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Differential Equations I MATB44H3F

MathSchoolinternational.com contain houndreds of Free Math e-Books. Which cover almost all topics of mathematics. To see an extisive list of Differential Equation eBooks . We hope mathematician or person who’s interested in mathematics like these books.

Differential Equations I MATB44H3F . This is an other great mathematics book cover the following topics of Differential Equations.

  • 1. Introduction
    Preliminaries, Sample Application of Differential Equations

  • 2. First Order Ordinary Differential Equations
    Separable Equations, Exact Differential Equations, Integrating Factors, Linear First Order Equations, Substitutions (Bernoulli Equation, Homogeneous Equations, Substitution to Reduce Second Order Equations to First), Order

  • 3. Applications and Examples of First Order ode’s
    Orthogonal Trajectories, Exponential Growth and Decay, Population Growth, Predator-Prey Models, Newton’s Law of Cooling, Water Tanks, Motion of Objects Falling Under Gravity with Air Resistance, Escape Velocity, Planetary Motion, Particle Moving on a Curve

  • 4. Linear Differential Equations
    Homogeneous Linear Equations, Linear Differential Equations with Constant Coefficients, Nonhomogeneous Linear Equations

  • 5. Second Order Linear Equations
    Reduction of Order, Undetermined Coefficients, Shortcuts for Undetermined Coefficients, Variation of Parameters

  • 6. Applications of Second Order Differential Equations
    Motion of Object Hanging from a Spring, Electrical Circuits

  • 7. Higher Order Linear Differential Equations
    Undetermined Coefficients, Variation of Parameters, Substitutions: Euler’s Equation

  • 8. Power Series Solutions to Linear Differential Equations
    Introduction, Background Knowledge Concerning Power Series, Analytic Equations, Power Series Solutions: Levels of Success, Level 1: Finding a finite number of coefficients, Level 2: Finding the recursion relation, Solutions Near a Singular Point, Functions Defined via Differential Equations (Chebyshev Equation, Legendre Equation, Airy Equation, Laguerre’s Equation, Bessel Equation)

  • 9. Linear Systems
    Preliminaries, Computing e^T, The 2 × 2 Case in Detail, The Non-Homogeneous Case, Phase Portraits, Real Distinct Eigenvalues, Complex Eigenvalues, Repeated Real Roots

  • 10. Existence and Uniqueness Theorems
    Picard’s Method, Existence and Uniqueness Theorem for First Order ODE’s, Existence and Uniqueness Theorem for Linear First Order ODE’s, Existence and Uniqueness Theorem for Linear Systems

  • 11. Numerical Approximations
    Euler’s Method, Error Bounds, Improved Euler’s Method, Runge-Kutta Methods

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