Feb 5, 2003 
67 videos 
MIT 18.03 Differential Equations - Spring 2006
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 coefficients and variation of parameters; Sinusoidal and exponential signals: oscillations, damping, resonance; Complex numbers and exponentials; Fourier series, periodic solutions; Delta functions, convolution, and Laplace transform methods; Matrix and first order linear systems: eigenvalues and eigenvectors; and Non-linear autonomous systems: critical point analysis and phase plane diagrams.
Course Homepage 18.03 Differential Equations Spring 2006
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Unit I: First Order Differential Equations
Complex Numbers and Euler's Formula
Mar 5, 2013 3332 views
Sinusoidal Functions
Mar 5, 2013 2276 views
Separable Equations
Mar 5, 2013 6185 views
Solutions of First Order Linear Equations
Mar 5, 2013 4238 views
Direction Fields
Mar 5, 2013 3173 views
Sinusoidal Inputs
Mar 5, 2013 2574 views
Autonomous Equations and Phase Lines
Mar 5, 2013 2431 views
Euler's Method
Mar 5, 2013 3047 views
Linear Equations
Mar 5, 2013 2665 views
First Order Constant Coefficient Linear ODE's
Mar 5, 2013 2431 views
Unit II: Second Order Constant Coefficient Linear Equations
Gain and Phase Lag
Mar 5, 2013 2340 views
Frequency Response
Mar 5, 2013 2299 views
Undetermined Coefficients
Mar 5, 2013 2498 views
Homogeneous Constant Coefficient Equations: Real Roots
Mar 5, 2013 2548 views
Forced Oscillations
Mar 5, 2013 2325 views
Pure Resonance
Mar 5, 2013 3334 views
Homogeneous Constant Coefficient Equations: Any Roots
Mar 5, 2013 3098 views
Unit III: Fourier Series and Laplace Transform
Pole Diagrams
Mar 5, 2013 2582 views
Computing Fourier Series
Mar 5, 2013 2796 views
Step and Delta Functions: Integration and Generalized Derivatives
Mar 5, 2013 3201 views
Linear ODE's with Periodic Input
Mar 5, 2013 2404 views
Convolution and Green's Formula
Mar 5, 2013 2620 views
Unit Step and Impulse Response
Mar 5, 2013 3070 views
Partial Fractions and Laplace Inverse
Mar 5, 2013 2592 views
Laplace Transform: Basics
Mar 5, 2013 8386 views
Manipulating Fourier Series
Mar 5, 2013 2429 views
IV: First-order Systems
Linear Systems of Equations
Mar 5, 2013 8089 views
Linearization
Mar 5, 2013 2750 views
Phase Portraits
Mar 5, 2013 2775 views
Damped Harmonic Oscillators
Mar 5, 2013 2894 views
Linear Systems: Matrix Methods
Mar 5, 2013 3345 views
Linear Systems: Complex Roots
Mar 5, 2013 2869 views
Trace-Determinant Diagram
Mar 5, 2013 2737 views
Matrix Exponentials
Mar 5, 2013 2535 views
Laplace: Solving ODE's
Mar 5, 2013 3010 views
Lecture 1: The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves
Jan 19, 2009 52793 views
Lecture 2: Euler's Numerical Method for y'=f(x,y) and its Generalizations
Jan 19, 2009 21411 views
Lecture 3: Solving First-order Linear ODE's; Steady-state and Transient Solution...
Jan 19, 2009 18330 views
Lecture 4: First-order Substitution Methods: Bernouilli and Homogeneous ODE's
Jan 19, 2009 13578 views
Lecture 5: First-order Autonomous ODE's: Qualitative Methods, Applications
Jan 19, 2009 10495 views
Lecture 6: Complex Numbers and Complex Exponentials
Jan 19, 2009 15640 views
Lecture 7: First-order Linear with Constant Coefficients: Behavior of Solutions,...
Jan 19, 2009 10509 views
Lecture 8: Continuation; Applications to Temperature, Mixing, RC-circuit, Decay...
Jan 19, 2009 8102 views
Lecture 9: Solving Second-order Linear ODE's with Constant Coefficients: The Thr...
Jan 19, 2009 10204 views
Lecture 10: Continuation: Complex Characteristic Roots; Undamped and Damped Osci...
Jan 19, 2009 8372 views
Lecture 11: Theory of General Second-order Linear Homogeneous ODE's: Superpositi...
Jan 19, 2009 8147 views
Lecture 12: Continuation: General Theory for Inhomogeneous ODE's. Stability Crit...
Jan 19, 2009 7555 views
Lecture 13: Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Fo...
Jan 19, 2009 8150 views
Lecture 14: Interpretation of the Exceptional Case: Resonance
Jan 19, 2009 7162 views
Lecture 15: Introduction to Fourier Series; Basic Formulas for Period 2(pi)
Jan 19, 2009 25871 views
Lecture 16: Continuation: More General Periods; Even and Odd Functions; Periodic...
Jan 19, 2009 9463 views
Lecture 17: Finding Particular Solutions via Fourier Series; Resonant Terms; Hea...
Jan 19, 2009 8293 views
Lecture 19: Introduction to the Laplace Transform; Basic Formulas
Jan 19, 2009 36994 views
Lecture 20: Derivative Formulas; Using the Laplace Transform to Solve Linear ODE...
Jan 19, 2009 14799 views
Lecture 21: Convolution Formula: Proof, Connection with Laplace Transform, Appli...
Jan 19, 2009 15317 views
Lecture 22: Using Laplace Transform to Solve ODE's with Discontinuous Inputs
Jan 19, 2009 10949 views
Lecture 23: Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer F...
Jan 19, 2009 10504 views
Lecture 24: Introduction to First-order Systems of ODE's; Solution by Eliminatio...
Jan 19, 2009 7357 views
Lecture 25: Homogeneous Linear Systems with Constant Coefficients: Solution via ...
Jan 19, 2009 9894 views
Lecture 26: Continuation: Repeated Real Eigenvalues, Complex Eigenvalues
Jan 19, 2009 7404 views
Lecture 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant C...
Jan 19, 2009 7360 views
Lecture 28: Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix...
Jan 19, 2009 7508 views
Lecture 29: Matrix Exponentials; Application to Solving Systems
Jan 19, 2009 6313 views
Lecture 30: Decoupling Linear Systems with Constant Coefficients
Jan 19, 2009 6796 views
Lecture 31: Non-linear Autonomous Systems: Finding the Critical Points and Sketc...
Jan 19, 2009 9348 views
Lecture 32: Limit Cycles: Existence and Non-existence Criteria
Jan 19, 2009 16626 views
Lecture 33: Relation Between Non-linear Systems and First-order ODE's; Structura...
Jan 19, 2009 7663 views