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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.
Author(s): Eusebius Doedel
391 Pages 
Introduction To Numerical Analysis by MIT
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
NA Pages
Lecture Notes on Numerical Analysis by Peter J. Olver
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.
Author(s): Peter J. Olver
NA Pages
Introduction to Numerical Methods
This note explains the following topics: IEEE Arithmetic, Root Finding, Systems of equations, Least-squares approximation, Interpolation, Integration and Ordinary differential equations.
Author(s): Jeffrey R. Chasnov
63 Pages
Lecture notes on Numerical Analysis of Partial Differential Equation
This note explains the following topics: finite difference method for the Laplacian, Linear algebraic solve, Finite element methods for elliptic equation and Time-dependent problem.
Author(s): Douglas N. Arnold
88 Pages