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Biblioteca

MARC Lista (tabellare)
Advanced linear algebra with applications / / Mohammad Ashraf, Vincenzo De Filippis, Mohammad Aslam Siddeeque
Advanced linear algebra with applications / / Mohammad Ashraf, Vincenzo De Filippis, Mohammad Aslam Siddeeque
Autore Ashraf Mohammad <1959->
Pubbl/distr/stampa Singapore : , : Springer Nature Singapore Pte Ltd., , [2022]
Descrizione fisica 1 online resource (504 pages)
Disciplina 512.5
Soggetto topico Algebras, Linear
Àlgebra lineal
Soggetto genere / forma Llibres electrònics
ISBN 981-16-2166-7
981-16-2167-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910743231903321
Ashraf Mohammad <1959->  
Singapore : , : Springer Nature Singapore Pte Ltd., , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Advanced linear algebra with applications / / Mohammad Ashraf, Vincenzo De Filippis, Mohammad Aslam Siddeeque
Advanced linear algebra with applications / / Mohammad Ashraf, Vincenzo De Filippis, Mohammad Aslam Siddeeque
Autore Ashraf Mohammad <1959->
Pubbl/distr/stampa Singapore : , : Springer Nature Singapore Pte Ltd., , [2022]
Descrizione fisica 1 online resource (504 pages)
Disciplina 512.5
Soggetto topico Algebras, Linear
Àlgebra lineal
Soggetto genere / forma Llibres electrònics
ISBN 981-16-2166-7
981-16-2167-5
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISA-996549467103316
Ashraf Mohammad <1959->  
Singapore : , : Springer Nature Singapore Pte Ltd., , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Advanced linear and matrix algebra / / Nathaniel Johnston
Advanced linear and matrix algebra / / Nathaniel Johnston
Autore Johnston Nathaniel
Edizione [1st ed. 2021.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (XVI, 494 p. 123 illus., 108 illus. in color.)
Disciplina 512.5
Soggetto topico Algebras, Linear
Matrices
Àlgebra lineal
Matrius (Matemàtica)
Algebra
Soggetto genere / forma Llibres electrònics
ISBN 3-030-52815-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Chapter 1: Vector Spaces -- Chapter 2: Matrix Decompositions -- Chapter 3: Tensors and Multilinearity -- Appendix A: Mathematical Preliminaries -- Appendix B: Additional Proofs -- Appendix C: Selected Exercise Solutions.
Record Nr. UNISA-996466403803316
Johnston Nathaniel  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Advanced linear and matrix algebra / / Nathaniel Johnston
Advanced linear and matrix algebra / / Nathaniel Johnston
Autore Johnston Nathaniel
Edizione [1st ed. 2021.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (XVI, 494 p. 123 illus., 108 illus. in color.)
Disciplina 512.5
Soggetto topico Algebras, Linear
Matrices
Àlgebra lineal
Matrius (Matemàtica)
Algebra
Soggetto genere / forma Llibres electrònics
ISBN 3-030-52815-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Chapter 1: Vector Spaces -- Chapter 2: Matrix Decompositions -- Chapter 3: Tensors and Multilinearity -- Appendix A: Mathematical Preliminaries -- Appendix B: Additional Proofs -- Appendix C: Selected Exercise Solutions.
Record Nr. UNINA-9910483059803321
Johnston Nathaniel  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Application-inspired linear algebra / / Heather A. Moon, Thomas J. Asaki, Marie A. Snipes
Application-inspired linear algebra / / Heather A. Moon, Thomas J. Asaki, Marie A. Snipes
Autore Moon Heather A.
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (538 pages)
Disciplina 512.5
Collana Springer Undergraduate Texts in Mathematics and Technology
Soggetto topico Algebras, Linear
Àlgebra lineal
Soggetto genere / forma Llibres electrònics
ISBN 3-030-86155-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Outline of Text -- Using This Text -- Exercises -- Computational Tools -- Ancillary Materials -- Acknowledgements -- Contents -- About the Authors -- Introduction To Applications -- 1.1 A Sample of Linear Algebra in Our World -- 1.1.1 Modeling Dynamical Processes -- 1.1.2 Signals and Data Analysis -- 1.1.3 Optimal Design and Decision-Making -- 1.2 Applications We Use to Build Linear Algebra Tools -- 1.2.1 CAT Scans -- 1.2.2 Diffusion Welding -- 1.2.3 Image Warping -- 1.3 Advice to Students -- 1.4 The Language of Linear Algebra -- 1.5 Rules of the Game -- 1.6 Software Tools -- 1.7 Exercises -- Vector Spaces -- 2.1 Exploration: Digital Images -- 2.1.1 Exercises -- 2.2 Systems of Equations -- 2.2.1 Systems of Equations -- 2.2.2 Techniques for Solving Systems of Linear Equations -- 2.2.3 Elementary Matrix -- 2.2.4 The Geometry of Systems of Equations -- 2.2.5 Exercises -- 2.3 Vector Spaces -- 2.3.1 Images and Image Arithmetic -- 2.3.2 Vectors and Vector Spaces -- 2.3.3 The Geometry of the Vector Space mathbbR3 -- 2.3.4 Properties of Vector Spaces -- 2.3.5 Exercises -- 2.4 Vector Space Examples -- 2.4.1 Diffusion Welding and Heat States -- 2.4.2 Function Spaces -- 2.4.3 Matrix Spaces -- 2.4.4 Solution Spaces -- 2.4.5 Other Vector Spaces -- 2.4.6 Is My Set a Vector Space? -- 2.4.7 Exercises -- 2.5 Subspaces -- 2.5.1 Subsets and Subspaces -- 2.5.2 Examples of Subspaces -- 2.5.3 Subspaces of mathbbRn -- 2.5.4 Building New Subspaces -- 2.5.5 Exercises -- Vector Space Arithmetic and Representations -- 3.1 Linear Combinations -- 3.1.1 Linear Combinations -- 3.1.2 Matrix Products -- 3.1.3 The Matrix Equation Ax=b -- 3.1.4 The Matrix Equation Ax=0 -- 3.1.5 The Principle of Superposition -- 3.1.6 Exercises -- 3.2 Span -- 3.2.1 The Span of a Set of Vectors -- 3.2.2 To Span a Set of Vectors -- 3.2.3 Span X is a Vector Space.
3.2.4 Exercises -- 3.3 Linear Dependence and Independence -- 3.3.1 Linear Dependence and Independence -- 3.3.2 Determining Linear (In)dependence -- 3.3.3 Summary of Linear Dependence -- 3.3.4 Exercises -- 3.4 Basis and Dimension -- 3.4.1 Efficient Heat State Descriptions -- 3.4.2 Basis -- 3.4.3 Constructing a Basis -- 3.4.4 Dimension -- 3.4.5 Properties of Bases -- 3.4.6 Exercises -- 3.5 Coordinate Spaces -- 3.5.1 Cataloging Heat States -- 3.5.2 Coordinates in mathbbRn -- 3.5.3 Example Coordinates of Abstract Vectors -- 3.5.4 Brain Scan Images and Coordinates -- 3.5.5 Exercises -- Linear Transformations -- 4.1 Explorations: Computing Radiographs and the Radiographic Transformation -- 4.1.1 Radiography on Slices -- 4.1.2 Radiographic Scenarios and Notation -- 4.1.3 A First Example -- 4.1.4 Radiographic Setup Example -- 4.1.5 Exercises -- 4.2 Transformations -- 4.2.1 Transformations are Functions -- 4.2.2 Linear Transformations -- 4.2.3 Properties of Linear Transformations -- 4.2.4 Exercises -- 4.3 Explorations: Heat Diffusion -- 4.3.1 Heat States as Vectors -- 4.3.2 Heat Evolution Equation -- 4.3.3 Exercises -- 4.3.4 Extending the Exploration: Application to Image Warping -- 4.4 Matrix Representations of Linear Transformations -- 4.4.1 Matrix Transformations between Euclidean Spaces -- 4.4.2 Matrix Transformations -- 4.4.3 Change of Basis Matrix -- 4.4.4 Exercises -- 4.5 The Determinants of a Matrix -- 4.5.1 Determinant Calculations and Algebraic Properties -- 4.6 Explorations: Re-Evaluating Our Tomographic Goal -- 4.6.1 Seeking Tomographic Transformations -- 4.6.2 Exercises -- 4.7 Properties of Linear Transformations -- 4.7.1 One-To-One Transformations -- 4.7.2 Properties of One-To-One Linear Transformations -- 4.7.3 Onto Linear Transformations -- 4.7.4 Properties of Onto Linear Transformations -- 4.7.5 Summary of Properties.
4.7.6 Bijections and Isomorphisms -- 4.7.7 Properties of Isomorphic Vector Spaces -- 4.7.8 Building and Recognizing Isomorphisms -- 4.7.9 Inverse Transformations -- 4.7.10 Left Inverse Transformations -- 4.7.11 Exercises -- Invertibility -- 5.1 Transformation Spaces -- 5.1.1 The Nullspace -- 5.1.2 Domain and Range Spaces -- 5.1.3 One-to-One and Onto Revisited -- 5.1.4 The Rank-Nullity Theorem -- 5.1.5 Exercises -- 5.2 Matrix Spaces and the Invertible Matrix Theorem -- 5.2.1 Matrix Spaces -- 5.2.2 The Invertible Matrix Theorem -- 5.2.3 Exercises -- 5.3 Exploration: Reconstruction Without an Inverse -- 5.3.1 Transpose of a Matrix -- 5.3.2 Invertible Transformation -- 5.3.3 Application to a Small Example -- 5.3.4 Application to Brain Reconstruction -- Diagonalization -- 6.1 Exploration: Heat State Evolution -- 6.2 Eigenspaces and Diagonalizable Transformations -- 6.2.1 Eigenvectors and Eigenvalues -- 6.2.2 Computing Eigenvalues and Finding Eigenvectors -- 6.2.3 Using Determinants to Find Eigenvalues -- 6.2.4 Eigenbases -- 6.2.5 Diagonalizable Transformations -- 6.2.6 Exercises -- 6.3 Explorations: Long-Term Behavior and Diffusion Welding Process Termination Criterion -- 6.3.1 Long-Term Behavior in Dynamical Systems -- 6.3.2 Using MATLAB/OCTAVE to Calculate Eigenvalues and Eigenvectors -- 6.3.3 Termination Criterion -- 6.3.4 Reconstruct Heat State at Removal -- 6.4 Markov Processes and Long-Term Behavior -- 6.4.1 Matrix Convergence -- 6.4.2 Long-Term Behavior -- 6.4.3 Markov Processes -- 6.4.4 Exercises -- Inner Product Spaces and Pseudo-Invertibility -- 7.1 Inner Products, Norms, and Coordinates -- 7.1.1 Inner Product -- 7.1.2 Vector Norm -- 7.1.3 Properties of Inner Product Spaces -- 7.1.4 Orthogonality -- 7.1.5 Inner Product and Coordinates -- 7.1.6 Exercises -- 7.2 Projections -- 7.2.1 Coordinate Projection -- 7.2.2 Orthogonal Projection.
7.2.3 Gram-Schmidt Process -- 7.2.4 Exercises -- 7.3 Orthogonal Transformations -- 7.3.1 Orthogonal Matrices -- 7.3.2 Orthogonal Diagonalization -- 7.3.3 Completing the Invertible Matrix Theorem -- 7.3.4 Symmetric Diffusion Transformation -- 7.3.5 Exercises -- 7.4 Exploration: Pseudo-Inverting the Non-invertible -- 7.4.1 Maximal Isomorphism Theorem -- 7.4.2 Exploring the Nature of the Data Compression Transformation -- 7.4.3 Additional Exercises -- 7.5 Singular Value Decomposition -- 7.5.1 The Singular Value Decomposition -- 7.5.2 Computing the Pseudo-Inverse -- 7.5.3 Exercises -- 7.6 Explorations: Pseudo-Inverse Tomographic Reconstruction -- 7.6.1 The First Pseudo-Inverse Brain Reconstructions -- 7.6.2 Understanding the Effects of Noise. -- 7.6.3 A Better Pseudo-Inverse Reconstruction -- 7.6.4 Using Object-Prior Information -- 7.6.5 Additional Exercises -- Conclusions -- 8.1 Radiography and Tomography Example -- 8.2 Diffusion -- 8.3 Your Next Mathematical Steps -- 8.3.1 Modeling Dynamical Processes -- 8.3.2 Signals and Data Analysis -- 8.3.3 Optimal Design and Decision Making -- 8.4 How to move forward -- 8.5 Final Words -- A Transmission Radiography and Tomography: A Simplified Overview -- A.1 What is Radiography? -- A.2 The Incident X-ray Beam -- A.3 X-Ray Beam Attenuation -- A.4 Radiographic Energy Detection -- A.5 The Radiographic Transformation Operator -- A.6 Multiple Views and Axial Tomography -- A.7 Model Summary -- A.8 Model Assumptions -- A.9 Additional Resources -- B The Diffusion Equation -- C Proof Techniques -- C.1 Logic -- C.2 Proof structure -- C.3 Direct Proof -- C.4 Contrapositive -- C.5 Proof by Contradiction -- C.6 Disproofs and Counterexamples -- C.7 The Principle of Mathematical Induction -- C.8 Etiquette -- D Fields -- D.1 Exercises.
Record Nr. UNISA-996479369703316
Moon Heather A.  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Application-inspired linear algebra / / Heather A. Moon, Thomas J. Asaki, Marie A. Snipes
Application-inspired linear algebra / / Heather A. Moon, Thomas J. Asaki, Marie A. Snipes
Autore Moon Heather A.
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (538 pages)
Disciplina 512.5
Collana Springer Undergraduate Texts in Mathematics and Technology
Soggetto topico Algebras, Linear
Àlgebra lineal
Soggetto genere / forma Llibres electrònics
ISBN 3-030-86155-4
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Outline of Text -- Using This Text -- Exercises -- Computational Tools -- Ancillary Materials -- Acknowledgements -- Contents -- About the Authors -- Introduction To Applications -- 1.1 A Sample of Linear Algebra in Our World -- 1.1.1 Modeling Dynamical Processes -- 1.1.2 Signals and Data Analysis -- 1.1.3 Optimal Design and Decision-Making -- 1.2 Applications We Use to Build Linear Algebra Tools -- 1.2.1 CAT Scans -- 1.2.2 Diffusion Welding -- 1.2.3 Image Warping -- 1.3 Advice to Students -- 1.4 The Language of Linear Algebra -- 1.5 Rules of the Game -- 1.6 Software Tools -- 1.7 Exercises -- Vector Spaces -- 2.1 Exploration: Digital Images -- 2.1.1 Exercises -- 2.2 Systems of Equations -- 2.2.1 Systems of Equations -- 2.2.2 Techniques for Solving Systems of Linear Equations -- 2.2.3 Elementary Matrix -- 2.2.4 The Geometry of Systems of Equations -- 2.2.5 Exercises -- 2.3 Vector Spaces -- 2.3.1 Images and Image Arithmetic -- 2.3.2 Vectors and Vector Spaces -- 2.3.3 The Geometry of the Vector Space mathbbR3 -- 2.3.4 Properties of Vector Spaces -- 2.3.5 Exercises -- 2.4 Vector Space Examples -- 2.4.1 Diffusion Welding and Heat States -- 2.4.2 Function Spaces -- 2.4.3 Matrix Spaces -- 2.4.4 Solution Spaces -- 2.4.5 Other Vector Spaces -- 2.4.6 Is My Set a Vector Space? -- 2.4.7 Exercises -- 2.5 Subspaces -- 2.5.1 Subsets and Subspaces -- 2.5.2 Examples of Subspaces -- 2.5.3 Subspaces of mathbbRn -- 2.5.4 Building New Subspaces -- 2.5.5 Exercises -- Vector Space Arithmetic and Representations -- 3.1 Linear Combinations -- 3.1.1 Linear Combinations -- 3.1.2 Matrix Products -- 3.1.3 The Matrix Equation Ax=b -- 3.1.4 The Matrix Equation Ax=0 -- 3.1.5 The Principle of Superposition -- 3.1.6 Exercises -- 3.2 Span -- 3.2.1 The Span of a Set of Vectors -- 3.2.2 To Span a Set of Vectors -- 3.2.3 Span X is a Vector Space.
3.2.4 Exercises -- 3.3 Linear Dependence and Independence -- 3.3.1 Linear Dependence and Independence -- 3.3.2 Determining Linear (In)dependence -- 3.3.3 Summary of Linear Dependence -- 3.3.4 Exercises -- 3.4 Basis and Dimension -- 3.4.1 Efficient Heat State Descriptions -- 3.4.2 Basis -- 3.4.3 Constructing a Basis -- 3.4.4 Dimension -- 3.4.5 Properties of Bases -- 3.4.6 Exercises -- 3.5 Coordinate Spaces -- 3.5.1 Cataloging Heat States -- 3.5.2 Coordinates in mathbbRn -- 3.5.3 Example Coordinates of Abstract Vectors -- 3.5.4 Brain Scan Images and Coordinates -- 3.5.5 Exercises -- Linear Transformations -- 4.1 Explorations: Computing Radiographs and the Radiographic Transformation -- 4.1.1 Radiography on Slices -- 4.1.2 Radiographic Scenarios and Notation -- 4.1.3 A First Example -- 4.1.4 Radiographic Setup Example -- 4.1.5 Exercises -- 4.2 Transformations -- 4.2.1 Transformations are Functions -- 4.2.2 Linear Transformations -- 4.2.3 Properties of Linear Transformations -- 4.2.4 Exercises -- 4.3 Explorations: Heat Diffusion -- 4.3.1 Heat States as Vectors -- 4.3.2 Heat Evolution Equation -- 4.3.3 Exercises -- 4.3.4 Extending the Exploration: Application to Image Warping -- 4.4 Matrix Representations of Linear Transformations -- 4.4.1 Matrix Transformations between Euclidean Spaces -- 4.4.2 Matrix Transformations -- 4.4.3 Change of Basis Matrix -- 4.4.4 Exercises -- 4.5 The Determinants of a Matrix -- 4.5.1 Determinant Calculations and Algebraic Properties -- 4.6 Explorations: Re-Evaluating Our Tomographic Goal -- 4.6.1 Seeking Tomographic Transformations -- 4.6.2 Exercises -- 4.7 Properties of Linear Transformations -- 4.7.1 One-To-One Transformations -- 4.7.2 Properties of One-To-One Linear Transformations -- 4.7.3 Onto Linear Transformations -- 4.7.4 Properties of Onto Linear Transformations -- 4.7.5 Summary of Properties.
4.7.6 Bijections and Isomorphisms -- 4.7.7 Properties of Isomorphic Vector Spaces -- 4.7.8 Building and Recognizing Isomorphisms -- 4.7.9 Inverse Transformations -- 4.7.10 Left Inverse Transformations -- 4.7.11 Exercises -- Invertibility -- 5.1 Transformation Spaces -- 5.1.1 The Nullspace -- 5.1.2 Domain and Range Spaces -- 5.1.3 One-to-One and Onto Revisited -- 5.1.4 The Rank-Nullity Theorem -- 5.1.5 Exercises -- 5.2 Matrix Spaces and the Invertible Matrix Theorem -- 5.2.1 Matrix Spaces -- 5.2.2 The Invertible Matrix Theorem -- 5.2.3 Exercises -- 5.3 Exploration: Reconstruction Without an Inverse -- 5.3.1 Transpose of a Matrix -- 5.3.2 Invertible Transformation -- 5.3.3 Application to a Small Example -- 5.3.4 Application to Brain Reconstruction -- Diagonalization -- 6.1 Exploration: Heat State Evolution -- 6.2 Eigenspaces and Diagonalizable Transformations -- 6.2.1 Eigenvectors and Eigenvalues -- 6.2.2 Computing Eigenvalues and Finding Eigenvectors -- 6.2.3 Using Determinants to Find Eigenvalues -- 6.2.4 Eigenbases -- 6.2.5 Diagonalizable Transformations -- 6.2.6 Exercises -- 6.3 Explorations: Long-Term Behavior and Diffusion Welding Process Termination Criterion -- 6.3.1 Long-Term Behavior in Dynamical Systems -- 6.3.2 Using MATLAB/OCTAVE to Calculate Eigenvalues and Eigenvectors -- 6.3.3 Termination Criterion -- 6.3.4 Reconstruct Heat State at Removal -- 6.4 Markov Processes and Long-Term Behavior -- 6.4.1 Matrix Convergence -- 6.4.2 Long-Term Behavior -- 6.4.3 Markov Processes -- 6.4.4 Exercises -- Inner Product Spaces and Pseudo-Invertibility -- 7.1 Inner Products, Norms, and Coordinates -- 7.1.1 Inner Product -- 7.1.2 Vector Norm -- 7.1.3 Properties of Inner Product Spaces -- 7.1.4 Orthogonality -- 7.1.5 Inner Product and Coordinates -- 7.1.6 Exercises -- 7.2 Projections -- 7.2.1 Coordinate Projection -- 7.2.2 Orthogonal Projection.
7.2.3 Gram-Schmidt Process -- 7.2.4 Exercises -- 7.3 Orthogonal Transformations -- 7.3.1 Orthogonal Matrices -- 7.3.2 Orthogonal Diagonalization -- 7.3.3 Completing the Invertible Matrix Theorem -- 7.3.4 Symmetric Diffusion Transformation -- 7.3.5 Exercises -- 7.4 Exploration: Pseudo-Inverting the Non-invertible -- 7.4.1 Maximal Isomorphism Theorem -- 7.4.2 Exploring the Nature of the Data Compression Transformation -- 7.4.3 Additional Exercises -- 7.5 Singular Value Decomposition -- 7.5.1 The Singular Value Decomposition -- 7.5.2 Computing the Pseudo-Inverse -- 7.5.3 Exercises -- 7.6 Explorations: Pseudo-Inverse Tomographic Reconstruction -- 7.6.1 The First Pseudo-Inverse Brain Reconstructions -- 7.6.2 Understanding the Effects of Noise. -- 7.6.3 A Better Pseudo-Inverse Reconstruction -- 7.6.4 Using Object-Prior Information -- 7.6.5 Additional Exercises -- Conclusions -- 8.1 Radiography and Tomography Example -- 8.2 Diffusion -- 8.3 Your Next Mathematical Steps -- 8.3.1 Modeling Dynamical Processes -- 8.3.2 Signals and Data Analysis -- 8.3.3 Optimal Design and Decision Making -- 8.4 How to move forward -- 8.5 Final Words -- A Transmission Radiography and Tomography: A Simplified Overview -- A.1 What is Radiography? -- A.2 The Incident X-ray Beam -- A.3 X-Ray Beam Attenuation -- A.4 Radiographic Energy Detection -- A.5 The Radiographic Transformation Operator -- A.6 Multiple Views and Axial Tomography -- A.7 Model Summary -- A.8 Model Assumptions -- A.9 Additional Resources -- B The Diffusion Equation -- C Proof Techniques -- C.1 Logic -- C.2 Proof structure -- C.3 Direct Proof -- C.4 Contrapositive -- C.5 Proof by Contradiction -- C.6 Disproofs and Counterexamples -- C.7 The Principle of Mathematical Induction -- C.8 Etiquette -- D Fields -- D.1 Exercises.
Record Nr. UNINA-9910574049803321
Moon Heather A.  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Applied Linear Algebra, Probability and Statistics : A Volume in Honour of C. R. Rao and Arbind K. Lal / / edited by Ravindra B. Bapat, Manjunatha Prasad Karantha, Stephen J. Kirkland, Samir Kumar Neogy, Sukanta Pati, Simo Puntanen
Applied Linear Algebra, Probability and Statistics : A Volume in Honour of C. R. Rao and Arbind K. Lal / / edited by Ravindra B. Bapat, Manjunatha Prasad Karantha, Stephen J. Kirkland, Samir Kumar Neogy, Sukanta Pati, Simo Puntanen
Autore Bapat Ravindra B
Edizione [1st ed. 2023.]
Pubbl/distr/stampa Singapore : , : Springer Nature Singapore : , : Imprint : Springer, , 2023
Descrizione fisica 1 online resource (540 pages)
Disciplina 512.5
Altri autori (Persone) KaranthaManjunatha Prasad
KirklandStephen J
NeogySamir Kumar
PatiSukanta
PuntanenSimo
Collana Indian Statistical Institute Series
Soggetto topico Algebras, Linear
Probabilities
Statistics
Graph theory
Stochastic processes
Game theory
Linear Algebra
Probability Theory
Statistical Theory and Methods
Graph Theory
Stochastic Processes
Game Theory
Àlgebra lineal
Probabilitats
Estadística
Soggetto genere / forma Llibres electrònics
ISBN 981-9923-10-7
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Chapter 1. On Some Matrix Versions of Covariance, Harmonic Mean and other Inequalities: An Overview -- Chapter 2. The Impact of Professor C. R. Rao's Research used in solving problems in Applied Probability -- Chapter 3. Upper ounds for the Euclidean distances between the BLUEs under the partitioned linear fixed model and the corresponding mixed model -- Chapter 4. Nucleolus Computation for some Structured TU Games via Graph Theory and Linear Algebra -- Chapter 5. From Linear System of Equations to Artificial Intelligence - The evolution Journey of Computer Tomographic Image Reconstruction Algorithms -- Chapter 6. Shapley Value and other Axiomatic Extensions to Shapley Value -- Chapter 7. An Accelerated Block Randomized Kaczmarz Methos -- Chapter 8. Nullity of Graphs - A Survey and Some New Results -- Chapter 9. Some Observations on Algebraic Connectivity of Graphs -- Chapter 10. Orthogonality for iadjoints f Operators -- Chapter 11. Permissible covariance structures for simultaneous retention of BLUEs in small and big linear models -- Chapter 12. On some Special Matrices and its Applications in Linear Complementarity Problem -- Chapter 3. On Nearest Matrix with Partially Specified Eigen Structure -- Chapter 14. Equality of BLUEs for Full, Small, and Intermediate Linear Models under Covariance Change, with links to Data Confidentiality and Encryption.-Chapter 15. Statistical Inference for Middle Censored Data with Applications. etc.
Record Nr. UNINA-9910736008903321
Bapat Ravindra B  
Singapore : , : Springer Nature Singapore : , : 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
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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. UNISA-996499871503316
Karpfinger Christian  
Berlin, Germany : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui