Differential equation

This paper presents the design and development of a Neural Netwwork-Adaptive backstepping (NN-Adaptive backstepping) controller to track the trajectory of a differentially controlled mobile robot. The controller is designed based on the robot dynamics equation and on the basis of the Backstepping controller.

11p visergeyne 18-06-2024 0 0   Download

Part 1 book "Advanced calculus" includes content: Introduction, vector spaces, finite dimensional vector spaces, the differential calculus, compactness and completeness, scalar product spaces, differential equations, multilinear functionals.

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Ebook "Advanced mathematical methods for scientists and engineers" presents the following content: Algebra, calculus, functions of a complex variable, ordinary differential equations, partial differential equations, calculus of variations, nonlinear differential equations.

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presents the following content: Chapter 1 introduction, chapter 2 approximation of a function, chapter 3 numerical calculus, chapter 4 ordinary differential equations, chapter 5 numerical methods for matrices, chapter 6 spectral analysis, chapter 7 partial differential equations, chapter 8 molecular dynamics simulations, chapter 9 modeling continuous systems, chapter 10 monte carlo simulations, chapter 11 genetic algorithm and programming, chapter 12 numerical renormalization.

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Ebook Calculus: Early transcendentals (6th edition) presents the following content: Chapter 1 - functions and models, chapter 2 - limits and derivatives, chapter 3 - differentiaton rules, chapter 4 - applications of differentiation, chapter 5 – integrals, chapter 6 - applications of integration, chapter 7 - techniques of integration, chapter 8 - further applications of integration, chapter 9 - differential equations, chapter 10 - parametric equations and polar cords, chapter 11 - infinite sequences and series, chapter 12 - vectors and the geometry of space, chapter 13 - vector functions, ch...

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If you want to improve your understanding of calculus, then this book is for you. It can supplement standard texts at the high-school senior, trade-school, and college undergraduate levels. It can also serve as a self-teaching or home-schooling supplement. Prerequisites include intermediate algebra, geometry, and trigonometry. It will help if you’ve had some precalculus (sometimes called “analysis”) as well. This book contains three major sections. Part 1 involves differentiation in one variable. Part 2 is devoted to integration in one variable.

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We propose to write a text on ordinary differential equations that will be meaningful, accessible, and engaging for a student with a basic grounding in calculus (for example, the student who has studied Calculus Demystified by this author will be more than ready for Differential Equations Demystified). There will be many applications, many graphics, a plethora of worked examples, and hundreds of stimulating exercises. The student who completes this book will be ready to go on to advanced analytical work in applied mathematics, engineering, and other fields of mathematical science.

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This fifth edition of ‘Higher Engineering Mathematics’ covers essential mathematical material suitable for students studying Degrees, Foundation Degrees, Higher National Certificate and Diploma courses in Engineering disciplines. In this edition the material has been re-ordered into the following twelve convenient categories: number and algebra, geometry and trigonometry, graphs, vector geometry, complex numbers, matrices and determinants, differential calculus, integral calculus, differential equations, statistics and probability, Laplace transforms and Fourier series.

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Part 1 book "Electricity and magnetism for mathematicians - A guided path from Maxwell’s equations to Yang-Mills" includes content: A brief history, Maxwell's equations, electromagnetic waves, special relativity, mechanics and Maxwell's equations; mechanics, lagrangians, and the calculus of variations; potentials; lagrangians and electromagnetic forces; differential forms; the hodge operator.

144p dianmotminh01 20-05-2024 7 3   Download

Part 1 of ebook "Numerical methods using MATLAB® (Third edition)" provides readers with contents including: Chapter 1 - An introduction to Matlab®; Chapter 2 - Linear equations and eigensystems; Chapter 3 - Solution of nonlinear equations; Chapter 4 - Differentiation and integration; Chapter 5 - Solution of differential equations;...

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Part 2 book "Introduction to numerical programming" includes contents: Eigenvalue problems, modeling of tabulated functions, integration of functions, monte carlo method, ordinary differential equations, partial differential equations.

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The paper "Continuous Element formulations for free vibration of FGM annular plates resting on elastic foundation" introduces an efficient approach for analyzing the vibration of functionally graded annular plates resting on elastic foundation. The Continuous Element for annular plates on Winkler-Pasternak foundation is constructed based on the analytical closed form solution of the differential equations of the investigated structure.

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A new continuous element (CE) formulation has been presented in this paper for the vibration analysis of FGM joined conical-cylindrical shells surrounded by Pasternak elastic foundations. The differential equations of FGM conical shells are used including FGM cylindrical shells as a special case. Governing equations are obtained using thick shell theory of Reissner, taking into account the shear deflection effects.

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This study presents the continuous element formulation for analyzing the dynamic behavior of ring-stiffened cylindrical shells made of FGM material. Based on the solutions of the shell differential equations, the dynamic stiffness matrix is calculated. A procedure to assembly cylindrical and annular shells is introduced in order to compute the natural vibrational frequencies of FGM ring-stiffened cylindrical shells.

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In this paper, we consider a boundary value problem for a fully fourth-order nonlinear functional differential equation which contains all lower derivatives of proportional delay arguments. By the reduction of the problem to operator equation for the right-hand side nonlinear function, we establish the existence and uniqueness of the solution and construct iterative methods on both continuous and discrete levels for solving it.

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In this work, the free vibration analysis of Timoshenko microbeams made of the Functionally Graded Material (FGM) on the Winkler–Paternak elastic foundation based on the Modified Coupled Stress Theory (MCST) is investigated. Material characteristics of the beam vary throughout the thickness according to the power distribution and are estimated though Mori–Tanaka, Hashin–Shtrikman and Voigt homogenization techniques.

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This paper investigates the bending behavior of beams by considering: (1) the EulerBernoulli beam model, (2) Mindlin’s strain gradient elasticity theory, (3) the von Kármán strain assumptions. The principle of virtual work is used to derive the non-linear governing equations in form of a six-order partial differential equation.

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Part 1 book "Thomas’ calculus - Early transcendentals" includes content: Functions, limits and continuity, derivatives, applications of derivatives, integrals, applications of definite integrals, integrals and transcendental functions, techniques of integration, first order differential equations.

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Part 2 book "A step by step approach to the modeling of chemical engineering processes" includes content: Solving an algebraic equations system, solving an ordinary differential equations system, solving a partial differential equations system.

83p muasambanhan10 11-04-2024 4 1   Download

Ebook "Digital simulation in electrochemistry (Fourth edition)" explains how the partial differential equations (pdes) in electroanalytical chemistry can be solved numerically. It guides the reader through the topic in a very didactic way, by first introducing and discussing the basic equations along with some model systems as test cases systematically. Then it outlines basic numerical approximations for derivatives and techniques for the numerical solution of ordinary differential equations. Finally, more complicated methods for approaching the pdes are derived.

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