# Introduction to Differential Equations

Differential Equations is ______

Do cool Differential Equations stuff

Math Prerequisites: Precalculus, Algebra, Geometry, Trigonometry, Calculus I, Calculus II, Calculus III

The main book used in colleges today is ‘A First Course in Differential Equations.”

[expand title=”1.-INTRODUCTION TO DIFFERENTIAL EQUATIONS” rel=”submenu-highlander”]

[expandsub2 title=”1.1 -Definitions and Terminology” rel=”submenu-highlander1″]

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[expandsub4 title=”Ordinary Differential Equations – Intro” rel=”submenu-highlander2″]

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[expandsub4 title=”Differential Equations – Basic Idea of What It Means to be a Solution” rel=”submenu-highlander2″]

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[expandsub4 title=”Basic Differential Equation with an Initial Condition” rel=”submenu-highlander2″]

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[expandsub2 title=”1.3 -Differential Equations as Mathematical Models” rel=”submenu-highlander1″]

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[expandsub2 title=”2.1-Solution Curves Without a Solution” rel=”submenu-highlander1″]

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[expandsub4 title=”Separable Differential Equations – Intro” rel=”submenu-highlander2″]

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[expandsub4 title=”Separable Differential Equations – Intro” rel=”submenu-highlander2″]

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[expandsub4 title=”Example 1 – Separable Differential Equations” rel=”submenu-highlander2″]

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[expandsub4 title=”Example 2 – Separable Differential Equations” rel=”submenu-highlander2″]

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[expandsub4 title=”Example 3 – Separable Differential Equations” rel=”submenu-highlander2″]

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[expandsub4 title=”Example 4 – Separable Differential Equations” rel=”submenu-highlander2″]

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[expandsub4 title=”Initial-Value Separable Differential Equation” rel=”submenu-highlander2″]

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[expandsub4 title=”Separable Equation – Exponential Change” rel=”submenu-highlander2″]

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[expandsub4 title=”Solving a Separable Differential Equation, Another Example #1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Solving a Separable Differential Equation, Another Example #2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Solving a Separable Differential Equation, Another Example #3″ rel=”submenu-highlander2″]

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[expandsub4 title=”Solving a Separable Differential Equation, Another Example #4, Initial Condition” rel=”submenu-highlander2″]

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[expandsub4 title=”Solving a Separable Differential Equation, Another Example #5, Initial Condition” rel=”submenu-highlander2″]

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[expandsub4 title=”Linear Differential Equations & Integrating Factors – Intro” rel=”submenu-highlander2″]

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[expandsub4 title=”Linear Differential Equation – Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Linear Differential Equation – Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Linear Differential Equation – Example 3″ rel=”submenu-highlander2″]

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[expandsub4 title=”Linear Differential Equation – Example 4″ rel=”submenu-highlander2″]

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[expandsub4 title=”Linear Equation – Initial-Value Problem” rel=”submenu-highlander2″]

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[expandsub4 title=”Exact Differential Equations – Intro” rel=”submenu-highlander2″]

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[expandsub4 title=”Exact Differential Equations – Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Exact Differential Equations – Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Exact Differential Equations – Example 3″ rel=”submenu-highlander2″]

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[expandsub4 title=”Homogeneous First Order Equations – Intro” rel=”submenu-highlander2″]

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[expandsub4 title=”Bernoulli First Order Equations – Intro” rel=”submenu-highlander2″]

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[expandsub4 title=”Bernoulli First Order Equations – Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Bernoulli First Order Equations – Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Bernoulli Equation for Differential Equations , Part 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Bernoulli Equation for Differential Equations , Part 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Bernoulli Equation for Differential Equations , Part 3″ rel=”submenu-highlander2″]

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[expandsub4 title=”Change of Variables / Homogeneous Differential Equation – Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Change of Variables / Homogeneous Differential Equation – Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Change of Variables / Homogeneous Differential Equation – Example 3″ rel=”submenu-highlander2″]

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[expandsub4 title=”Change of Variables / Homogeneous Differential Equation – Example 4″ rel=”submenu-highlander2″]

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[expandsub2 title=”2.6 A Numerical Method” rel=”submenu-highlander1″]

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[expand title=”3.-MODELING WITH FIRST-ORDER DIFFERENTIAL EQUATIONS” rel=”submenu-highlander”]

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[expandsub4 title=”Mixture/Concentration Differential Equation – Linear Equation” rel=”submenu-highlander2″]

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[expandsub4 title=”Newtons’s Law of Cooling – Linear Differential Equation” rel=”submenu-highlander2″]

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[expandsub4 title=”Deriving the Logistic Growth Equation – Separable Equation” rel=”submenu-highlander2″]

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[expandsub4 title=”The Logistic Equation and Models for Population – Example 1, part 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”The Logistic Equation and Models for Population – Example 1, part 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”The Logistic Equation and the Analytic Solution” rel=”submenu-highlander2″]

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[expandsub2 title=”3.3-Modeling with Systems of First-Order DEs” rel=”submenu-highlander1″]

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[expandsub4 title=”Intro to Kirchhoff’s Law – First-Order Differential Equation” rel=”submenu-highlander2″]

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[expandsub4 title=”Solving Kirchhoff Differential Equation – Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Solving Kirchhoff Differential Equation – Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Reduction of Order, Basic Example” rel=”submenu-highlander2″]

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[expandsub2 title=”4.3-Homogeneous Linear Equations with Constant Coefficient” rel=”submenu-highlander1″]

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[expandsub4 title=”Second-Order Homogeneous Linear Equations with Constant Coefficients – Intro” rel=”submenu-highlander2″]

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[expandsub4 title=”Second-Order Differential Equations – Auxiliary Equation with Distinct Real Roots” rel=”submenu-highlander2″]

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[expandsub4 title=”Second-Order Differential Equations – Auxiliary Equation with Repeated Real Roots” rel=”submenu-highlander2″]

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[expandsub4 title=”Solving Higher-Order Differential Equations Using the Auxiliary Equation” rel=”submenu-highlander2″]

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[expandsub4 title=”Variation of Parameters – Introduction” rel=”submenu-highlander2″]

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[expandsub4 title=”Variation of Parameters – Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Variation of Parameters – Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Variation of Parameters – Example 3″ rel=”submenu-highlander2″]

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[expandsub4 title=”Cauchy-Euler Differential Equations (2nd Order)” rel=”submenu-highlander2″]

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[expandsub2 title=”4.9-Solving Systems of Linear DEs by Elimination” rel=”submenu-highlander1″]

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[expand title=”5.-MODELING WITH HIGHER-ORDER DIFFERENTIAL EQUATIONS” rel=”submenu-highlander”]

[expandsub2 title=”5.1-Linear Models: Initial-Value Problems” rel=”submenu-highlander1″]

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[expandsub2 title=”5.2-Linear Models: Boundary-Value Problems” rel=”submenu-highlander1″]

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[expand title=”6.-SERIES SOLUTIONS OF LINEAR EQUATIONS” rel=”submenu-highlander”]

[expandsub2 title=”6.1-Review of Power Series” rel=”submenu-highlander1″]

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[expandsub4 title=”Review of Power Series Basics” rel=”submenu-highlander2″]

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[expandsub4 title=”Power Series Solutions of Differential Equations” rel=”submenu-highlander2″]

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[expandsub4 title=”How to Derive a Power Series” rel=”submenu-highlander2″]

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[expandsub4 title=”Shifting the Index for Power Series” rel=”submenu-highlander2″]

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[expandsub4 title=”Solving Differential Equations with Power Series” rel=”submenu-highlander2″]

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[expandsub2 title=”7.1-Definition of the Laplace Transform” rel=”submenu-highlander1″]

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[expandsub4 title=”Laplace Transforms: Non-Mathematical Introduction” rel=”submenu-highlander2″]

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[expandsub4 title=”The Laplace Transform – The Basic Idea of How We Use It” rel=”submenu-highlander2″]

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[expandsub4 title=”The Laplace Transform, Basic Properties – Definitions and Derivatives” rel=”submenu-highlander2″]

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[expandsub2 title=”7.2-Inverse Transforms and Transforms of Derivatives” rel=”submenu-highlander1″]

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[expandsub4 title=”Laplace Transforms of Derivatives” rel=”submenu-highlander2″]

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[expandsub4 title=”Using Laplace Transforms to Solve Differential Equations” rel=”submenu-highlander2″]

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[expandsub4 title=”The Laplace Transform – More Derivatives” rel=”submenu-highlander2″]

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[expandsub4 title=”Unit Step Function – Intro” rel=”submenu-highlander2″]

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[expandsub4 title=”Laplace Transforms with Unit Step Functions” rel=”submenu-highlander2″]

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[expandsub4 title=”Laplace Transform Involving Heaviside Functions” rel=”submenu-highlander2″]

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[expandsub2 title=”7.5-The Dirac Delta Function” rel=”submenu-highlander1″]

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[expandsub4 title=”Unit Impulse & Dirac Delta Function” rel=”submenu-highlander2″]

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[expandsub2 title=”7.6-Systems of Linear Differential Equations” rel=”submenu-highlander1″]

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[expand title=”8.-SYSTEMS OF LINEAR FIRST-ORDER DIFFERENTIAL EQUATIONS” rel=”submenu-highlander”]

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[expandsub4 title=”Homogeneous Systems of Linear Equations – Intro to Eigenvalue/Eigenvector Method” rel=”submenu-highlander2″]

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[expandsub4 title=”How to Compute the Wronskian for a Group of Functions” rel=”submenu-highlander2″]

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[expandsub4 title=”Solving Linear Systems with Eigenvalue/Eigenvector Method – Example 1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Solving Linear Systems with Eigenvalue/Eigenvector Method – Example 2″ rel=”submenu-highlander2″]

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[expandsub4 title=”Solving a Linear 3-Variable System of Differential Equations – Example” rel=”submenu-highlander2″]

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[expand title=”9.-NUMERICAL SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS” rel=”submenu-highlander”]

[expandsub2 title=”9.1-Euler Methods and Error Analysis” rel=”submenu-highlander1″]

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[expandsub4 title=”Euler’s Method – Another Example #1″ rel=”submenu-highlander2″]

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[expandsub4 title=”Euler’s Method – Another Example #2″ rel=”submenu-highlander2″]

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[expandsub2 title=”9.4-Higher-Order Equations and Systems” rel=”submenu-highlander1″]

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