Lectures Problems And Solutions For Ordinary Differential Equations 2nd edition by Yuefan Deng – Ebook PDF Instant Download/Delivery: 9813226137, 978-9813226135
Full download Lectures Problems And Solutions For Ordinary Differential Equations 2nd edition after payment
Product details:
ISBN 10: 9813226137
ISBN 13: 978-9813226135
Author: Yuefan Deng
This unique book on ordinary differential equations addresses practical issues of composing and solving differential equations by demonstrating the detailed solutions of more than 1,000 examples. The initial draft was used to teach more than 10,000 advanced undergraduate students in engineering, physics, economics, as well as applied mathematics. It is a good source for students to learn problem-solving skills and for educators to find problems for homework assignments and tests. The 2nd edition, with at least 100 more examples and five added subsections, has been restructured to flow more pedagogically.
Readership: Undergraduate students and entry level graduate students in science and engineering who need to solve and compose ordinary differential equations.
Lectures Problems And Solutions For Ordinary Differential Equations 2nd Table of contents:
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 MODEL
2.4.1 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 DEs
4.1 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 Property
5.2.5 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 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 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
5.4 The Convolution of Two Functions
5.5 Applications
APPENDIX B LAPLACE TRANSFORMS
SELECTED LAPLACE TRANSFORMS
SELECTED PROPERTIES OF LAPLACE TRANSFORMS
APPENDIX C BASIC FORMULAS
APPENDIX D ABBREVIATIONS
REFERENCES
INDEX
People also search for Lectures Problems And Solutions For Ordinary Differential Equations 2nd :
lectures problems and solutions for ordinary differential equations pdf
lectures on quantum mechanics with problems exercises and solutions
problems in the classroom and solutions
lectures problems
challenging lectures