“…La constante e, también conocida como constante de Napier o número de Euler, la proporción áurea, π, los números primos, como los de Marsenne y Fermat, son algunos de los más celebres ejemplos de constantes matemáticas, así denominadas por expresar un valor fijo, pero no siempre determinado. …”

Tabla de Contenidos: “…Front Cover -- Indoor Navigation Strategies for Aerial Autonomous Systems -- Copyright -- Contents -- About the Authors -- Preface -- Acknowledgments -- Part 1 Background -- 1 State-of-the-Art -- 1.1 Mathematical Representation of the Vehicle Dynamics -- 1.2 Attitude Estimation Using Inertial Sensors -- 1.3 Delay Systems &amp -- Predictors -- 1.4 Data Fusion for UAV Localization -- 1.5 Control &amp -- Navigation Algorithms -- 1.6 Trajectory Generation &amp -- Tracking -- 1.7 Obstacle Avoidance -- 1.8 Teleoperation -- References -- 2 Modeling Approaches -- 2.1 Force and Moment in a Rotor -- 2.2 Euler-Lagrange Approach -- 2.3 Newton-Euler Approach -- 2.4 Quaternion Approach -- 2.5 Discussion -- References -- Part 2 Improving Sensor Signals for Control Purposes -- 3 Inertial Sensors Data Fusion for Orientation Estimation -- 3.1 Attitude Representation -- 3.2 Sensor Characterization -- 3.3 Attitude Estimation Algorithms -- 3.4 A Computationally-Efficient Kalman Filter -- 3.5 Discussion -- References -- 4 Delay Signals &amp -- Predictors -- 4.1 Observer-Predictor Algorithm for Compensation of Measurement Delays -- 4.2 State Predictor-Control Scheme -- 4.3 Discussion -- References -- 5 Data Fusion for UAV Localization -- 5.1 Sensor Data Fusion -- 5.2 Prototype and Numerical Implementation -- 5.3 Flight Tests and Experimental Results -- 5.4 OptiTrack Measurements vs EKF Estimation -- 5.5 Rotational Optical Flow Compensation -- 5.6 Discussion -- References -- Part 3 Navigation Schemes &amp -- Control Strategies -- 6 Nonlinear Control Algorithms with Integral Action -- 6.1 From PD to PID Controllers -- 6.2 Saturated Controllers with Integral Component -- 6.3 Integral and Adaptive Backstepping Control - IAB -- 6.4 Discussion -- References -- 7 Sliding Mode Control -- 7.1 From the Nonlinear Attitude Representation to Linear MIMO Expression…”

Tabla de Contenidos: “…<P><b>1 Introductory Concepts and Calculus Review 1</b></p> <p>1.1 Basic Tools of Calculus 1</p> <p>1.2 Error, Approximate Equality, and Asymptotic Order Notation 10</p> <p>1.3 A Primer on Computer Arithmetic 13</p> <p>1.4 A Word on Computer Languages and Software 17</p> <p>1.5 A Brief History of Scientific Computing 18</p> <p><b>2 A Survey of Simple Methods and Tools 19</b></p> <p>2.1 Horner's Rule and Nested Multiplication 19</p> <p>2.2 Difference Approximations to the Derivative 22</p> <p>2.3 Application: Euler's Method for Initial Value Problems 30</p> <p>2.4 Linear Interpolation 34</p> <p>2.5 Application-The Trapezoid Rule 38</p> <p>2.6 Solution of Tridiagonal Linear Systems 46</p> <p>2.7 Application: Simple Two-Point Boundary Value Problems 50</p> <p><b>3 Root-Finding 55</b></p> <p>3.1 The Bisection Method 55</p> <p>3.2 Newton's Method: Derivation and Examples 59</p> <p>3.3 How to Stop Newton's Method 63</p> <p>3.4 Application: Division Using Newton's Method 66</p> <p>3.5 The Newton Error Formula 69</p> <p>3.6 Newton's Method: Theory and Convergence 72</p> <p>3.7 Application: Computation of the Square Root 76</p> <p>3.8 The Secant Method: Derivation and Examples 79</p> <p>3.9 Fixed Point Iteration 83</p> <p>3.10 Roots of Polynomials (Part 1) 85</p> <p>3.11 Special Topics in Root-finding Methods 88</p> <p>3.12 Very High-order Methods and the Efficiency Index 98</p> <p><b>4 Interpolation and Approximation 101</b></p> <p>4.1 Lagrange Interpolation 101</p> <p>4.2 Newton Interpolation and Divided Differences 104</p> <p>4.3 Interpolation Error 114</p> <p>4.4 Application: Muller's Method and Inverse Quadratic Interpolation 119</p> <p>4.5 Application: More Approximations to the Derivative 121</p> <p>4.6 Hermite Interpolation 122</p> <p>4.7 Piecewise Polynomial Interpolation 125</p> <p>4.8 An Introduction to Splines 129</p> <p>4.9 Tension Splines 135</p> <p>4.10 Least Squares Concepts in Approximation 137</p> <p>4.11 Advanced Topics in Interpolation Error 142</p> <p><b>5 Numerical Integration 149</b></p> <p>5.1 A Review of the Definite Integral 149</p> <p>5.2 Improving the Trapezoid Rule 151</p> <p>5.3 Simpson's Rule and Degree of Precision 154</p> <p>5.4 The Midpoint Rule 162</p> <p>5.5 Application: Stirling's Formula 166</p> <p>5.6 Gaussian Quadrature 167</p> <p>5.7 Extrapolation Methods 173</p> <p>5.8 Special Topics in Numerical Integration 177</p> <p><b>6 Numerical Methods for Ordinary Differential Equations 185</b></p> <p>6.1 The Initial Value Problem-Background 185</p> <p>6.2 Euler's Method 187</p> <p>6.3 Analysis of Euler's Method 189</p> <p>6.4 Variants of Euler's Method 190</p> <p>6.5 Single Step Methods-Runge-Kutta 197</p> <p>6.6 Multistep Methods 200</p> <p>6.7 Stability Issues 204</p> <p>6.8 Application to Systems of Equations 206</p> <p>6.9 Adaptive Solvers 210</p> <p>6.10 Boundary Value Problems 212</p> <p><b>7 Numerical Methods for the Solution of Systems of Equations 217</b></p> <p>7.1 Linear Algebra Review 217</p> <p>7.2 Linear Systems and Gaussian Elimination 218</p> <p>7.3 Operation Counts 223</p> <p>7.4 The <i>LU </i>Factorization 224</p> <p>7.5 Perturbation, Conditioning and Stability 229</p> <p>7.6 SPD Matrices and the Cholesky Decomposition 235</p> <p>7.7 Application: Numerical Solution of Linear Least Squares Problems 236</p> <p>7.8 Sparse and Structured Matrices 240</p> <p>7.9 Iterative Methods for Linear Systems -- A Brief Survey 241</p> <p>7.10 Nonlinear Systems: Newton's Method and Related Ideas 242</p> <p>7.11 Application: Numerical Solution of Nonlinear BVP's 244</p> <p><b>8 Approximate Solution of the Algebraic Eigenvalue Problem 247</b></p> <p>8.1 Eigenvalue Review 247</p> <p>8.2 Reduction to Hessenberg Form 249</p> <p>8.3 Power Methods 250</p> <p>8.4 Bisection and Inertia to Compute Eigenvalues of Symmetric Matrices 253</p> <p>8.5 An Overview of the <i>QR </i>Iteration 257</p> <p>8.6 Application: Roots of Polynomials, II 260</p> <p>8.7 Application: Computation of Gaussian Quadrature Rules 261</p> <p><b>9 A Survey of Numerical Methods for Partial Differential Equations 265</b></p> <p>9.1 Difference Methods for the Diffusion Equation 265</p> <p>9.2 Finite Element Methods for the Diffusion Equation 270</p> <p>9.3 Difference Methods for Poisson Equations 271</p> <p><b>10 An Introduction to Spectral Methods 277</b></p> <p>10.1 Spectral Methods for Two-Point Boundary Value Problems 277</p> <p>10.2 Spectral Methods in Two Dimensions 279</p> <p>10.3 Spectral Methods for Time-Dependent Problems 282</p> <p>10.4 Clenshaw-Curtis Quadrature 283</p>…”

Tabla de Contenidos: “…Variation of Parameters""""Non-Homogeneous Equations with Variable Coefficients. Cauchyâ€?Euler Equations""; ""The Laplace Transform""; ""Orthogonal Polynomials""; ""Chebychev Polynomials of the First and Second Kind""; ""Legendre Polynomials""; ""Associated Legendre Polynomials""; ""Hermite Polynomials""; ""Generalized Laguerre Polynomials""; ""Laguerre Polynomials""; ""Jacobi Polynomials""; ""Gegenbauer Polynomials""; ""Bessel and Airy Functions""; ""Chapter 4: Differential Equations Via Approximation Methods""…”

Tabla de Contenidos:

Tabla de Contenidos: “…Contiene: Introduction -- v.1: Les demonstrations de Tertullien, Origéne, Eusebe -- v.2: Eusebe, Saint Agustin, Montaigne, Bacon, Grotius, Descartes -- v.3: Richelieu, Arnaud, De Choiseul, Duplessis-Praslin, Pascal, Pelisson, Nicole -- v.4: Boyle, Bossuet, Bourdaloue, Locke, Lami, Burnet, Malebranche, Lesley, Leibnitz, labruyere, Fénelon -- v.5: Huet et Clarke -- v.6: Duguet, Stonhope, Bayle, Leclerc, Dupin -- v.7: Jacquelot, Tillotson, De Haller, Sherlock, Le Moine, Pope, Leland -- v.8: Racine, Massillon, Ditton, Derham, D'Aguesseau, De Polignac -- v.9: Saurin, Buffier, Warburton, Tournemine, Bentley, Littleton, Fabricius, Addison, De Bernis, Jean-Jacques Rousseau -- v.10: De Para Du Phanjas, Stanislas I, Turgot, Statler, Wets, Beauzèe -- v.11: Bergier, Gerdil, Thomas, Bonnet, De Crillon, Euler, Delamare, Caraccioli, Jennings -- v.12: Duchamel, Ligouri, Butler, Bullet, Vauvenargues, Guénard, Blair, De Pompignan, Deluc, porteus, Gérad -- v.13: Diessbach, Jacques, Lamourette, Laharpe, Le Coz, Duvoisin, De la Luzerne, Scimitt, Pointer -- v.14: Moore, Silvio Pellico, Lingard, Brunati Manzoni, Paley, Perrone, Dorleans, Campien, Pèrennès -- v.15: Wiseman, Buckland, marcel de Serres, Keith, Chalmers -- v.16: Wisseman, Dupin Ainé, S.S. …”

“…Para cumplir con semejante fin, el autor, el académico de la RAE, Premio Nacional de Ensayo, José Manuel Sánchez Ron, ha seleccionado cien libros que sobresalen en la historia de la ciencia, hasta el punto que se puede decir de esta obra que constituye una nueva Biblioteca de Alejandría para la ciencia, en la que figuran los mejores científicos de la historia, personalidades como Aristóteles, Galeno, Galileo, Newton, Euler, Lavoisier, Buffon, Darwin, Maxwell, Einstein, Fossey, Dawkins o Hawking, entre muchos otros. …”

Tabla de Contenidos: “…Introductory Remarks -- 9.2. Euler's Equation -- 9.3. Isoperimetric Problems and the Like -- 9.3.1. …”

Tabla de Contenidos: “…Homogeneous coordinates; 2.3. Simulation; 2.3.1. Euler's method; 2.3.2. Runge-Kutta method; 2.3.3. …”

Tabla de Contenidos: “…Chapter 13: Securing the Control of Euler-Lagrange Systems in Networked Environments with Model-Free Sliding Mode ControlChapter 14: Defenses against Packet-Dropping Attacks in Wireless Multihop Ad Hoc Networks; Chapter 15: Security Issues in Machine-to-Machine Communication; Chapter 16: Authentication in Wireless Mesh Networks; Chapter 17: Wireless-Based Application-Layer Cross-Layer Design with Simultaneous Quality of Service and Security Support; Chapter 18: Security, Trust, and Privacy in Opportunistic Multihop Wireless Networks; Back Cover…”

Tabla de Contenidos: “…Jahrhundert am Beispiel der Basler Mathematiker und Naturwissenschaftler Daniel Bernoulli und Leonhard Euler -- Register…”

Tabla de Contenidos: “…Bergier, Gerdil, Thomas, Bonnet, De Crillon, Euler, Delamare, Caraccioli, Jennings -- v.12. Duchamel, Ligouri, Butler, Bullet, Vauvenargues, Guénard, Blair, De Pompignan, Deluc, porteus, Gérad -- v.13. …”

Tabla de Contenidos: “…TEORÍA DE CONJUNTOS -- 1.1 DEFINICIONES INICIALES -- 1.2 RELACIONES ENTRE CONJUNTOS -- 1.3 OPERACIONES ENTRE CONJUNTOS -- 1.4 DIAGRAMAS DE VENN EULER -- 1.5 APLICACIONES DE LOS CONJUNTOS EN LA SOLUCIÓN DE (...) -- 1.6 EJERCICIOS DE PRÁCTICA I -- 1.7 MATEMÁTICAS EN LA WEB -- 2. …”
Acceso restringido con credenciales UPSA

“…Deep theories were developed from the classic time of Euler and Gauss onwards to this day that made the solutions ofmanyof theseproblemspossible.Algorithmicsolutionsandtheirproperties became an object of study in their own right. …”

“…The book also illustrates how results of Euler and Gauss can be fully understood only in the context of class field theory, and in addition, explores a selection of the magnificent formulas of complex multiplication. …”

“…The text focuses on variational models, their corresponding Euler–Lagrange equations, and numerical implementations for image processing. …”

Tabla de Contenidos: “…7.1 Formulación del problema de valor inicial7.2 Método de Euler; 7.3 Métodos de Taylor; 7.4 Método de Euler modificado; 7.5 Métodos de Runge-Kutta; 7.6 Métodos de predicción-corrección; 7.7 Ecuaciones diferenciales ordinarias de ordensuperior y sistemas de ecuaciones diferencialesordinarias; 7.8 Formulación del problema de valores en la frontera; 7.9 Ecuaciones diferenciales rígidas; 8 Ecuaciones diferenciales parciales; 8.1 Obtención de algunas ecuaciones diferencialesparciales a partir de la modelación de fenómenosfísicos; 8.2 Aproximación de derivadas por diferencias finitas…”

Tabla de Contenidos: “…Ecuación de continuidad; 7.2. Ecuación de Euler; 7.3. Flujos de densidad constante; 7.4. Flujos adiabáticos; 7.5. …”