Course: MIT 18.03 Differential Equations, Spring 2006 Dnatube

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Lec 1 - MIT 18.03 Differential Equations ...

"Lec 1 - MIT 18.03 Differential Equations, Spring 2006" The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 2 - MIT 18.03 Differential Equations ...

"Lec 2 - MIT 18.03 Differential Equations, Spring 2006" Euler's Numerical Method for y'=f(x,y) and its Generalizations. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 3 - MIT 18.03 Differential Equations ...

"Lec 3 - MIT 18.03 Differential Equations, Spring 2006" Solving First-order Linear ODE's; Steady-state and Transient Solutions. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 4 - MIT 18.03 Differential Equations ...

"Lec 4 - MIT 18.03 Differential Equations, Spring 2006" First-order Substitution Methods: Bernouilli and Homogeneous ODE's. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 5 - MIT 18.03 Differential Equations ...

"Lec 5 - MIT 18.03 Differential Equations, Spring 2006" First-order Autonomous ODE's: Qualitative Methods, Applications. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 6 - MIT 18.03 Differential Equations ...

"Lec 6 - MIT 18.03 Differential Equations, Spring 2006" Complex Numbers and Complex Exponentials. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 7 - MIT 18.03 Differential Equation ...

"Lec 7 - MIT 18.03 Differential Equations, Spring 2006" First-order Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Methods. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 8 - MIT 18.03 Differential Equation ...

"Lec 8 - MIT 18.03 Differential Equations, Spring 2006" Continuation; Applications to Temperature, Mixing, RC-circuit, Decay, and Growth Models. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 9 - MIT 18.03 Differential Equations ...

"Lec 9 - MIT 18.03 Differential Equations, Spring 2006" Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 10 - MIT 18.03 Differential Equation ...

"Lec 10 - MIT 18.03 Differential Equations, Spring 2006" Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 11 - MIT 18.03 Differential Equation ...

"Lec 11 - MIT 18.03 Differential Equations, Spring 2006" Theory of General Second-order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 12 - MIT 18.03 Differential Equation ...

"Lec 12 - MIT 18.03 Differential Equations, Spring 2006" Continuation: General Theory for Inhomogeneous ODE's. Stability Criteria for the Constant-coefficient ODE's. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 13 - MIT 18.03 Differential Equation ...

"Lec 13 - MIT 18.03 Differential Equations, Spring 2006" Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Formulas Involving Exponentials. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 14 - MIT 18.03 Differential Equation ...

"Lec 14 - MIT 18.03 Differential Equations, Spring 2006" Interpretation of the Exceptional Case: Resonance. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 15 - MIT 18.03 Differential Equation ...

"Lec 15 - MIT 18.03 Differential Equations, Spring 2006" Introduction to Fourier Series; Basic Formulas for Period 2(pi). View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 16 - MIT 18.03 Differential Equation ...

"Lec 16 - MIT 18.03 Differential Equations, Spring 2006" Continuation: More General Periods; Even and Odd Functions; Periodic Extension. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 17 - MIT 18.03 Differential Equation ...

"Lec 17 - MIT 18.03 Differential Equations, Spring 2006" Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 18 - MIT 18.03 Differential Equatio ...

"Lec 18 - MIT 18.03 Differential Equations, Spring 2006" Introduction to the Laplace Transform; Basic Formulas. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 19 - MIT 18.03 Differential Equatio ...

"Lec 19 - MIT 18.03 Differential Equations, Spring 2006" Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 20 - MIT 18.03 Differential Equatio ...

"Lec 20 - MIT 18.03 Differential Equations, Spring 2006" Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 21 - MIT 18.03 Differential Equatio ...

"Lec 21 - MIT 18.03 Differential Equations, Spring 2006" Using Laplace Transform to Solve ODE's with Discontinuous Inputs. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 22 - MIT 18.03 Differential Equatio ...

"Lec 22 - MIT 18.03 Differential Equations, Spring 2006" Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 23 - MIT 18.03 Differential Equatio ...

"Lec 23 - MIT 18.03 Differential Equations, Spring 2006" Introduction to First-order Systems of ODE's; Solution by Elimination, Geometric Interpretation of a System. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 24 - MIT 18.03 Differential Equatio ...

"Lec 24 - MIT 18.03 Differential Equations, Spring 2006" Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case). View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 25 - MIT 18.03 Differential Equatio ...

"Lec 25 - MIT 18.03 Differential Equations, Spring 2006" Continuation: Repeated Real Eigenvalues, Complex Eigenvalues. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 26 - MIT 18.03 Differential Equatio ...

"Lec 26 - MIT 18.03 Differential Equations, Spring 2006" Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 27 - MIT 18.03 Differential Equatio ...

"Lec 27 - MIT 18.03 Differential Equations, Spring 2006" Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 28 - MIT 18.03 Differential Equatio ...

"Lec 28 - MIT 18.03 Differential Equations, Spring 2006" Matrix Exponentials; Application to Solving Systems. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 29 - MIT 18.03 Differential Equatio ...

"Lec 29 - MIT 18.03 Differential Equations, Spring 2006" Decoupling Linear Systems with Constant Coefficients. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 30 - MIT 18.03 Differential Equatio ...

"Lec 30 - MIT 18.03 Differential Equations, Spring 2006" Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec 31 - MIT 18.03 Differential Equatio ...

"Lec 31 - MIT 18.03 Differential Equations, Spring 2006" Limit Cycles: Existence and Non-existence Criteria. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu
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Lec Last - MIT 18.03 Differential Equat ...

"Lec Last - MIT 18.03 Differential Equations, Spring 20066" Relation Between Non-linear Systems and First-order ODE's; Structural Stability of a System, Borderline Sketching Cases; Illustrations Using Volterra's Equation and Principle. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at...

MIT 18.03 Differential Equations, Spring 2006


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Differential Equations are the language in which the laws of nature are expressed. Understanding properties of solutions of differential equations is fundamental to much of contemporary science and engineering. Ordinary differential equations (ODE's) deal with functions of one variable, which can often be thought of as time. Topics include: Solution of first-order ODE's by analytical, graphical and numerical methods; Linear ODE's, especially second order with constant coefficients; Undetermined
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COURSE NAME: MIT 18.03 Differential Equations, Spring 2006

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