Yuefan, Deng. creator text Electronic books. Electronic books. si Singapore, SINGAPORE World Scientific Publishing Co Pte Ltd 2017 monographic eng

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1 online resource (572) PREFACE; CHAPTER 1 FIRST-ORDER DIFFERENTIAL EQUATIONS; 1.1 DEFINITION OF DIFFERENTIAL EQUATIONS; 1.2 SLOPE FIELDS AND SOLUTION CURVES; 1.3 SEPARATION OF VARIABLES; 1.4 FIRST-ORDER LINEAR DES; 1.5 THE SUBSTITUTION METHODS; 1.5.1 Polynomial Substitution; 1.5.2 Homogeneous DEs; 1.5.3 Bernoulli DEs; 1.6 RICCATI DES; 1.7 THE EXACT DES; 1.8 SUMMARY; CHAPTER 2 MATHEMATICAL MODELS; 2.1 Newton's Law of Cooling; 2.2 Torricelli's Law for Draining; 2.3 The Population Model; 2.3.1 Introduction; 2.3.2 General Population Equation; 2.3.3 The Logistic Equation; 2.3.4 Doomsday vs. Extinction. 2.4 Acceleration-Velocity Model2.4.1 Newton's Laws of Motion; 2.4.2 Velocity and Acceleration Models; 2.4.3 Air Resistance Model; 2.4.4 Gravitational Acceleration; 2.5 Windy Day Plane Landing; 2.6 A Swimmer's Problem; 2.7 River Ferryboat-Docking Problem; 2.8 Equation for Compound Interest; CHAPTER 3 LINEAR DEs OF HIGHER ORDER; 3.1 Classifications of Linear DEs; 3.2 Linear Independence; 3.3 Homogeneous DEs; 3.3.1 DEs with Constant Coefficients; 3.3.2 DEs with Variable Coefficients; 3.4 Inhomogeneous Linear DEs; 3.4.1 Method of Undetermined Coefficients; 3.4.2 Variation of Parameters. CHAPTER 4 SYSTEMS OF LINEAR DEs4.1 Basics of System of DEs; 4.2 First-Order Systems and Applications; 4.2.1 One Block and One Spring; 4.2.2 Two Blocks and Two Springs; 4.2.3 Kirchhoff Circuit Laws; 4.3 The Substitution Method; 4.4 The Operator Method; 4.5 The Eigen-Analysis Method; 4.6 Examples of Systems of DEs; 4.6.1 Predator-prey DEs; 4.6.2 Cascade of Tanks; CHAPTER 5 LAPLACE TRANSFORMS; 5.1 Laplace Transforms; 5.2 Properties of Laplace Transforms; 5.2.1 Laplace Transforms for Polynomials; 5.2.2 The Translator Property; 5.2.3 Transforms of Step and Delta Functions. 5.2.4 The t-multiplication Property5.2.5 Periodic Functions; 5.2.6 Differentiation and Integration Property; 5.3 Inverse Laplace Transforms; 5.4 The Convolution of Two Functions; 5.5 Applications; APPENDIX A SOLUTIONS TO PROBLEMS; Chapter 1 First-Order DEs; 1.1 Definition of DEs; 1.2 Slope Fields and Solution Curves; 1.3 Separation of Variables; 1.4 First-Order Linear DEs; 1.5 Substitution Methods; 1.6 Riccati DEs; 1.7 The Exact DEs; Chapter 2 Mathematical Models; 2.1 Newton's Law of Cooling; 2.2 Torricelli's Law for Draining; 2.3 Population Model; 2.4 Acceleration-Velocity Model. 2.5 Windy Day Plane Landing2.6 A Swimmer's Problem; 2.7 River Ferryboat-Docking Problem; 2.8 Equation for Compound Interest; Chapter 3 Linear DEs of Higher Order; 3.1 Classification of Linear DEs; 3.2 Linear Independence; 3.3 Homogeneous DEs; 3.4 Inhomogeneous Linear DEs; Chapter 4 Systems of Linear DEs; 4.1 Basics of System of DEs; 4.2 First-Order Systems and Applications; 4.3 Substitution Method; 4.4 The Operator Method; 4.5 The Eigen-Analysis Method; 4.6 Examples of Systems; Chapter 5 Laplace Transforms; 5.2 Properties of Laplace Transforms; 5.3 Inverse Laplace Transforms. Includes bibliographical references and index. Differential equations Differential equations, Linear Laplace transformation Differential equations Differential equations, Linear Laplace transformation MATHEMATICS Calculus MATHEMATICS Mathematical Analysis QA372 .D42 2018 515/.352 Deng, Yuefan. Singapore ; Hackensack, NJ : World Scientific Publishing Co. Pte. Ltd., 2018 Second edition. (DLC) 2017029777 (OCoLC)1006521906 9813226145 9789813226142 1033968 MIL http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=1589397 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=1589397 IDEBK 170929 20210825161917.0 on1003202086 eng