[PDF] Differential Equations With Applications and Historical Notes Text Book Free Download, Differential Equations With Applications and Historical Notes by George F. Simmons Free Engineering Book Download

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Differential Equations With Applications and Historical Notes Details Book Details
Book Name Differential Equations With Applications and Historical Notes
Author George F. Simmons
Publisher George F. Simmons
File Type PDF
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Differential Equations With Applications and Historical Notes : Table of Contents

The Nature of Differential Equations Separable Equations
General Remarks on Solutions
Families of Curves Orthogonal Trajectories
Growth Decay Chemical Reactions and Mixing
Falling Bodies and Other Motion Problems
The Brachistochrone Fermat and the Bernoullis
The Normal Distribution Curve or Bell Curve and
Its Differential Equation
First Order Equations
Homogeneous Equations
Exact Equations
Integrating Factors
Linear Equations
Reduction of Order
The Hanging Chain Pursuit Curves
Simple Electric Circuits
Second Order Linear Equations
The General Solution of the Homogeneous Equation
The Use of a Known Solution to find Another
The Homogeneous Equation with Constant Coefficients
The Method of Undetermined Coefficients
The Method of Variation of Parameters
Vibrations in Mechanical and Electrical Systems
Newton s Law of Gravitation and The Motion of the Planets
Higher Order Linear Equations Coupled
Harmonic Oscillators
Operator Methods for Finding Particular Solutions
Qualitative Properties of Solutions
Oscillations and the Sturm Separation Theorem
The Sturm Comparison Theorem
Power Series Solutions and Special Functions
Introduction A Review of Power Series
Series Solutions of First Order Equations
Second Order Linear Equations Ordinary Points
Regular Singular Points
Regular Singular Points Continued
Gauss s Hypergeometric Equation
The Point at Infinity
Fourier Series and Orthogonal Functions
The Fourier Coefficients
The Problem of Convergence
Even and Odd Functions Cosine and Sine Series
Extension to Arbitrary Intervals
Orthogonal Functions
The Mean Convergence of Fourier Series
Partial Differential Equations and Boundary Value Problems
Introduction Historical Remarks
Eigenvalues Eigenfunctions and the Vibrating String
The Heat Equation
The Dirichlet Problem for a Circle Poisson s Integral
Sturm Liouville Problems
Some Special Functions of Mathematical Physics
Legendre Polynomials
Properties of Legendre Polynomials
Bessel Functions The Gamma Function
Properties of Bessel Functions
Laplace Transforms
A Few Remarks on the Theory
Applications to Differential Equations
Derivatives and Integrals of Laplace Transforms
Convolutions and Abel s Mechanical Problem
More about Convolutions The Unit Step and
Impulse Functions
Systems of First Order Equations
General Remarks on Systems
Linear Systems
Homogeneous Linear Systems with Constant Coefficients
Nonlinear Systems Volterra s Prey Predator Equations
Nonlinear Equations
Autonomous Systems The Phase Plane and Its Phenomena
Types of Critical Points Stability
Critical Points and Stability for Linear Systems
Stability By Liapunov s Direct Method
Simple Critical Points of Nonlinear Systems
Nonlinear Mechanics Conservative Systems
Periodic Solutions The Poincaré Bendixson Theorem
The Calculus of Variations
Introduction Some Typical Problems of the Subject
Euler s Differential Equation for an Extremal
Isoperimetric Problems
The Existence and Uniqueness of Solutions
The Method of Successive Approximations
Picard s Theorem
Systems The Second Order Linear Equation
Numerical Methods
The Method of Euler Errors
An Improvement to Euler
Higher Order Methods Systems

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