Tabla de Contenidos: “…Cover -- Contents -- Preface -- Part I: Preliminaries -- Chapter 1: Sets and Relations -- 1.1 Sets and subsets -- 1.2 Relations and functions -- 1.3 Equivalence relations and partitions -- 1.4 The cardinality of a set -- Chapter 2: Number Systems -- 2.1 Integers -- 2.2 Congruence modulo n -- 2.3 Rational, real and complex numbers -- 2.4 Ordering -- 2.5 Matrices -- 2.6 Determinants -- Part II: Group Theory -- Chapter 3: Groups -- 3.1 Binary systems -- 3.2 Groups -- 3.3 Elementary properties of groups -- 3.4 Finite groups and group tables -- Chapter 4: Subgroups and Quotient Groups -- 4.1 Subgroups -- 4.2 Cyclic groups -- 4.3 Cosets of a subgroup -- 4.4 Lagrange's theorem -- 4.5 Normal subgroups -- 4.6 Quotient groups -- Chapter 5: Homomorphisms of Groups -- 5.1 Definition and examples -- 5.2 Fundamental theorem of homomorphisms -- 5.3 Isomorphism theorems -- 5.4 Automorphisms -- Chapter 6: Permutation Groups -- 6.1 Cayley's theorem -- 6.2 The symmetric group Sn -- 6.3 Cycles -- 6.4 Alternating group An and dihedral group Dn -- Chapter 7: Group Actions on Sets -- 7.1 Action of a group on a set -- 7.2 Orbits and stabilizers -- 7.3 Certain counting techniques -- 7.4 Cauchy and Sylow theorems -- Chapter 8: Structure Theory of Groups -- 8.1 Direct products -- 8.2 Finitely generated abelian groups -- 8.3 Invariants of finite abelian groups -- 8.4 Groups of small order -- Part III: Ring Theory -- Chapter 9: Rings -- 9.1 Examples and elementary properties -- 9.2 Certain special elements in rings -- 9.3 The characteristic of a ring -- 9.4 Subrings -- 9.5 Homomorphisms of rings -- 9.6 Certain special types of rings -- 9.7 Integral domains and fields -- Chapter 10: Ideals and Quotient Rings -- 10.1 Ideals -- 10.2 Quotient rings -- 10.3 Chinese remainder theorem -- 10.4 Prime ideals -- 10.5 Maximal ideals -- 10.6 Embeddings of rings…”

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Tabla de Contenidos: “…About this book -- STEP -- Worked Problems ; Worked problem 1 ; Worked problem 2 ; Problems-- ‡a P1 An integer equation P2 Partitions of 10 and 20 P3 Mathematical deduction P4 Divisibility P5 The modulus function P6 The regular Reuleaux heptagon P7 Chain of equations P8 Trig. equations P9 Integration by substitution P10 True or false P11 Egyptian fractions P12 Maximising with constraints P13 Binomial expansion P14 Sketching subsets of the plane P15 More sketching subsets of the plane P16 Non-linear simultaneous equations P17 Inequalities P18 Inequalities from cubics P19 Logarithms P20 Cosmological models P21 Melting snowballs P22 Gregory's series P23 Intersection of ellipses P24 Sketching x m ( 1 - x ) n P25 Inequalities by area estimates P26 Simultaneous integral equations P27 Relation between coefficients of quartic for real roots P28 Fermat numbers P29 Telescoping series P30 Integer solutions of cubics P31 The harmonic series P32 Integration by substitution P33 More curve sketching P34 Trig sum P35 Roots o ‡a f a cubic equation P36 Root counting P37 Irrationality of e P38 Discontinuous integrands P39 A difficult integral P40 Estimating the value of an integral P41 Integrating the modulus function P42 Geometry P43 The t substitution P44 A differential-difference equation P45 Lagrange's identity P46 Bernoulli polynomials P47 Vector geometry P48 Solving a quartic P49 Areas and volumes P50 More curve sketching P51 Spherical loaf P52 Snowploughing P53 Tortoise and hare P54 How did the chicken cross the road? …”

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: “…-- 1.2 Practical Aspects of Vibration Analysis -- 1.2.1 Step 1: Mathematical Modelling -- 1.2.2 Step 2: Derivation of Governing Equations -- 1.2.3 Step 3: Solution of Governing Equations -- 1.2.4 Step 4: Interpretation of Results -- Conclusion -- Chapter 2: Single Degree-of-Freedom Vibration Systems -- 2.1 Definition of Degrees-of-Freedom -- 2.2 Single Degree-of-Freedom System -- 2.2.1 Rigid-Body Oscillations -- 2.2.2 Spring−Mass−Damper Systems -- 2.3 Equation of Motion for Singledegree-of-Freedom System (SDOF) -- 2.3.1 Free Vibrations of Single Degree-of-Freedom System-Viscous Damping -- 2.3.2 Free Vibrations of Single Degree-of-Freedom System-Coulomb and Hysteretic Damping -- 2.4 Forced Vibrations of Single Degree-of-Freedomsystem to Harmonic Excitation Force -- 2.4.1 Response of an Undamped System to Harmonic Excitation Force -- 2.4.2 Response of a Damped System Under Harmonic Force -- 2.4.3 Mechanical-Impedance Method -- 2.4.4 Forced Vibrations with Coulomb Damping -- 2.4.5 Forced Vibration with Hysteretic Damping -- 2.4.6 Response of SDOF Systems Subjected to a General Periodic Force -- Conclusion -- Exercises -- Chapter 3: Two Degrees-of-Freedom Systems -- 3.1 Equations of Motion -- 3.1.1 Analysis of Free Vibrations of an Undamped System -- 3.1.2 Lagrange's Equations -- 3.2 Analysis of Free Vibrations of Damped Systems -- 3.2.1 Orthogonality Principle -- 3.3 Semi-Definite System -- 3.4 Forced Vibration of Two Degrees-of-Freedom System -- 3.4.1 Tuned Absorber -- Conclusion -- Exercises…”