# Partial Differential Equations for Scientists and Engineers Book 2018 Best Study Materials

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## Description

### Candidates can get Best Partial Differential Equations for Scientists and EngineersBooks 2018 also a Top List of Main Study Materials for 2017-2018 entrance exam in India.

• Partial Differential Equations for Scientists and Engineers: 9 (Dover Books on Mathematics)
by Stanley J. Farlow

### Syllabus:-

• Chapter I Introduction (2 – 3 weeks for Chapters 1 and 2)
• 1.1Some Basic Mathematical Models; Direction Fields
• 1.2 Solutions of Some Differential Equations

1.3 Classification of Differential Equations

• 1.4 Historical Remarks
• Chapter 2 First Order Differential Equations(2 – 3 weeks for Chapters 1 and 2)
• 2.1 Linear Equations with Variable Coefficients
• 2.2 Separable Equations
• 2.3 Modeling with First Order Equations  (optional)
• 2.4 Differences Between Linear and Nonlinear Equations
• 2.5 Autonomous Equations and Population Dynamics  (optional)
• 2.6 Exact Equations and Integrating Factors
• 2.7 Numerical Approximations: Euler’s Method   (optional unless you do Ch 8)
• 2.8 The Existence and Uniqueness Theorem
• 2.9 First Order Difference Equations 115 (optional unless you do stability)
• Chapter 3 Second Order Linear Equations (2 – 3 weeks)
• 3.1 Homogeneous Equations with Constant Coefficients
• 3.2 Fundamental Solutions of Linear Homogeneous Equations
• 3.3 Complex Roots of the Characteristic Equation
• 3.4   Repeated Roots; Reduction of Order
• 3.5   Nonhomogeneous Equations; Method of Undetermined Coefficients
• 3.6   Variation of Parameters   (optional)
• 3.7 Mechanical and Electrical Vibrations   (optional)
• 3.8 Forced Vibrations   (optional)
• Chapter 4 Higher Order Linear Equations (cover quickly)
• 4.1 General Theory of nth Order Linear Equations
• 4.2 Homogeneous Equations with Constant Coefficients
• 4.3 The Method of Undertermined Coefficients  (optional)
• 4.4 The Method of Variation of Parameters
• Chapter 5 Series Solutions of Second Order Linear Equations (2 weeks)
• 5.1 Review of Power Series  (optional)
• 5.2 Series Solutions near an Ordinary Point, Part I
• 5.3 Series Solutions near an Ordinary Point, Part II
• 5.4 Euler Equations, Regular Singular Points
• 5.5 Series Solutions near a Regular Singular Point, Part I
• 5.6 Series Solutions near a Regular Singular Point, Part II
• Chapter 6 The Laplace Transform (1 week: Important for some Engineers)
• 6.1 Definition of the Laplace Transform
• 6.2 Solution of Initial Value Problems
• 6.3 Step Functions
• 6.4 Differential Equations with Discontinuous Forcing Functions
• 6.5 Impulse Functions
• 6.6 The Convolution Integral
• Chapter 7 Systems of First Order Linear Equations (1 – 2 weeks)
• Chapter 8 Numerical Methods (1 week if covered) (optional)
• Chapter 9 Nonlinear Differential Equations and Stability
• Chapter 10 Partial Differential Equations and Fourier Series (3 weeks)
• 10.1 Two Point Boundary Value Problems
• 10.2 Fourier Series
• 10.3 The Fourier Convergence Theorem
• 10.4 Even and Odd Functions
• 10.5 Separation of Variables; Heat Conduction in a Rod
• 10.6 Other Heat Conduction Problems (optional)
• 10.7 The Wave Equation; Vibrations of an Elastic String
• 10.8 Laplace’s Equation (optional)
• Appendix A Derivation of the Heat Equation (optional)
• Appendix B Derivation of the Wave Equation (optional)

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