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Differential Equations Problem Solver

Author: David R. Arterburn
Publisher: Research & Education Assoc.
ISBN: 0738668303
Size: 49.62 MB
Format: PDF, ePub, Docs
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Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies. Here in this highly useful reference is the finest overview of differential equations currently available, with hundreds of differential equations problems that cover everything from integrating factors and Bernoulli's equation to variation of parameters and undetermined coefficients. Each problem is clearly solved with step-by-step detailed solutions. DETAILS - The PROBLEM SOLVERS are unique - the ultimate in study guides. - They are ideal for helping students cope with the toughest subjects. - They greatly simplify study and learning tasks. - They enable students to come to grips with difficult problems by showing them the way, step-by-step, toward solving problems. As a result, they save hours of frustration and time spent on groping for answers and understanding. - They cover material ranging from the elementary to the advanced in each subject. - They work exceptionally well with any text in its field. - PROBLEM SOLVERS are available in 41 subjects. - Each PROBLEM SOLVER is prepared by supremely knowledgeable experts. - Most are over 1000 pages. - PROBLEM SOLVERS are not meant to be read cover to cover. They offer whatever may be needed at a given time. An excellent index helps to locate specific problems rapidly. TABLE OF CONTENTS Introduction Units Conversion Factors Chapter 1: Classification of Differential Equations Chapter 2: Separable Differential Equations Variable Transformation u = ax + by Variable Transformation y = vx Chapter 3: Exact Differential Equations Definitions and Examples Solving Exact Differential Equations Making a Non-exact Differential Equation Exact Chapter 4: Homogenous Differential Equations Identifying Homogenous Differential Equations Solving Homogenous Differential Equations by Substitution and Separation Chapter 5: Integrating Factors General Theory of Integrating Factors Equations of Form dy/dx + p(x)y = q(x) Grouping to Simplify Solutions Solution Directly From M(x, y)dx + N(x, y)dy = 0 Chapter 6: Method of Grouping Chapter 7: Linear Differential Equations Integrating Factors Bernoulli's Equation Chapter 8: Riccati's Equation Chapter 9: Clairaut's Equation Geometrical Construction Problems Chapter 10: Orthogonal Trajectories Elimination of Constants Orthogonal Trajectories Differential Equations Derived from Considerations of Analytical Geometry Chapter 11: First Order Differential Equations: Applications I Gravity and Projectile Hooke's Law, Springs Angular Motion Over-hanging Chain Chapter 12: First Order Differential Equations: Applications II Absorption of Radiation Population Dynamics Radioactive Decay Temperature Flow from an Orifice Mixing Solutions Chemical Reactions Economics One-Dimensional Neutron Transport Suspended Cable Chapter 13: The Wronskian and Linear Independence Determining Linear Independence of a Set of Functions Using the Wronskian in Solving Differential Equations Chapter 14: Second Order Homogenous Differential Equations with Constant Coefficients Roots of Auxiliary Equations: Real Roots of Auxiliary: Complex Initial Value Higher Order Differential Equations Chapter 15: Method of Undetermined Coefficients First Order Differential Equations Second Order Differential Equations Higher Order Differential Equations Chapter 16: Variation of Parameters Solution of Second Order Constant Coefficient Differential Equations Solution of Higher Order Constant Coefficient Differential Equations Solution of Variable Coefficient Differential Equations Chapter 17: Reduction of Order Chapter 18: Differential Operators Algebra of Differential Operators Properties of Differential Operators Simple Solutions Solutions Using Exponential Shift Solutions by Inverse Method Solution of a System of Differential Equations Chapter 19: Change of Variables Equation of Type (ax + by + c)dx + (dx + ey + f)dy = 0 Substitutions for Euler Type Differential Equations Trigonometric Substitutions Other Useful Substitutions Chapter 20: Adjoint of a Differential Equation Chapter 21: Applications of Second Order Differential Equations Harmonic Oscillator Simple Pendulum Coupled Oscillator and Pendulum Motion Beam and Cantilever Hanging Cable Rotational Motion Chemistry Population Dynamics Curve of Pursuit Chapter 22: Electrical Circuits Simple Circuits RL Circuits RC Circuits LC Circuits Complex Networks Chapter 23: Power Series Some Simple Power Series Solutions May Be Expanded Finding Power Series Solutions Power Series Solutions for Initial Value Problems Chapter 24: Power Series about an Ordinary Point Initial Value Problems Special Equations Taylor Series Solution to Initial Value Problem Chapter 25: Power Series about a Singular Point Singular Points and Indicial Equations Frobenius Method Modified Frobenius Method Indicial Roots: Equal Special Equations Chapter 26: Laplace Transforms Exponential Order Simple Functions Combination of Simple Functions Definite Integral Step Functions Periodic Functions Chapter 27: Inverse Laplace Transforms Partial Fractions Completing the Square Infinite Series Convolution Chapter 28: Solving Initial Value Problems by Laplace Transforms Solutions of First Order Initial Value Problems Solutions of Second Order Initial Value Problems Solutions of Initial Value Problems Involving Step Functions Solutions of Third Order Initial Value Problems Solutions of Systems of Simultaneous Equations Chapter 29: Second Order Boundary Value Problems Eigenfunctions and Eigenvalues of Boundary Value Problem Chapter 30: Sturm-Liouville Problems Definitions Some Simple Solutions Properties of Sturm-Liouville Equations Orthonormal Sets of Functions Properties of the Eigenvalues Properties of the Eigenfunctions Eigenfunction Expansion of Functions Chapter 31: Fourier Series Properties of the Fourier Series Fourier Series Exppansions Sine and Cosine Expansions Chapter 32: Bessel and Gamma Functions Properties of the Gamma Function Solutions to Bessel's Equation Chapter 33: Systems of Ordinary Differential Equations Converting Systems of Ordinary Differential Equations Solutions of Ordinary Differential Equation Systems Matrix Mathematics Finding Eigenvalues of a Matrix Converting Systems of Ordinary Differential Equations into Matrix Form Calculating the Exponential of a Matrix Solving Systems by Matrix Methods Chapter 34: Simultaneous Linear Differential Equations Definitions Solutions of 2 x 2 Systems Checking Solution and Linear Independence in Matrix Form Solution of 3 x 3 Homogenous System Solution of Non-homogenous System Chapter 35: Method of Perturbation Chapter 36: Non-Linear Differential Equations Reduction of Order Dependent Variable Missing Independent Variable Missing Dependent and Independent Variable Missing Factorization Critical Points Linear Systems Non-Linear Systems Liapunov Function Analysis Second Order Equation Perturbation Series Chapter 37: Approximation Techniques Graphical Methods Successive Approximation Euler's Method Modified Euler's Method Chapter 38: Partial Differential Equations Solutions of General Partial Differential Equations Heat Equation Laplace's Equation One-Dimensional Wave Equation Chapter 39: Calculus of Variations Index WHAT THIS BOOK IS FOR Students have generally found differential equations a difficult subject to understand and learn. Despite the pub.

The Differential Equations Problem Solver

Author: Research and Education Association
Publisher: Research & Education Assoc.
ISBN: 9780878915132
Size: 63.79 MB
Format: PDF, Kindle
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This book is intended to help students in differential equations to find their way through the complex material which involves a wide variety of concepts. Topic by topic, and problem by problem, the book provides detailed illustrations of solution methods which are usually not apparent to students.

Numerical Solutions For Partial Differential Equations

Author: Victor Grigor'e Ganzha
Publisher: CRC Press
ISBN: 1351427504
Size: 59.34 MB
Format: PDF, ePub
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Partial differential equations (PDEs) play an important role in the natural sciences and technology, because they describe the way systems (natural and other) behave. The inherent suitability of PDEs to characterizing the nature, motion, and evolution of systems, has led to their wide-ranging use in numerical models that are developed in order to analyze systems that are not otherwise easily studied. Numerical Solutions for Partial Differential Equations contains all the details necessary for the reader to understand the principles and applications of advanced numerical methods for solving PDEs. In addition, it shows how the modern computer system algebra Mathematica® can be used for the analytic investigation of such numerical properties as stability, approximation, and dispersion.

Solving Ordinary Differential Equations I

Author: Ernst Hairer
Publisher: Springer Science & Business Media
ISBN: 9783540566700
Size: 55.87 MB
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This book deals with methods for solving nonstiff ordinary differential equations. The first chapter describes the historical development of the classical theory, and the second chapter includes a modern treatment of Runge-Kutta and extrapolation methods. Chapter three begins with the classical theory of multistep methods, and concludes with the theory of general linear methods. The reader will benefit from many illustrations, a historical and didactic approach, and computer programs which help him/her learn to solve all kinds of ordinary differential equations. This new edition has been rewritten and new material has been included.

Algorithmic Lie Theory For Solving Ordinary Differential Equations

Author: Fritz Schwarz
Publisher: CRC Press
ISBN: 9781584888901
Size: 39.97 MB
Format: PDF, Mobi
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Despite the fact that Sophus Lie's theory was virtually the only systematic method for solving nonlinear ordinary differential equations (ODEs), it was rarely used for practical problems because of the massive amount of calculations involved. But with the advent of computer algebra programs, it became possible to apply Lie theory to concrete problems. Taking this approach, Algorithmic Lie Theory for Solving Ordinary Differential Equations serves as a valuable introduction for solving differential equations using Lie's theory and related results. After an introductory chapter, the book provides the mathematical foundation of linear differential equations, covering Loewy's theory and Janet bases. The following chapters present results from the theory of continuous groups of a 2-D manifold and discuss the close relation between Lie's symmetry analysis and the equivalence problem. The core chapters of the book identify the symmetry classes to which quasilinear equations of order two or three belong and transform these equations to canonical form. The final chapters solve the canonical equations and produce the general solutions whenever possible as well as provide concluding remarks. The appendices contain solutions to selected exercises, useful formulae, properties of ideals of monomials, Loewy decompositions, symmetries for equations from Kamke's collection, and a brief description of the software system ALLTYPES for solving concrete algebraic problems.

Differential Equations

Author: P. Mohana Shankar
Publisher: CRC Press
ISBN: 1351385739
Size: 29.46 MB
Format: PDF, ePub
View: 1975
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The book takes a problem solving approach in presenting the topic of differential equations. It provides a complete narrative of differential equations showing the theoretical aspects of the problem (the how's and why's), various steps in arriving at solutions, multiple ways of obtaining solutions and comparison of solutions. A large number of comprehensive examples are provided to show depth and breadth and these are presented in a manner very similar to the instructor's class room work. The examples contain solutions from Laplace transform based approaches alongside the solutions based on eigenvalues and eigenvectors and characteristic equations. The verification of the results in examples is additionally provided using Runge-Kutta offering a holistic means to interpret and understand the solutions. Wherever necessary, phase plots are provided to support the analytical results. All the examples are worked out using MATLAB® taking advantage of the Symbolic Toolbox and LaTex for displaying equations. With the subject matter being presented through these descriptive examples, students will find it easy to grasp the concepts. A large number of exercises have been provided in each chapter to allow instructors and students to explore various aspects of differential equations.

Ordinary Differential Equations

Author: David N. Cheban
Publisher:
ISBN: 9789814335959
Size: 25.68 MB
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This is a textbook on ordinary differential equations in their applied aspects and it caters to students with a physico-mathematical profile, as well as those in informatics and cybernetics. This book also caters to educators who study the pedagogy of teaching mathematics, especially on differential equations. Containing over 400 solved examples and problems, its main objective is to promote a deep understanding on the theory, develop concrete mathematical thinking of students, nurture the skills in finding solutions to the problems, and understand their physical essence. This book completely covers all parts of the course on ordinary differential equations taught at universities: first-order differential equations, high-order differential equations, systems of differential equations, stability theory and so on.

Problems In Differential Equations

Author: J. L. Brenner
Publisher: Courier Corporation
ISBN: 0486782824
Size: 29.88 MB
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More than 900 problems and answers explore applications of differential equations to vibrations, electrical engineering, mechanics, and physics. Problem types include both routine and nonroutine, and stars indicate advanced problems. 1963 edition.