Lecture Notes on Numerical Analysis of Nonlinear Equations
Lecture Notes on Numerical Analysis of Nonlinear Equations
Lecture Notes on Numerical Analysis of Nonlinear Equations
This book
covers the following topics: The Implicit Function Theorem, A Predator-Prey
Model, The Gelfand-Bratu Problem, Numerical Continuation, Following Folds,
Numerical Treatment of Bifurcations, Examples of Bifurcations, Boundary Value
Problems, Orthogonal Collocation , Hopf Bifurcation and Periodic Solutions,
Computing Periodic Solutions, Periodic Orbit Folds , Stable and Unstable
Manifolds.
This PDF covers the following topics related to
Numerical Analysis : Series and Sequences, Integrals as Sums and Derivatives
as Differences, Interpolation, Nonlinear Equations, Methods for Ordinary
Differential Equations, Fourier Analysis, Spectral Interpolation,
Differentiation, Quadrature.
Author(s): Prof. Laurent Demanet, Massachusetts
Institute of Technology
This lecture note
explains the following topics: Computer Arithmetic, Numerical Solution of Scalar
Equations, Matrix Algebra, Gaussian Elimination, Inner Products and Norms,
Eigenvalues and Singular Values, Iterative Methods for Linear Systems, Numerical
Computation of Eigenvalues, Numerical Solution of Algebraic Systems, Numerical
Solution of Ordinary Differential Equations, Numerical Solution of the Heat and
Wave Equations, Approximation and Interpolation, The Finite Element Method.
This note explains the following topics:
Differential and Difference Equations, Numerical Solution of Differential
Equations and Numerical linear algebra.
This note covers the following topics: Approximation and
Interpolation, Numerical Quadrature, Direct Methods of Numerical Linear Algebra,
Numerical solution of nonlinear systems and optimization, Numerical Solution of
Ordinary Differential Equations, Numerical Solution of Partial Differential
Equations and e Iterative Methods of Numerical Linear Algebra.
This note covers the
following topics: Numerical Solution of Algebraic Equations, Gauss Elimination
Method, LU Decomposition Method, Iterative Methods, Successive Over-Relaxation (SOR)
Method.
Author(s): Dragica
Vasileska, Associate Professor, Arizona State University
This text includes the following chapters: Introduction to MATLAB,
Root Approximations and Partial Fraction Expansion, Sinusoids and Complex
Numbers, Matrices and Determinants, Review of Differential Equations, Power
Series, Finite Differences and Interpolation, Linear and Parabolic Regression,
Solution of Differential Equations by Numerical Methods, Integration by
Numerical Methods, Difference Equations, The Gamma and Beta Functions, Bessel,
Legendre, and Chebyshev Polynomials.