Download PDF For Free: Differential Equations With Applications and Historical Notes Third Edition by George F. Simmons
Preface to Differential Equations eBook
- 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