Alvaro Meseguer - Fundamentals of Numerical Mathematics for Physicists and Engineers

3 Chapter 3Figure 3.1 Numerical differentiation: starting from the known values of a ...Figure 3.2 From top to bottom, finite difference formulas (3.3), (3.4), (3.5...Figure 3.3 Centered difference formula (3.5) applied on a set of equidistant...

4 Chapter 4Figure 4.1 Geometrical representation of simple interpolatory quadratures fo...Figure 4.2 Areas associated with the composite trapezoidal rule (hatched reg...Figure 4.3 Areas associated with the composite Simpson's rule (hatched regio...Figure 4.4 Absolute quadrature errors of composite trapezoidal and Simpson r...Figure 4.5 Chebyshev polynomials (solid black), (dashed black), (solid...Figure 4.6 Absolute quadrature error in the Clenshaw–Curtis quadrature appro...Figure 4.7 Computation of the length of the ellipse . (a) We compute the ...Figure 4.8 Semi‐logarithmic plot of the absolute quadrature errors correspon...Figure 4.9 Cotangent transformation applied on the abscissas (4.89) for Figure 4.10 Absolute quadrature error of cotangent quadrature formula (4.8...Figure 4.11 Hyperbolic tangent transformation applied on the abscissas ....Figure 4.12 Absolute quadrature errors of the approximation of integral (4...

5 Chapter 5Figure 5.1 Linear fitting. The gray disks are the experimental observations....Figure 5.2 The resulting vector is the reflection of across the line ....Figure 5.3 (a) Properties (5.137). (b) There are two possible reflectors (ac...Figure 5.4 QR‐factorization of a non‐square matrix .Figure 5.5 Classical Gram–Schmidt (CGS) algorithm.Figure 5.6 CGS and QR‐factorization equivalence.Figure 5.7 Near parallelism between and results in a vector with very ...

6 Chapter 6Figure 6.1 Geometrical interpretation of a system of two nonlinear equations...Figure 6.2 (a) Solutions of system (6.21) showing the first three iterates o...Figure 6.3 Parameter‐dependent solution branches of (6.25).Figure 6.4 (a) Rotating pendulum. (b) Trivial solution branch and new solu...Figure 6.5 Continuation methods. (a) Natural continuation fails in the prese...Figure 6.6 Level curve of Himmelblau's function (6.46). (a) Starting the s...

7 Chapter 7Figure 7.1 DFT of . (a) Fourier coefficients provided by Code 22. (b) Dis...Figure 7.2 Sampling process. (a) The ordinates (gray circles) are the samp...Figure 7.3 (a) The signal is sampled using measurements every time uni...Figure 7.4 Fourier differentiation of function . (a) Sampled function at ...Figure 7.5 Exponential convergence of Fourier differentiation of function ....Figure 7.6 Differentiation of function in Fourier space, following Figure ...