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 3337 views
Sinusoidal Functions
Mar 5, 2013 2280 views
Separable Equations
Mar 5, 2013 6190 views
Solutions of First Order Linear Equations
Mar 5, 2013 4246 views
Direction Fields
Mar 5, 2013 3180 views
Sinusoidal Inputs
Mar 5, 2013 2580 views
Autonomous Equations and Phase Lines
Mar 5, 2013 2437 views
Euler's Method
Mar 5, 2013 3061 views
Linear Equations
Mar 5, 2013 2673 views
First Order Constant Coefficient Linear ODE's
Mar 5, 2013 2436 views
Unit II: Second Order Constant Coefficient Linear Equations
Gain and Phase Lag
Mar 5, 2013 2347 views
Frequency Response
Mar 5, 2013 2310 views
Undetermined Coefficients
Mar 5, 2013 2503 views
Homogeneous Constant Coefficient Equations: Real Roots
Mar 5, 2013 2554 views
Forced Oscillations
Mar 5, 2013 2334 views
Pure Resonance
Mar 5, 2013 3340 views
Homogeneous Constant Coefficient Equations: Any Roots
Mar 5, 2013 3104 views
Unit III: Fourier Series and Laplace Transform
Pole Diagrams
Mar 5, 2013 2584 views
Computing Fourier Series
Mar 5, 2013 2800 views
Step and Delta Functions: Integration and Generalized Derivatives
Mar 5, 2013 3204 views
Linear ODE's with Periodic Input
Mar 5, 2013 2406 views
Convolution and Green's Formula
Mar 5, 2013 2624 views
Unit Step and Impulse Response
Mar 5, 2013 3080 views
Partial Fractions and Laplace Inverse
Mar 5, 2013 2595 views
Laplace Transform: Basics
Mar 5, 2013 8391 views
Manipulating Fourier Series
Mar 5, 2013 2432 views
IV: First-order Systems
Linear Systems of Equations
Mar 5, 2013 8093 views
Linearization
Mar 5, 2013 2756 views
Phase Portraits
Mar 5, 2013 2780 views
Damped Harmonic Oscillators
Mar 5, 2013 2898 views
Linear Systems: Matrix Methods
Mar 5, 2013 3351 views
Linear Systems: Complex Roots
Mar 5, 2013 2872 views
Trace-Determinant Diagram
Mar 5, 2013 2739 views
Matrix Exponentials
Mar 5, 2013 2541 views
Laplace: Solving ODE's
Mar 5, 2013 3015 views
Lecture 1: The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves
Jan 19, 2009 52796 views
Lecture 2: Euler's Numerical Method for y'=f(x,y) and its Generalizations
Jan 19, 2009 21415 views
Lecture 3: Solving First-order Linear ODE's; Steady-state and Transient Solution...
Jan 19, 2009 18339 views
Lecture 4: First-order Substitution Methods: Bernouilli and Homogeneous ODE's
Jan 19, 2009 13584 views
Lecture 5: First-order Autonomous ODE's: Qualitative Methods, Applications
Jan 19, 2009 10500 views
Lecture 6: Complex Numbers and Complex Exponentials
Jan 19, 2009 15648 views
Lecture 7: First-order Linear with Constant Coefficients: Behavior of Solutions,...
Jan 19, 2009 10522 views
Lecture 8: Continuation; Applications to Temperature, Mixing, RC-circuit, Decay...
Jan 19, 2009 8105 views
Lecture 9: Solving Second-order Linear ODE's with Constant Coefficients: The Thr...
Jan 19, 2009 10208 views
Lecture 10: Continuation: Complex Characteristic Roots; Undamped and Damped Osci...
Jan 19, 2009 8379 views
Lecture 11: Theory of General Second-order Linear Homogeneous ODE's: Superpositi...
Jan 19, 2009 8150 views
Lecture 12: Continuation: General Theory for Inhomogeneous ODE's. Stability Crit...
Jan 19, 2009 7560 views
Lecture 13: Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Fo...
Jan 19, 2009 8154 views
Lecture 14: Interpretation of the Exceptional Case: Resonance
Jan 19, 2009 7168 views
Lecture 15: Introduction to Fourier Series; Basic Formulas for Period 2(pi)
Jan 19, 2009 25878 views
Lecture 16: Continuation: More General Periods; Even and Odd Functions; Periodic...
Jan 19, 2009 9468 views
Lecture 17: Finding Particular Solutions via Fourier Series; Resonant Terms; Hea...
Jan 19, 2009 8298 views
Lecture 19: Introduction to the Laplace Transform; Basic Formulas
Jan 19, 2009 37001 views
Lecture 20: Derivative Formulas; Using the Laplace Transform to Solve Linear ODE...
Jan 19, 2009 14809 views
Lecture 21: Convolution Formula: Proof, Connection with Laplace Transform, Appli...
Jan 19, 2009 15328 views
Lecture 22: Using Laplace Transform to Solve ODE's with Discontinuous Inputs
Jan 19, 2009 10956 views
Lecture 23: Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer F...
Jan 19, 2009 10511 views
Lecture 24: Introduction to First-order Systems of ODE's; Solution by Eliminatio...
Jan 19, 2009 7367 views
Lecture 25: Homogeneous Linear Systems with Constant Coefficients: Solution via ...
Jan 19, 2009 9903 views
Lecture 26: Continuation: Repeated Real Eigenvalues, Complex Eigenvalues
Jan 19, 2009 7407 views
Lecture 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant C...
Jan 19, 2009 7368 views
Lecture 28: Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix...
Jan 19, 2009 7518 views
Lecture 29: Matrix Exponentials; Application to Solving Systems
Jan 19, 2009 6320 views
Lecture 30: Decoupling Linear Systems with Constant Coefficients
Jan 19, 2009 6803 views
Lecture 31: Non-linear Autonomous Systems: Finding the Critical Points and Sketc...
Jan 19, 2009 9358 views
Lecture 32: Limit Cycles: Existence and Non-existence Criteria
Jan 19, 2009 16640 views
Lecture 33: Relation Between Non-linear Systems and First-order ODE's; Structura...
Jan 19, 2009 7669 views