TY  - BOOK
AU  - Yuefan,Deng
TI  - Lectures
SN  - 9813226145
AV  - QA372 .D42 2018
U1  - 515/.352 23
PY  - 2017///
CY  - Singapore, SINGAPORE
PB  - World Scientific Publishing Co Pte Ltd
KW  - Differential equations
KW  - Differential equations, Linear
KW  - Laplace transformation
KW  - fast
KW  - MATHEMATICS
KW  - Calculus
KW  - bisacsh
KW  - Mathematical Analysis
KW  - Electronic books
N1  - Includes bibliographical references and index; 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
UR  - http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=1589397
ER  -