Weak maximum principle and introduction to the fundamental solution. Cdrom handbook of differential equations c academic. Freely browse and use ocw materials at your own pace. Differential equations department of mathematics, hong. I thank eunghyun hyun lee for his help with these notes during the 200809. We end these notes solving our first partial differential equation, the heat equation. Ordinary differential equations michigan state university. This video contains procedures to solve different type of differential equationsdifferential equations are very important for the gate exam. This book originated from my class notes for math 286 at the. Jalal shatah eduardo corona spring 2009 contents i introduction 1 1 1st order pdes.
Differential equations pauls online math notes lamar university. In this case, laplaces equation models a twodimensional system at steady state in time. Assumed background is calculus and a little physics. An ordinary differential equation ode is a differential equation for a function of a single variable, e.
Pdf differential equations and linear algebra lecture. Cs537 numerical analysis lecture numerical solution of ordinary differential equations professor jun zhang department of computer science university of kentucky lexington, ky 40206. These lecture notes are intended for the courses introduction to mathematical methods and introduction to mathematical methods in economics. Fundamental solution and the global cauchy problem. Lecture notes introduction to partial differential.
Linear second order odes, homogeneous linear odes, nonhomogeneous linear odes, laplace transforms, linear algebraic equations, linear algebraic eigenvalue problems and systems of differential equations. Differential equations and linear algebra lecture notes. Thus we cannot hope to have a general theory for equations of type 1. Fourier series andpartial differential equations lecture notes. An ode contains ordinary derivatives and a pde contains partial derivatives. Lecture notes on ordinary differential equations department of. This section provides the lecture notes from the course and the schedule of lecture topics. Find materials for this course in the pages linked along the left. These are introductory notes on ordinary and partial differential equations. Note that the highest order of derivative of unknown function y appearing in the relation. Despite the fact that these are my class notes, they should be accessible to anyone wanting to learn how to solve differential equations or needing a refresher.
Lecture notes on ordinary differential equations subramanian, dr. Arnold, geometrical methods in the theory of ordinary differential equations. Note that many of the methods for a single differential equation may be generalized to handle systems. Lecture numerical solution of ordinary differential equations. What follows are my lecture notes for a first course in differential equations, taught at the hong kong university of science and technology. They contain a number of results of a general nature, and in particular an introduction to selected parts of the theory of di. Lecture notes differential equations mathematics mit.
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