Exercises -- 36 Numerics of Ordinary Differential Equations I -- 36.1 First Procedure -- 36.2 Runge-Kutta Method -- 36.3 Multistep Methods -- 36.4 Exercises -- 37 Linear Mappings and Transformation Matrices -- 37.1 Definitions and Examples -- 37.2 Image, Kernel and the Dimensional Formula -- 37.3 Coordinate Vectors -- 37.4 Transformation Matrices -- 37.5 Exercises -- 38 Base Transformation -- 38.1 The Tansformation Matrix of the Composition of Linear Mappings -- 38.2 Base Transformation -- 38.3 The Two Methods for Determining Transformation Matrices -- 38.4 Exercises -- 39 Diagonalization: Eigenvalues and Eigenvectors -- 39.1 Eigenvalues and Eigenvectors of Matrices -- 39.2 Diagonalizing Matrices -- 39.3 The Characteristic Polynomial of a Matrix.
39.4 Diagonalization of Real Symmetric Matrices -- 39.5 Exercises -- 40 Numerical Calculation of Eigenvalues and Eigenvectors -- 40.1 Gerschgorin Circles -- 40.2 Vector Iteration -- 40.3 The Jacobian Method -- 40.4 The QR-Method -- 40.5 Exercises -- 41 Quadrics -- 41.1 Terms and First Examples -- 41.2 Transformation to Normal Form -- 41.3 Exercises -- 42 Schur Decomposition and Singular Value Decomposition -- 42.1 The Schur Decomposition -- 42.2 Calculation of the Schur Decomposition -- 42.3 Singular Value Decomposition -- 42.4 Determination of the Singular Value Decomposition -- 42.5 Exercises -- 43 The Jordan Normal Form I -- 43.1 Existence of the Jordan Normal Form -- 43.2 Generalized Eigenspaces -- 43.3 Exercises -- 44 The Jordan Normal Form II -- 44.1 Construction of a Jordan Base -- 44.2 Number and Size of Jordan Boxes -- 44.3 Exercises -- 45 Definiteness and Matrix Norms -- 45.1 Definiteness of Matrices -- 45.2 Matrix Norms -- 45.2.1 Norms -- 45.2.2 Induced Matrix Norm -- 45.3 Exercises -- 46 Functions of Several Variables -- 46.1 The Functions and Their Representations -- 46.2 Some Topological Terms -- 46.3 Consequences, Limits, Continuity -- 46.4 Exercises -- 47 Partial Differentiation: Gradient, Hessian Matrix, Jacobian Matrix -- 47.1 The Gradient -- 47.2 The Hessian Matrix -- 47.3 The Jacobian Matrix -- 47.4 Exercises -- 48 Applications of Partial Derivatives -- 48.1 The (Multidimensional) Newton Method -- 48.2 Taylor Development -- 48.2.1 The Zeroth, First and Second Taylor Polynomial -- 48.2.2 The General Taylor polynomial -- 48.3 Exercises -- 49 Extreme Value Determination -- 49.1 Local and Global Extrema -- 49.2 Determination of Extrema and Extremal Points -- 49.3 Exercises -- 50 Extreme Value Determination Under Constraints -- 50.1 Extrema Under Constraints -- 50.2 The Substitution Method -- 50.3 The Method of Lagrange Multipliers.
50.4 Extrema Under Multiple Constraints.
Record Nr. UNISA-996499871503316
Karpfinger Christian  
Berlin, Germany : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Calculus of one variable / / M. Thamban Nair
Calculus of one variable / / M. Thamban Nair
Autore Nair M. Thamban
Edizione [Second edition.]
Pubbl/distr/stampa Cham, Switzerland : , : ANE Books Pvt. Ltd. : , : Springer, , [2021]
Descrizione fisica 1 online resource (350 pages)
Disciplina 515
Soggetto topico Calculus
Càlcul
Soggetto genere / forma Llibres electrònics
ISBN 9783030886370
9783030886363
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910520303003321
Nair M. Thamban  
Cham, Switzerland : , : ANE Books Pvt. Ltd. : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Calculus of one variable / / M. Thamban Nair
Calculus of one variable / / M. Thamban Nair
Autore Nair M. Thamban
Edizione [Second edition.]
Pubbl/distr/stampa Cham, Switzerland : , : ANE Books Pvt. Ltd. : , : Springer, , [2021]
Descrizione fisica 1 online resource (350 pages)
Disciplina 515
Soggetto topico Calculus
Càlcul
Soggetto genere / forma Llibres electrònics
ISBN 9783030886370
9783030886363
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISA-996466547003316
Nair M. Thamban  
Cham, Switzerland : , : ANE Books Pvt. Ltd. : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Calculus off the beaten path : a journey through its fundamental ideas / / Ignacio Zalduendo
Calculus off the beaten path : a journey through its fundamental ideas / / Ignacio Zalduendo
Autore Zalduendo Ignacio
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (225 pages)
Disciplina 515
Collana Springer undergraduate mathematics series
Soggetto topico Calculus
Càlcul
Soggetto genere / forma Llibres electrònics
ISBN 9783031157653
9783031157646
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Introduction -- 2400 Years of Calculus -- Calculus and Education -- 1 The Real Numbers -- The Rational Line -- Density of Q -- Some Basic Notions -- Irrationality of Q -- From Eudoxus to Dedekind -- The Real Line -- Dyadic Series-A Construction of R -- The Scarcity of Q -- The Completeness of R -- Cardinality -- Exercises -- 2 Sequences and Series -- Sequences -- Limits of Sequences -- Cantor's Nested Intervals Theorem -- Subsequences -- Series -- The Harmonic Series -- Series of Positive Terms -- Series with Positive and Negative Terms -- The Riemann Series Theorem -- Absolute and Unconditional Convergence -- Exercises -- 3 Functions -- The Elementary Functions -- Polynomials -- Circular Functions -- The Exponential Function: Bernoulli's Inequality -- Irrationality of e -- Convergence of k=1∞(1+ak) and of k=1∞ak -- Hyperbolic Functions -- Injectivity and Inverse Functions -- Curves in the Plane: Parametrized Curves -- The Cycloid -- Pythagorean Triples -- Continuity -- Bolzano and Weierstrass -- Limits -- Limits in Ancient Greece: The Area of a Circle -- Three Important Limits -- Exercises -- 4 The Derivative -- Derivative -- Tangents -- Newton-Raphson -- Derivatives of the Elementary Functions -- The Chain Rule -- Derivative of the Inverse Function -- The Derivative of a Parametrized Curve -- First Derivative, Tangent Line, and Growth -- The Mean Value Theorems -- L'Hôpital's Rule -- Snell's Law -- The Brachistochrone -- Exercises -- 5 The Integral -- Measure and Integral -- The Fundamental Theorem of Calculus -- A Pause for Comments -- Buffon's Needle -- Irrationality of π -- Improper Integrals -- Integration and Sums: Linearity of the Integral -- Uniform Convergence-The Weierstrass M-Test -- Gregory's Series -- Integration and Products: Integration by Parts -- Stirling's Formula.
Integration and Composition: Integration by Substitution -- A Note on Notation -- Length of Curves. The Catenary -- Area Enclosed by a Simple Closed Curve -- Exercises -- 6 More Derivatives -- Second Derivative, Best-Fitting Parabola, and Curvature -- The Taylor Polynomial of Order Two -- Curvature -- Random Walk and the Gauss Curve -- The Taylor Series -- Exercises -- 7 Convexity and the Isoperimetric Inequality -- The Arithmetic-Geometric Inequality -- Convexity -- Young, Hölder, Jensen, Cauchy-Schwarz… -- The Isoperimetric Inequality -- Exercises -- 8 More Integrals -- Volume -- Double Integrals -- The Basel Problem -- Solids of Revolution -- Integration of e -- Density Functions, Barycenter, and Expectation -- Center of Mass or Barycenter -- Pappus' Theorem -- The Method -- Surface Area -- Normal Distribution. Gauss, Laplace, and Stirling -- Exercises -- 9 The Gamma Function -- The Gamma Function -- Weierstrass' Formula -- Growth of the Harmonic Series, Again -- Exercises -- Bibliography -- Index.
Record Nr. UNINA-9910624321703321
Zalduendo Ignacio  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Calculus off the beaten path : a journey through its fundamental ideas / / Ignacio Zalduendo
Calculus off the beaten path : a journey through its fundamental ideas / / Ignacio Zalduendo
Autore Zalduendo Ignacio
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (225 pages)
Disciplina 515
Collana Springer undergraduate mathematics series
Soggetto topico Calculus
Càlcul
Soggetto genere / forma Llibres electrònics
ISBN 9783031157653
9783031157646
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Introduction -- 2400 Years of Calculus -- Calculus and Education -- 1 The Real Numbers -- The Rational Line -- Density of Q -- Some Basic Notions -- Irrationality of Q -- From Eudoxus to Dedekind -- The Real Line -- Dyadic Series-A Construction of R -- The Scarcity of Q -- The Completeness of R -- Cardinality -- Exercises -- 2 Sequences and Series -- Sequences -- Limits of Sequences -- Cantor's Nested Intervals Theorem -- Subsequences -- Series -- The Harmonic Series -- Series of Positive Terms -- Series with Positive and Negative Terms -- The Riemann Series Theorem -- Absolute and Unconditional Convergence -- Exercises -- 3 Functions -- The Elementary Functions -- Polynomials -- Circular Functions -- The Exponential Function: Bernoulli's Inequality -- Irrationality of e -- Convergence of k=1∞(1+ak) and of k=1∞ak -- Hyperbolic Functions -- Injectivity and Inverse Functions -- Curves in the Plane: Parametrized Curves -- The Cycloid -- Pythagorean Triples -- Continuity -- Bolzano and Weierstrass -- Limits -- Limits in Ancient Greece: The Area of a Circle -- Three Important Limits -- Exercises -- 4 The Derivative -- Derivative -- Tangents -- Newton-Raphson -- Derivatives of the Elementary Functions -- The Chain Rule -- Derivative of the Inverse Function -- The Derivative of a Parametrized Curve -- First Derivative, Tangent Line, and Growth -- The Mean Value Theorems -- L'Hôpital's Rule -- Snell's Law -- The Brachistochrone -- Exercises -- 5 The Integral -- Measure and Integral -- The Fundamental Theorem of Calculus -- A Pause for Comments -- Buffon's Needle -- Irrationality of π -- Improper Integrals -- Integration and Sums: Linearity of the Integral -- Uniform Convergence-The Weierstrass M-Test -- Gregory's Series -- Integration and Products: Integration by Parts -- Stirling's Formula.
Integration and Composition: Integration by Substitution -- A Note on Notation -- Length of Curves. The Catenary -- Area Enclosed by a Simple Closed Curve -- Exercises -- 6 More Derivatives -- Second Derivative, Best-Fitting Parabola, and Curvature -- The Taylor Polynomial of Order Two -- Curvature -- Random Walk and the Gauss Curve -- The Taylor Series -- Exercises -- 7 Convexity and the Isoperimetric Inequality -- The Arithmetic-Geometric Inequality -- Convexity -- Young, Hölder, Jensen, Cauchy-Schwarz… -- The Isoperimetric Inequality -- Exercises -- 8 More Integrals -- Volume -- Double Integrals -- The Basel Problem -- Solids of Revolution -- Integration of e -- Density Functions, Barycenter, and Expectation -- Center of Mass or Barycenter -- Pappus' Theorem -- The Method -- Surface Area -- Normal Distribution. Gauss, Laplace, and Stirling -- Exercises -- 9 The Gamma Function -- The Gamma Function -- Weierstrass' Formula -- Growth of the Harmonic Series, Again -- Exercises -- Bibliography -- Index.
Record Nr. UNISA-996499870903316
Zalduendo Ignacio  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Fractals in engineering : theoretical aspects and numerical approximations / / edited by Maria Rosaria Lancia and Anna Rozanova-Pierrat
Fractals in engineering : theoretical aspects and numerical approximations / / edited by Maria Rosaria Lancia and Anna Rozanova-Pierrat
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (179 pages) : illustrations
Disciplina 658.4034
Collana SEMA SIMAI Springer
Soggetto topico Calculus
Applied mathematics
Functions
Harmonic analysis
Mathematical analysis
Càlcul
Matemàtica aplicada
Funcions
Anàlisi harmònica
Anàlisi matemàtica
Soggetto genere / forma Llibres electrònics
ISBN 3-030-61803-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Editors and Contributors -- About the Editors -- Contributors -- A Numerical Approach to a Nonlinear Diffusion Model for Self-Organized Criticality Phenomena -- 1 Introduction -- 2 The Basic Model -- 3 Numerical Approximation on a Fixed Grid -- 4 Approximation on a Synchronized Family of Grids -- 5 Numerical Tests -- References -- Approximation of 3D Stokes Flows in Fractal Domains -- 1 Introduction -- 2 Preliminaries -- 3 Existence and Uniqueness Results -- 4 Regularity in Weighted Sobolev Spaces -- 5 Mean Shear Stress -- 6 Numerical Approximation -- 7 Numerical Simulations -- References -- ∞-Laplacian Obstacle Problems in Fractal Domains -- 1 Introduction -- 2 Fractal Domains, Approximating Domains and Fibers -- 3 Setting and Asymptotic Behavior -- 4 Uniqueness and Perspectives -- 5 Uniform and Error Estimates -- References -- Discretization of the Koch Snowflake Domain with Boundary and Interior Energies -- 1 Introduction -- 2 Dirichlet Form on the Koch Snowflake -- 3 Dirichlet Form on the Snowflake Domain -- 4 Inductive Mesh Construction and Discrete Energy Forms -- 5 Numerical Results -- 5.1 Algorithm and Implementation -- 5.2 The Eigenvalue Counting Function -- 5.3 Eigenvectors and Eigenvalues in the Low Eigenvalue Regime -- 5.4 Localization in the High Eigenvalue Regime -- 6 A Landscape Approach to High Frequency Localization -- References -- On the Dimension of the Sierpinski Gasket in l2 -- 1 Introduction -- 2 Invariant Sets -- 2.1 Infinite Dimensional Sierpinski Gasket -- 2.2 Hausdorff Dimension of Invariant Sets -- 2.3 N-Dimensional Simplices -- 3 Invariant Measures -- References -- On the External Approximation of Sobolev Spaces by M-Convergence -- 1 Introduction -- 2 Sobolev Space Approximations -- 3 The M-Convergence Result -- 4 Proof of Lemma 1 -- 5 Proof of Lemma 2 -- 6 Comments -- References.
Generalization of Rellich-Kondrachov Theorem and Trace Compactness for Fractal Boundaries -- 1 Introduction -- 2 Sobolev Extension Domains -- 3 Trace on the Boundary and Green Formulas -- 3.1 Framework of d-Sets and Markov's Local Inequality -- 3.2 General Framework of Closed Subsets of Rn -- 3.3 Integration by Parts and the Green Formula -- 4 Sobolev Admissible Domains and the Generalization of the Rellich-Kondrachov Theorem -- 5 Compactness of the Trace -- 6 Application to the Poisson Boundary Valued and Spectral Problems -- References.
Record Nr. UNISA-996466550503316
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Fractals in engineering : theoretical aspects and numerical approximations / / edited by Maria Rosaria Lancia and Anna Rozanova-Pierrat
Fractals in engineering : theoretical aspects and numerical approximations / / edited by Maria Rosaria Lancia and Anna Rozanova-Pierrat
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (179 pages) : illustrations
Disciplina 658.4034
Collana SEMA SIMAI Springer
Soggetto topico Calculus
Applied mathematics
Functions
Harmonic analysis
Mathematical analysis
Càlcul
Matemàtica aplicada
Funcions
Anàlisi harmònica
Anàlisi matemàtica
Soggetto genere / forma Llibres electrònics
ISBN 3-030-61803-X
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- Editors and Contributors -- About the Editors -- Contributors -- A Numerical Approach to a Nonlinear Diffusion Model for Self-Organized Criticality Phenomena -- 1 Introduction -- 2 The Basic Model -- 3 Numerical Approximation on a Fixed Grid -- 4 Approximation on a Synchronized Family of Grids -- 5 Numerical Tests -- References -- Approximation of 3D Stokes Flows in Fractal Domains -- 1 Introduction -- 2 Preliminaries -- 3 Existence and Uniqueness Results -- 4 Regularity in Weighted Sobolev Spaces -- 5 Mean Shear Stress -- 6 Numerical Approximation -- 7 Numerical Simulations -- References -- ∞-Laplacian Obstacle Problems in Fractal Domains -- 1 Introduction -- 2 Fractal Domains, Approximating Domains and Fibers -- 3 Setting and Asymptotic Behavior -- 4 Uniqueness and Perspectives -- 5 Uniform and Error Estimates -- References -- Discretization of the Koch Snowflake Domain with Boundary and Interior Energies -- 1 Introduction -- 2 Dirichlet Form on the Koch Snowflake -- 3 Dirichlet Form on the Snowflake Domain -- 4 Inductive Mesh Construction and Discrete Energy Forms -- 5 Numerical Results -- 5.1 Algorithm and Implementation -- 5.2 The Eigenvalue Counting Function -- 5.3 Eigenvectors and Eigenvalues in the Low Eigenvalue Regime -- 5.4 Localization in the High Eigenvalue Regime -- 6 A Landscape Approach to High Frequency Localization -- References -- On the Dimension of the Sierpinski Gasket in l2 -- 1 Introduction -- 2 Invariant Sets -- 2.1 Infinite Dimensional Sierpinski Gasket -- 2.2 Hausdorff Dimension of Invariant Sets -- 2.3 N-Dimensional Simplices -- 3 Invariant Measures -- References -- On the External Approximation of Sobolev Spaces by M-Convergence -- 1 Introduction -- 2 Sobolev Space Approximations -- 3 The M-Convergence Result -- 4 Proof of Lemma 1 -- 5 Proof of Lemma 2 -- 6 Comments -- References.
Generalization of Rellich-Kondrachov Theorem and Trace Compactness for Fractal Boundaries -- 1 Introduction -- 2 Sobolev Extension Domains -- 3 Trace on the Boundary and Green Formulas -- 3.1 Framework of d-Sets and Markov's Local Inequality -- 3.2 General Framework of Closed Subsets of Rn -- 3.3 Integration by Parts and the Green Formula -- 4 Sobolev Admissible Domains and the Generalization of the Rellich-Kondrachov Theorem -- 5 Compactness of the Trace -- 6 Application to the Poisson Boundary Valued and Spectral Problems -- References.
Record Nr. UNINA-9910484636403321
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui