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″]

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”1.2 -Initial-Value Problems” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


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

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]

[/expand]


[expand title=”2.-FIRST-ORDER DIFFERENTIAL EQUATIONS” rel=”submenu-highlander”]

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

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”2.2 -Separable Equations” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”2.3-Linear Equations” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]


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

[embedyt] https://www.youtube.com/watch?v=K4p-J2wRKjg[/embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”2.4-Exact Equations” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”2.5-Solutions by Substitutions”] rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


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

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]

[/expand]


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

[expandsub2 title=”3.1-Linear Models” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”3.2-Nonlinear Models” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]


[expandsub4 title=”Logistic Differential Equation” rel=”submenu-highlander2″]

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


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

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt] https://www.youtube.com/watch?v=w_oRY1trPhI[/embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]

[/expand]


[expand title=”4.-HIGHER-ORDER DIFFERENTIAL EQUATIONS” rel=”submenu-highlander”]

[expandsub2 title=”4.1-Preliminary Theory—Linear Equations” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”4.2-Reduction of Order” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


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

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”4.4-Undetermined Coefficients—Superposition Approach” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”4.5-Undetermined Coefficients—Annihilator Approach” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”4.6-Variation of Parameters” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”4.7-Cauchy-Euler Equation” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”4.8-Green’s Functions” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


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

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”4.10-Nonlinear Differential Equations” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]

[/expand]


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

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

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


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

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”5.3-Nonlinear Models” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]

[/expand]


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

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

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”6.2-Solutions About Ordinary Points” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”6.3-Solutions About Singular Points” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”6.4-Special Functions” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]

[/expand]


[expand title=”7.-THE LAPLACE TRANSFORM” rel=”submenu-highlander”]

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

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


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

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”7.3-Operational Properties I” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”7.4-Operational Properties II” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


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

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


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

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]

[/expand]


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

[expandsub2 title=”8.1-Preliminary Theory—Linear Systems” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”8.2-Homogeneous Linear Systems” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]

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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”8.3-Nonhomogeneous Linear Systems” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”8.4-Matrix Exponential” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]

[/expand]


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

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

[expandsub3 title=”Videos”]

[expandsub4 title=”Euler’s Method” rel=”submenu-highlander2″]

[embedyt]

[/expandsub4]

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

[embedyt]

[/expandsub4]


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

[embedyt]

[/expandsub4]


[expandsub4 title=”Improved Euler Method” rel=”submenu-highlander2″]

[embedyt]

[/expandsub4]

[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”9.2-Runge-Kutta Methods” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”9.3-Multistep Methods” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


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

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]


[expandsub2 title=”9.5-Second-Order Boundary-Value Problems” rel=”submenu-highlander1″]

[expandsub3 title=”Videos”]vids[/expandsub3]

[expandsub3 title=”Notes”]Good Shit[/expandsub3]
[/expandsub2]

[/expand]