Differential Equations An in-depth study of Differential Equations and how they are used in life. Learn more », © 2001–2018 If you're seeing this message, it means we're having trouble loading external resources on our website. : Proof : Write X t = U tV t, where dV t = (t)dt + (t)dB t, and ﬁnd and . » Included are most of the standard topics in 1st and 2nd order differential equations, Laplace transforms, systems of differential eqauations, series solutions as well as a brief introduction to boundary value problems, Fourier series and partial differntial equations. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. There will be homework attached to each lecture. ), Learn more at Get Started with MIT OpenCourseWare, MIT OpenCourseWare makes the materials used in the teaching of almost all of MIT's subjects available on the Web, free of charge. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Learn the basics, starting with Intro to differential equations, Complex and repeated roots of characteristic equation, Laplace transform to solve a differential equation. Lecture 1: The Geometrical View of y'= f(x,y), Lecture 2: Euler's Numerical Method for y'=f(x,y), Lecture 3: Solving First-order Linear ODEs, Lecture 4: First-order Substitution Methods, Lecture 6: Complex Numbers and Complex Exponentials, Lecture 7: First-order Linear with Constant Coefficients, Lecture 9: Solving Second-order Linear ODE's with Constant Coefficients, Lecture 10: Continuation: Complex Characteristic Roots, Lecture 11: Theory of General Second-order Linear Homogeneous ODEs, Lecture 12: Continuation: General Theory for Inhomogeneous ODEs, Lecture 13: Finding Particular Solutions to Inhomogeneous ODEs, Lecture 14: Interpretation of the Exceptional Case: Resonance, Lecture 15: Introduction to Fourier Series, Lecture 16: Continuation: More General Periods, Lecture 17: Finding Particular Solutions via Fourier Series, Lecture 19: Introduction to the Laplace Transform, Lecture 22: Using Laplace Transform to Solve ODEs with Discontinuous Inputs, Lecture 24: Introduction to First-order Systems of ODEs, Lecture 25: Homogeneous Linear Systems with Constant Coefficients, Lecture 26: Continuation: Repeated Real Eigenvalues, Lecture 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients, Lecture 28: Matrix Methods for Inhomogeneous Systems, Lecture 30: Decoupling Linear Systems with Constant Coefficients, Lecture 31: Non-linear Autonomous Systems, Lecture 33: Relation Between Non-linear Systems and First-order ODEs. Khan Academy is a 501(c)(3) nonprofit organization. Our mission is to provide a free, world-class education to anyone, anywhere. Courses Your use of the MIT OpenCourseWare site and materials is subject to our Creative Commons License and other terms of use. Video Lectures. » Suitable for senior mathematics students, the text begins with an examination of differential equations of the first order in one unknown function. Included in these notes are links to short tutorial videos posted on YouTube. » These video lectures of Professor Arthur Mattuck teaching 18.03 were recorded live in the Spring of 2003 and do not correspond precisely to the lectures taught in the Spring of 2010. Note: Lecture 18, 34, and 35 are not available. What follows are my lecture notes for a ﬁrst course in differential equations, taught at the Hong Kong University of Science and Technology. » Consider the equation dX t = (a(t) + b(t)X t)dt + (c(t) + d(t)X t)dB t; with initial condition ˘= x, where a, b, c and d are continuous functions. With more than 2,400 courses available, OCW is delivering on the promise of open sharing of knowledge. The videotaping was made possible by The d'Arbeloff Fund for Excellence in MIT Education. Find materials for this course in the pages linked along the left. Freely browse and use OCW materials at your own pace. Homework for Tuesday lectures is due the following Monday. No enrollment or registration. Learn differential equations for free—differential equations, separable equations, exact equations, integrating factors, and homogeneous equations, and more. Use OCW to guide your own life-long learning, or to teach others. Knowledge is your reward. Differential Equations are the language in which the laws of nature are expressed. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. ; where U t = exp Z t 0 b(s)ds + Z t 0 d(s)dB s 1 2 Z t 0 d2(s)ds! Video lectures; Captions/transcript; Lecture notes; Assignments: problem sets with solutions; Course Description. We don't offer credit or certification for using OCW. Donate or volunteer today! Made for sharing. Mathematics Download files for later. Topics include first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. These video lectures of Professor Arthur Mattuck teaching 18.03 were recorded live in the Spring of 2003 and do not correspond precisely to the lectures taught in the Spring of 2010. Send to friends and colleagues. The d'Arbeloff Fund for Excellence in MIT Education. This table ( PDF ) provides a correlation between the video and the lectures in the 2010 version of the course. There's no signup, and no start or end dates. If you're seeing this message, it means we're having trouble loading external resources on our website. MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum. Home Massachusetts Institute of Technology. This table (PDF) provides a correlation between the video and the lectures in the 2010 version of the course. The solution to this equation is given by X t = U t x + Z t 0 [a(s) c(s)d(s)]U 1 s ds + Z t 0 c(s) U 1 s dB s! Much of the material of Chapters 2-6 and 8 has been adapted from the widely Modify, remix, and reuse (just remember to cite OCW as the source. Homework and Lecture Notes. This is one of over 2,200 courses on OCW.

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