This course covers topics such as linear, exact, and homogeneous differential equations, Bernoulli differential equations, applications of first-order linear differential equations, theory of linear equations, power series solutions of differential equations, Laplace transforms, and linear systems of differential equations. The course aims to teach students how to solve various types of differential equations using different methods and tools. The teaching method includes lectures and examples to illustrate the concepts. This course is intended for individuals interested in gaining a deeper understanding of differential equations and their applications.
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
