Video lectures; Captions/transcript; Lecture notes; Assignments: problem sets with solutions; Course Description. Our mission is to provide a free, world-class education to anyone, anywhere. What follows are my lecture notes for a first course in differential equations, taught at the Hong Kong University of Science and Technology. Homework for Tuesday lectures is due the following Monday. Learn the basics, starting with Intro to differential equations, Complex and repeated roots of characteristic equation, Laplace transform to solve a differential equation. Massachusetts Institute of Technology. There will be homework attached to each lecture. Use OCW to guide your own life-long learning, or to teach others. Topics include first-order scalar and vector equations, basic properties of linear vector equations, and two-dimensional nonlinear autonomous systems. Homework and Lecture Notes. Donate or volunteer today! Courses 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. This is one of over 2,200 courses on OCW. Send to friends and colleagues. » An in-depth study of Differential Equations and how they are used in life. The d'Arbeloff Fund for Excellence in MIT Education. Note: Lecture 18, 34, and 35 are not available. Made for sharing. Mathematics With more than 2,400 courses available, OCW is delivering on the promise of open sharing of knowledge. Knowledge is your reward. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. If you're seeing this message, it means we're having trouble loading external resources on our website. Suitable for senior mathematics students, the text begins with an examination of differential equations of the first order in one unknown function. Find materials for this course in the pages linked along the left. ), 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. We don't offer credit or certification for using OCW. Learn more », © 2001–2018 Freely browse and use OCW materials at your own pace. Khan Academy is a 501(c)(3) nonprofit organization. : Proof : Write X t = U tV t, where dV t = (t)dt + (t)dB t, and find and . There's no signup, and no start or end dates. To log in and use all the features of Khan Academy, please enable JavaScript in your browser. 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. Home If you're seeing this message, it means we're having trouble loading external resources on our website. This table (PDF) provides a correlation between the video and the lectures in the 2010 version of the course. No enrollment or registration. » Much of the material of Chapters 2-6 and 8 has been adapted from the widely » The videotaping was made possible by The d'Arbeloff Fund for Excellence in MIT Education. MIT OpenCourseWare is a free & open publication of material from thousands of MIT courses, covering the entire MIT curriculum. ; 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! If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Differential Equations are the language in which the laws of nature are expressed. 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! Differential Equations 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. 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. Your use of the MIT OpenCourseWare site and materials is subject to our Creative Commons License and other terms of use. Included in these notes are links to short tutorial videos posted on YouTube. Video Lectures. Modify, remix, and reuse (just remember to cite OCW as the source. 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.