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4434Differential Equations
http://www.merlot.org/merlot/viewMaterial.htm?id=556384
״Here are my online notes for my differential equations course that I teach here at Lamar University. Despite the fact that these are my “class notes”, they should be accessible to anyone wanting to learn how to solve differential equations or needing a refresher on differential equations.I’ve tried to make these notes as self contained as possible and so all the information needed to read through them is either from a Calculus or Algebra class or contained in other sections of the notes.״ Data Structures
http://www.merlot.org/merlot/viewMaterial.htm?id=440381
This is a free, online textbook, so its content is continually being updated and refined. According to the authors, "This book is about the creation and analysis of efficient data structures. This book covers: the primitive node structure; asymptotic notation for mathematically discussing performance characteristics; built-in arrays; list structures built from either nodes or arrays; iterators as an abstract model of enumerating the items in a sequence; stacks and queues for computing with last-in/first-out and first-in/first-out orderings; binary and general tree structures for searching or representing hierarchical relationships; min and max heaps for representing ordering based on priorities; graph structures for representing more general relationships between data elements; hash tables for the efficient retrieval of strings and other objects; and finally trade-offs between the structures, and strategies for picking the most appropriate ones.Difference Equations to Differential Equations: An Introduction to Calculus
http://www.merlot.org/merlot/viewMaterial.htm?id=447287
This is a free, online textbook. According to Textbook Revolution, this is a "Thorough, relatively concise calculus text. Includes many examples, graphs, and problems.״Differential Equations
http://www.merlot.org/merlot/viewMaterial.htm?id=906101
'This module consisst of two units, namely Introduction to Ordinary differential equations and higher order differential equations respectively. In unit one both homogeneous and non-homogeneous ordinary differential equations are discussed and their solutions obtained with a variety of techniques.Some of these techniques include the variation of parameters, the method of undetermined coefficients and the inverse operators. In unit two series solutions of differential equations are discussed .Also discussed are partial differential equations and their solution by separation of variables. Other topics discussed are Laplace transforms, Fourier series, Fourier transforms and their applications.Outline: SyllabusUnit 1: Introduction to Ordinary Differential EquationsLevel 2. Priority A. Calculus 3 is prerequisite.First order differential equations and applications. Second order differential equations. Homogeneous equations with constant coefficients. Equations with variable coefficients. Non-homogeneous equations. Undetermined coefficients. Variations of parameters. Inverse differential operators.Unit 2: Higher Order Differential Equations and ApplicationsLevel 2. Priority B. Differential Equations 1 is prerequisite.Series solution of second order linear ordinary differential equations. Special functions. Methods of separation of variables applied to second order partial differential equations. Spherical harmonics. Laplace transform and applications. Fourier series, Fourier transform and applications'ELEMENTARY DIFFERENTIAL EQUATIONS
http://www.merlot.org/merlot/viewMaterial.htm?id=826909
This book is designed for students in science, engineering and mathematics who have completed calculus through partial differentiation.The Table of Contents for this book is as follows:Chapter 1 Introduction 11.1 Applications Leading to Differential Equations1.2 First Order Equations 51.3 Direction Fields for First Order Equations 16Chapter 2 First Order Equations 302.1 Linear First Order Equations 302.2 Separable Equations 452.3 Existence and Uniqueness of Solutions of Nonlinear Equations 552.4 Transformation of Nonlinear Equations into Separable Equations 632.5 Exact Equations 732.6 Integrating Factors 83Chapter 3 Numerical Methods3.1 Euler’s Method 963.2 The Improved Euler Method and Related Methods 1093.3 The Runge-Kutta Method 119Chapter 4 Applications of First Order Equations1em 1304.1 Growth and Decay 1304.2 Cooling and Mixing 1404.3 Elementary Mechanics 1514.4 Autonomous Second Order Equations 1624.5 Applications to Curves 179Chapter 5 Linear Second Order Equations5.1 Homogeneous Linear Equations 1945.2 Constant Coefﬁcient Homogeneous Equations 2105.3 Nonhomgeneous Linear Equations 2215.4 The Method of Undetermined Coefﬁcients I 229iv5.5 The Method of Undetermined Coefﬁcients II 2385.6 Reduction of Order 2485.7 Variation of Parameters 255Chapter 6 Applcations of Linear Second Order Equations 2686.1 Spring Problems I 2686.2 Spring Problems II 2796.3 The RLC Circuit 2916.4 Motion Under a Central Force 297Chapter 7 Series Solutions of Linear Second Order Equations7.1 Review of Power Series 3077.2 Series Solutions Near an Ordinary Point I 3207.3 Series Solutions Near an Ordinary Point II 3357.4 Regular Singular Points Euler Equations 3437.5 The Method of Frobenius I 3487.6 The Method of Frobenius II 3657.7 The Method of Frobenius III 379Chapter 8 Laplace Transforms8.1 Introduction to the Laplace Transform 3948.2 The Inverse Laplace Transform 4068.3 Solution of Initial Value Problems 4148.4 The Unit Step Function 4218.5 Constant Coefﬁcient Equations with Piecewise Continuous ForcingFunctions 4318.6 Convolution 4418.7 Constant Cofﬁcient Equations with Impulses 4538.8 A Brief Table of Laplace TransformsChapter 9 Linear Higher Order Equations9.1 Introduction to Linear Higher Order Equations 4669.2 Higher Order Constant Coefﬁcient Homogeneous Equations 4769.3 Undetermined Coefﬁcients for Higher Order Equations 4889.4 Variation of Parameters for Higher Order Equations 498Chapter 10 Linear Systems of Differential Equations10.1 Introduction to Systems of Differential Equations 50810.2 Linear Systems of Differential Equations 51610.3 Basic Theory of Homogeneous Linear Systems 52210.4 Constant Coefﬁcient Homogeneous Systems I 530vi Contents10.5 Constant Coefﬁcient Homogeneous Systems II 54310.6 Constant Coefﬁcient Homogeneous Systems II 55710.7 Variation of Parameters for Nonhomogeneous Linear Systems 570NOTE: This book meets the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute's Open Textbook Initiative. http://www.aimath.org/textbooks/ELEMENTARY DIFFERENTIAL EQUATIONS WITH BOUNDARY VALUE PROBLEMS
http://www.merlot.org/merlot/viewMaterial.htm?id=826885
This book is designed for students in science, engineering and mathematics who have completed calculus through partial differentiation.The Table of Contents follows:Chapter 1 Introduction 11.1 Applications Leading to Differential Equations1.2 First Order Equations 51.3 Direction Fields for First Order Equations 16Chapter 2 First Order Equations 302.1 Linear First Order Equations 302.2 Separable Equations 452.3 Existence and Uniqueness of Solutions of Nonlinear Equations 552.4 Transformation of Nonlinear Equations into Separable Equations 622.5 Exact Equations 732.6 Integrating Factors 82Chapter 3 Numerical Methods3.1 Euler’s Method 963.2 The Improved Euler Method and Related Methods 1093.3 The Runge-Kutta Method 119Chapter 4 Applications of First Order Equations1em 1304.1 Growth and Decay 1304.2 Cooling and Mixing 1404.3 Elementary Mechanics 1514.4 Autonomous Second Order Equations 1624.5 Applications to Curves 179Chapter 5 Linear Second Order Equations5.1 Homogeneous Linear Equations 1945.2 Constant Coefﬁcient Homogeneous Equations 2105.3 Nonhomgeneous Linear Equations 2215.4 The Method of Undetermined Coefﬁcients I 2295.5 The Method of Undetermined Coefﬁcients II 2385.6 Reduction of Order 2485.7 Variation of Parameters 255Chapter 6 Applcations of Linear Second Order Equations 2686.1 Spring Problems I 2686.2 Spring Problems II 2796.3 The RLC Circuit 2906.4 Motion Under a Central Force 296Chapter 7 Series Solutions of Linear Second Order Equations7.1 Review of Power Series 3067.2 Series Solutions Near an Ordinary Point I 3197.3 Series Solutions Near an Ordinary Point II 3347.4 Regular Singular Points Euler Equations 3427.5 The Method of Frobenius I 3477.6 The Method of Frobenius II 3647.7 The Method of Frobenius III 378Chapter 8 Laplace Transforms8.1 Introduction to the Laplace Transform 3938.2 The Inverse Laplace Transform 4058.3 Solution of Initial Value Problems 4138.4 The Unit Step Function 4198.5 Constant Coefﬁcient Equations with Piecewise Continuous ForcingFunctions 4308.6 Convolution 4408.7 Constant Cofﬁcient Equations with Impulses 4528.8 A Brief Table of Laplace TransformsChapter 9 Linear Higher Order Equations9.1 Introduction to Linear Higher Order Equations 4659.2 Higher Order Constant Coefﬁcient Homogeneous Equations 4759.3 Undetermined Coefﬁcients for Higher Order Equations 4879.4 Variation of Parameters for Higher Order Equations 497Chapter 10 Linear Systems of Differential Equations10.1 Introduction to Systems of Differential Equations 50710.2 Linear Systems of Differential Equations 51510.3 Basic Theory of Homogeneous Linear Systems 52110.4 Constant Coefﬁcient Homogeneous Systems I 529vi Contents10.5 Constant Coefﬁcient Homogeneous Systems II 54210.6 Constant Coefﬁcient Homogeneous Systems II 55610.7 Variation of Parameters for Nonhomogeneous Linear Systems 568Chapter 11 Boundary Value Problems and Fourier Expansions 58011.1 Eigenvalue Problems for y00 + λy = 0 58011.2 Fourier Series I 58611.3 Fourier Series II 603Chapter 12 Fourier Solutions of Partial Differential EquationsChapter 13 Boundary Value Problems for Second Order Linear Equations NOTE: This book meets the evaluation criteria set by the Editorial Board of the American Institute of Mathematics in connection with the Institute's Open Textbook Initiative. http://www.aimath.org/textbooks/Introduction to differential equations
http://www.merlot.org/merlot/viewMaterial.htm?id=447304
This is a free, online textbook which was written from lecture notes. It is available as a pdf file or can be purchased as a book from the University of Hong Kong.Introductory Finite Difference Methods for PDEs
http://www.merlot.org/merlot/viewMaterial.htm?id=513454
This is a free, online textbook offered by Bookboon.com. "This book presents finite difference methods for solving partial differential equations (PDEs) and also general concepts like stability, boundary conditions etc. Material is in order of increasing complexity (from elliptic PDEs to hyperbolic systems) with related theory included in appendices. Each chapter has written and computer exercises with web links to worked solutions, programs, A/V presentations and case studies. Emphasis is on the practical and students are encouraged to do numerical experiments. This book is intended for undergraduates who know Calculus and introductory programming.״Linear Complementarity, Linear and Nonlinear Programming
http://www.merlot.org/merlot/viewMaterial.htm?id=436885
״This book provides an in-depth and clear treatment of all the important practical, technical, computational, geometric, and mathematical aspects of the Linear Complementarity Problem, Quadratic Programming, and their various applications. It discusses clearly the various algorithms for solving the LCP, presents their efficient implementation for the computer, and discusses their computational complexity. It presents the practical applications of these algorithms and extensions of these algorithms to solve general nonlinear programming problems. Finally, it surveys new methods for solving linear programs, such as Khachiyan's and Karmarkar's.״״You can download each chapter in postscript format by clicking the link following each chapter in the table of contents. You can also download the compressed version of the entire book.״Monotone Operators in Banach Space andNonlinear Partial Differential Equations
http://www.merlot.org/merlot/viewMaterial.htm?id=448067
This is a free, online book originallly published in 1997. The chapters include the following:1. Linear Problems...an Introduction 2. Nonlinear Stationary Problems 3. Nonlinear Evolution Problems 4. Accretive Operators and Nonlinear Cauchy Problems.ISBN 0-8218-3193-3SURV/49.E