Differential equations :
Borres, Maria Catherine
Differential equations : theory and applications / Maria Catherine Borres. - ix, 411 pages : illustrations ; 24 cm
Includes bibliographical references and index.
Cover; Half Title Page; Title Page; Copyright Page; About the Author; Table of Contents; Preface; Chapter 1 Basic Concepts of Differential Equations; 1.1. Introduction; 1.2. The Bernoulli Equation; 1.3. Differential Equations of Higher Order; 1.4. The Wronskian; Chapter 2 Fundamental Concepts of Partial Differential Equations; 2.1. Introduction; 2.2. Classification of Second Order PDE; 2.3. Summary and Discussion; 2.4. Classification of Second Order PDE; Chapter 3 Application of Differential Equations In Mechanics; 3.1. Introduction; 3.2. Projectile Motion; 3.3. Summary and Discussion Chapter 4 Elliptic Differential Equation4.1. Introduction; 4.2. Boundary Value Problem (BVPs); 4.3. Some Important Mathematical Tools; 4.4. Properties Of Harmonic Functions; 4.5. Separation Of Variables; 4.6. Dirichlet Problem For A Rectangle; 4.7. The Neumann Problem For A Rectangle; 4.8. Interior Dirichlet Problem For A Circle; 4.9. Exterior Dirichlet Problem For A Circle; 4.10. Interior Neumann Problem For A Circle; 4.11. Solution Of Laplace Equation In Cylindrical Coordinates; 4.12. Solution Of Laplace Equation In Spherical Coordinates; 4.13. Miscellaneous Example 4.14. Summary And DiscussionsChapter 5 Hyperbolic Differential Equation; 5.1 Introduction; 5.2. Solution Of One-Dimensional Wave Equation by Canonical Reduction; 5.3. The Initial Value Problem; D'alembert's Solution; 5.4. Summary And Discussion; Chapter 6 Parabolic Differential Equations; 6.1. Introduction; 6.2. Boundary Conditions; 6.3. Elementary Solutions Of The Diffusion Equation; 6.4. Dirac Delta Function; 6.5. Separation Of Variables Method; 6.6. Maximum-Minimum Principle and Consequences; 6.7. Miscellaneous Example; 6.8. Boundary Conditions; Chapter 7 Laplace Transform Methods 7.1. Introduction7.2. Transform Of Some Elementary Functions; 7.3. Properties Of Laplace Transform; 7.4. Transform Of A Periodic Function; 7.5. Transform Of Error Function; 7.6. Transform Of Bessel's Function; 7.7. Transform Of Dirac Delta Function; 7.8. Convolution Theorem (Faltung Theorem); Chapter 8 Green's Function; 8.1. Introduction; 8.2. The Eigenfunction Method; 8.3. Summary and Discussion; References; Index
Examines several aspects of differential equations, including an extensive explanation of higher order differential equations. The book includes applications of differential equations in mechanics and different types of differential equations, and provides the reader with a clear understanding of theory and application of differential equations.
College of Engineering and Computer Studies Bachelor of Science in Civil Engineering College of Engineering and Computer Studies Bachelor of Science in Computer Engineering College of Engineering and Computer Studies Bachelor of Science in Electronics Engineering
Text in English
9781773614038 (hbk)
Differential equations.
515.35 B64 2019
Differential equations : theory and applications / Maria Catherine Borres. - ix, 411 pages : illustrations ; 24 cm
Includes bibliographical references and index.
Cover; Half Title Page; Title Page; Copyright Page; About the Author; Table of Contents; Preface; Chapter 1 Basic Concepts of Differential Equations; 1.1. Introduction; 1.2. The Bernoulli Equation; 1.3. Differential Equations of Higher Order; 1.4. The Wronskian; Chapter 2 Fundamental Concepts of Partial Differential Equations; 2.1. Introduction; 2.2. Classification of Second Order PDE; 2.3. Summary and Discussion; 2.4. Classification of Second Order PDE; Chapter 3 Application of Differential Equations In Mechanics; 3.1. Introduction; 3.2. Projectile Motion; 3.3. Summary and Discussion Chapter 4 Elliptic Differential Equation4.1. Introduction; 4.2. Boundary Value Problem (BVPs); 4.3. Some Important Mathematical Tools; 4.4. Properties Of Harmonic Functions; 4.5. Separation Of Variables; 4.6. Dirichlet Problem For A Rectangle; 4.7. The Neumann Problem For A Rectangle; 4.8. Interior Dirichlet Problem For A Circle; 4.9. Exterior Dirichlet Problem For A Circle; 4.10. Interior Neumann Problem For A Circle; 4.11. Solution Of Laplace Equation In Cylindrical Coordinates; 4.12. Solution Of Laplace Equation In Spherical Coordinates; 4.13. Miscellaneous Example 4.14. Summary And DiscussionsChapter 5 Hyperbolic Differential Equation; 5.1 Introduction; 5.2. Solution Of One-Dimensional Wave Equation by Canonical Reduction; 5.3. The Initial Value Problem; D'alembert's Solution; 5.4. Summary And Discussion; Chapter 6 Parabolic Differential Equations; 6.1. Introduction; 6.2. Boundary Conditions; 6.3. Elementary Solutions Of The Diffusion Equation; 6.4. Dirac Delta Function; 6.5. Separation Of Variables Method; 6.6. Maximum-Minimum Principle and Consequences; 6.7. Miscellaneous Example; 6.8. Boundary Conditions; Chapter 7 Laplace Transform Methods 7.1. Introduction7.2. Transform Of Some Elementary Functions; 7.3. Properties Of Laplace Transform; 7.4. Transform Of A Periodic Function; 7.5. Transform Of Error Function; 7.6. Transform Of Bessel's Function; 7.7. Transform Of Dirac Delta Function; 7.8. Convolution Theorem (Faltung Theorem); Chapter 8 Green's Function; 8.1. Introduction; 8.2. The Eigenfunction Method; 8.3. Summary and Discussion; References; Index
Examines several aspects of differential equations, including an extensive explanation of higher order differential equations. The book includes applications of differential equations in mechanics and different types of differential equations, and provides the reader with a clear understanding of theory and application of differential equations.
College of Engineering and Computer Studies Bachelor of Science in Civil Engineering College of Engineering and Computer Studies Bachelor of Science in Computer Engineering College of Engineering and Computer Studies Bachelor of Science in Electronics Engineering
Text in English
9781773614038 (hbk)
Differential equations.
515.35 B64 2019
