What can't be ignored / 1: |
The MATLAB and Octave environments / 1.1: |
Real numbers / 1.2: |
How we represent them / 1.2.1: |
How we operate with floating-point numbers / 1.2.2: |
Complex numbers / 1.3: |
Matrices / 1.4: |
Vectors / 1.4.1: |
Real functions / 1.5: |
The zeros / 1.5.1: |
Polynomials / 1.5.2: |
Integration and differentiation / 1.5.3: |
To err is not only human / 1.6: |
Talking about costs / 1.6.1: |
The MATLAB language / 1.7: |
MATLAB statements / 1.7.1: |
Programming in MATLAB / 1.7.2: |
Examples of differences between MATLAB and Octave languages / 1.7.3: |
What we haven't told you / 1.8: |
Exercises / 1.9: |
Nonlinear equations / 2: |
Some representative problems / 2.1: |
The bisection method / 2.2: |
The Newton method / 2.3: |
How to terminate Newton's iterations / 2.3.1: |
The Newton method for systems of nonlinear equations / 2.3.2: |
Fixed point iterations / 2.4: |
How to terminate fixed point iterations / 2.4.1: |
Acceleration using Aitken's method / 2.5: |
Algebraic polynomials / 2.6: |
Hörner's algorithm / 2.6.1: |
The Newton-Hörner method / 2.6.2: |
Approximation of functions and data / 2.7: |
Approximation by Taylor's polynomials / 3.1: |
Interpolation / 3.3: |
Lagrangian polynomial interpolation / 3.3.1: |
Stability of polynomial interpolation / 3.3.2: |
Interpolation at Chebyshev nodes / 3.3.3: |
Trigonometric interpolation and FFT / 3.3.4: |
Piecewise linear interpolation / 3.4: |
Approximation by spline functions / 3.5: |
The least-squares method / 3.6: |
Numerical differentiation and integration / 3.7: |
Approximation of function derivatives / 4.1: |
Numerical integration / 4.3: |
Midpoint formula / 4.3.1: |
Trapezoidal formula / 4.3.2: |
Simpson formula / 4.3.3: |
Interpolatory quadratures / 4.4: |
Simpson adaptive formula / 4.5: |
Linear systems / 4.6: |
Linear system and complexity / 5.1: |
The LU factorization method / 5.3: |
The pivoting technique / 5.4: |
How accurate is the solution of a linear system? / 5.5: |
How to solve a tridiagonal system / 5.6: |
Overdetermined systems / 5.7: |
What is hidden behind the MATLAB command / 5.8: |
Iterative methods / 5.9: |
How to construct an iterative method / 5.9.1: |
Richardson and gradient methods / 5.10: |
The conjugate gradient method / 5.11: |
When should an iterative method be stopped? / 5.12: |
To wrap-up: direct or iterative? / 5.13: |
Eigenvalues and eigenvectors / 5.14: |
The power method / 6.1: |
Convergence analysis / 6.2.1: |
Generalization of the power method / 6.3: |
How to compute the shift / 6.4: |
Computation of all the eigenvalues / 6.5: |
Ordinary differential equations / 6.6: |
The Cauchy problem / 7.1: |
Euler methods / 7.3: |
The Crank-Nicolson method / 7.3.1: |
Zero-stability / 7.5: |
Stability on unbounded intervals / 7.6: |
The region of absolute stability / 7.6.1: |
Absolute stability controls perturbations / 7.6.2: |
High order methods / 7.7: |
The predictor-corrector methods / 7.8: |
Systems of differential equations / 7.9: |
Some examples / 7.10: |
The spherical pendulum / 7.10.1: |
The three-body problem / 7.10.2: |
Some stiff problems / 7.10.3: |
Numerical approximation of boundary-value problems / 7.11: |
Approximation of boundary-value problems / 8.1: |
Finite difference approximation of the one-dimensional Poisson problem / 8.2.1: |
Finite difference approximation of a convection-dominated problem / 8.2.2: |
Finite element approximation of the one-dimensional Poisson problem / 8.2.3: |
Finite difference approximation of the two-dimensional Poisson problem / 8.2.4: |
Consistency and convergence of finite difference discretization of the Poisson problem / 8.2.5: |
Finite difference approximation of the one-dimensional heat equation / 8.2.6: |
Finite element approximation of the one-dimensional heat equation / 8.2.7: |
Hyperbolic equations: a scalar pure advection problem / 8.3: |
Finite difference discretization of the scalar transport equation / 8.3.1: |
Finite difference analysis for the scalar transport equation / 8.3.2: |
Finite element space discretization of the scalar advection equation / 8.3.3: |
The wave equation / 8.4: |
Finite difference approximation of the wave equation / 8.4.1: |
Solutions of the exercises / 8.5: |
References / 9.1: |
Index |
What can't be ignored / 1: |
The MATLAB and Octave environments / 1.1: |
Real numbers / 1.2: |