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

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Candidates can get Best Partial Differential Equations for Scientists and Engineers Books 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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