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Applied Calculus with R / / by Thomas J. Pfaff
| Applied Calculus with R / / by Thomas J. Pfaff |
| Autore | Pfaff Thomas J. |
| Edizione | [1st ed. 2023.] |
| Pubbl/distr/stampa | Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 |
| Descrizione fisica | 1 online resource (520 pages) |
| Disciplina | 515.0285 |
| Soggetto topico |
Mathematical statistics
Computer science - Mathematics Stochastic processes Calculus Mathematical Statistics Mathematical Applications in Computer Science Stochastic Calculus Càlcul Processament de dades R (Llenguatge de programació) |
| Soggetto genere / forma | Llibres electrònics |
| Soggetto non controllato | Mathematics |
| ISBN | 3-031-28571-9 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | A Brief Introduction to R -- Describing a Graph -- The Function Gallery -- I: Change and the Derivative -- How Fast is CO2 Increasing? -- The Idea of the Derivative -- Formulas Quantifying Change.-The Microscope Equation -- Successive Approximations to Estimate Derivatives -- The Derivative Graphically -- The Formal Derivative as a Limit -- Basic Derivative Rules -- Produce Rule -- Quotient Rule -- Chain Rule -- Derivatives with R -- End Behavior of a Function - L'Hospital's Rule -- II: Applications of the Derivative -- How Do We Know the Shape of a Function? -- Finding Extremes -- Optimization -- Derivatives of Functions of Two Variables -- Related Rates -- Surge Function -- Differential Equations - Preliminaries -- Differential Equations - Population Growth Models -- Differential Equations - Predator Prey -- Differential equations - SIR Model -- Project: The Gini Coefficient - Prelude to Section III -- III: Accumulation and the Integral -- Area Under Curves -- The Accumulation Function -- The Fundamental Theorem of Calculus -- Techniques of Integration - The u Substitution -- Techniques of Integration - Integration by Parts -- IV: Appendices - Algebra Review -- Algebra Review - Functions and Graphs -- Algebra Review - Adding and Multiplying Fractions -- Algebra Review - Exponents -- Algebra Review - Lines -- Algebra Review - Expanding, Factoring, and Roots -- Algebra Review - Function Composition -- Glossary -- Answers to Odd Problems -- R Code for Figures. |
| Record Nr. | UNINA-9910728948003321 |
Pfaff Thomas J.
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| Cham : , : Springer International Publishing : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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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 |
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Johar Syafiq
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| Cham : , : Springer Nature Switzerland : , : Imprint : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
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 |
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Ventre Aldo G. S.
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| Cham, Switzerland : , : Springer, , 2023 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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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 | ||
| ||
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 | ||
| ||
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 | ||
| ||
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 | ||
| ||
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 |
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Zalduendo Ignacio
|
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| Cham, Switzerland : , : Springer, , [2022] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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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 | ||
| ||
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 | ||
| ||
Soggetto topico
-
Càlcul
(23)
- Calculus (14)
- Differential equations (4)
- Mathematical analysis (4)
- Algebras, Linear (3)