Course - Differential Equations I

Course Level: Freshman

Topics covered in a first year course in differential equations. Need to understand basic differentiation and integration from Calculus before starting here.

Prerequisites
• Lecture 1 - Introduction to differential equations
• Lecture 2 - Separable Differential Equations
• Lecture 3 - Separable differential equations 2
• Lecture 4 - Exact Equations Intuition 1 (proofy)
• Lecture 5 - Exact Equations Intuition 2 (proofy)
• Lecture 6 - Exact Equations Example 1
• Lecture 7 - Exact Equations Example 2
• Lecture 8 - Exact Equations Example 3
• Lecture 9 - Integrating factors 1
• Lecture 10 - Integrating factors 2
• Lecture 11 - First order homegenous equations
• Lecture 12 - First order homogenous equations 2
• Lecture 13 - 2nd Order Linear Homogeneous Differential Equations 1
• Lecture 14 - 2nd Order Linear Homogeneous Differential Equations 2
• Lecture 15 - 2nd Order Linear Homogeneous Differential Equations 3
• Lecture 16 - 2nd Order Linear Homogeneous Differential Equations 4
• Lecture 17 - Complex roots of the characteristic equations 1
• Lecture 18 - Complex roots of the characteristic equations 2
• Lecture 19 - Complex roots of the characteristic equations 3
• Lecture 20 - Repeated roots of the characteristic equation
• Lecture 21 - Repeated roots of the characterisitic equations part 2
• Lecture 22 - Undetermined Coefficients 1
• Lecture 23 - Undetermined Coefficients 2
• Lecture 24 - Undetermined Coefficients 3
• Lecture 25 - Undetermined Coefficients 4
• Lecture 26 - Laplace Transform 1
• Lecture 27 - Laplace Transform 2
• Lecture 28 - Laplace Transform 3 (L{sin(at)})
• Lecture 29 - Laplace Transform 4
• Lecture 30 - Laplace Transform 5
• Lecture 31 - Laplace Transform 6
• Lecture 32 - Laplace Transform to solve an equation
• Lecture 33 - Laplace Transform solves an equation 2
• Lecture 34 - More Laplace Transform tools
• Lecture 35 - Using the Laplace Transform to solve a nonhomogenous eq
• Lecture 36 - Laplace Transform of _ L{t}
• Lecture 37 - Laplace Transform of t_n_ L{t_n}
• Lecture 38 - Laplace Transform of the Unit Step Function
• Lecture 39 - Inverse Laplace Examples
• Lecture 40 - Laplace_Step Function Differential Equation
• Lecture 41 - Dirac Delta Function
• Lecture 42 - Laplace Transform of the Dirac Delta Function
• Lecture 43 - Introduction to the Convolution
• Lecture 44 - The Convolution and the Laplace Transform
• Lecture 45 - Using the Convolution Theorem to Solve an Initial Value Prob