Applied Algebraic and Differential Calculus

Erscheinungsjahr 2022
ISBN: 978-1-77469-358-2
Verlag: Arcler Press
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 461 Seiten, Electronic book text, Format (B × H): 152 mm x 229 mm

Applied Algebraic and Differential Calculus is an edited book consisting of 18 open-access articles on mathematical analysis and computational methodologies for solving differential equations, as well as matrix eigenvalue, boundary value, and bifurcation problems. It includes a variety of algebraic and numerical strategies from decomposition to neural network based methods.Reading this book requires some knowledge in advanced calculus, differential equations, matrix computations.

This book is intended to reach an academic audience ranging from graduate student to experienced researchers.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra

Inhaltsverzeichnis

- Chapter 1 The Eight Epochs of Math as Regards Past and Future Matrix Computations
- Chapter 2 Solving Second-Order Differential Equations by Decomposition
- Chapter 3 Decomposition of Ordinary Differential Equations
- Chapter 4 Solution of Nonlinear Partial Differential Equations by Mixture Adomian Decomposition Method and Sumudu Transform
- Chapter 5 Higher Order Haar Wavelet Method for Solving Differential Equations
- Chapter 6 Solution of Fractional Differential Equation Systems and Computation of Matrix Mittag–Leffler Functions
- Chapter 7 Computation of Gram Matrix and Its Partial Derivative Using Precise Integration Method for Linear Time-Invariant Systems
- Chapter 8 Matrix Iteration Algorithms for Solving the Generalized Lyapunov Matrix Equation
- Chapter 9 A Brief Summary of the Finite Element Method for Differential Equations
- Chapter 10 An Efficient Finite Element Method and Error Analysis for Eigenvalue Problem of Schrödinger Equation with an Inverse Square Potential on Spherical Domain
- Chapter 11 Solving Fractional Differential Equations by Using Triangle Neural Network
- Chapter 12 A Novel Improved Extreme Learning Machine Algorithm in Solving Ordinary Differential Equations by Legendre Neural Network Methods
- Chapter 13 Bifurcation Theory of Dynamical Chaos
- Chapter 14 Bifurcation Analysis in a Two-Dimensional Neutral Differential Equation
- Chapter 15 Observations on the Computation of Eigenvalue and Eigenvector Jacobians
- Chapter 16 A Note on Some Nonlinear Principal Eigenvalue Problems
- Chapter 17 Eigenvalue Criteria for Existence of Positive Solutions to Fractional Boundary Value Problem
- Chapter 18 Boundary Value Problems of Nonlinear Mixed-Type Fractional Differential Equations

Über Autor(innen)

Olga Moreira is a Ph.D. in Astrophysics and B.Sc. in Physics and Applied Mathematics. She is an experienced technical writer and researcher which former fellowships include postgraduate positions at two of the most renown European institutions in the fields of Astrophysics and Space Science (the European Southern Observatory, and the European Space Agency). Presently, she is an independent scientist working on projects involving machine learning and neural networks research as well as peer-reviewing and edition of academic books.