Explore a comprehensive series of lectures on differential equations covering a wide range of topics. Begin with linear, exact, and homogeneous differential equations, then progress to Bernoulli equations and substitution methods. Learn about applications of first-order linear differential equations and linear models. Dive into the theory of linear equations, reduction of order, and constant coefficient equations with distinct, repeated, and complex roots. Study undetermined coefficients, variation of parameters, and Cauchy-Euler equations. Examine applications in spring-mass systems and power series solutions. Investigate the method of Frobenius, Bessel and Legendre equations, Laplace transforms, and their properties. Conclude with linear systems of differential equations, including repeated eigenvalues and phase portraits.
Overview
Syllabus
Linear, Exact, and Homogeneous Differential Equations Lecture.
Bernoulli Differential Equations and a General Substitution Method.
Applications of First Order Linear Differential Equations.
Linear Models:: Applications of Linear ODEs.
Differential Equations :: Theory of Linear Equations :: Reduction of Order.
Linear Differential Equations with Constant Coefficients :: Intro and Distinct Roots Example.
Linear Equations with Constant Coefficients :: Repeated and Complex Roots and Higher Order Equations.
Undetermined Coefficients and Variation of Parameters :: Discussion.
Cauchy Euler Differential Equations and Applications of Linear Equations :: Spring Mass Systems.
Applications of Linear Equations :: Spring Mass Systems Continued.
Power Series Solutions of Differential Equations.
Power Series Solutions of Differential Equations Continued.
Method of Frobenius and Special Equations :: Bessel and Legendre.
Laplace Transforms, Inverse Transforms, Partial Fractions, and Using Laplace for ODEs.
Laplace Shifting Theorems, Convolution and Other Properties.
Laplace Transform | Convolution | Integral Equations | Period Functions | Dirac Delta.
Linear Systems of Differential Equations Lecture 1.
Systems of Differential Equations Lecture 2: Repeated Eigenvalues and Phase Portraits.
Taught by
Jonathan Walters
