MIT 18.03 Differential Equations - Spring 2006
67 Lectures · Feb 5, 2003
About
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
Course features at MIT OpenCourseWare page:
*Syllabus *Calendar *Readings *Lecture Notes *Recitations *Assignment *Exams *Tools *Download Course Materials
Complete MIT OCW video collection at MIT OpenCourseWare - VideoLectures.NET
Related categories
Uploaded videos:
Lecture 1: The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves
Jan 19, 2009
·
52721 Views
Lecture 2: Euler's Numerical Method for y'=f(x,y) and its Generalizations
Jan 19, 2009
·
21375 Views
Lecture 3: Solving First-order Linear ODE's; Steady-state and Transient Solution...
Jan 19, 2009
·
18303 Views
Lecture 4: First-order Substitution Methods: Bernouilli and Homogeneous ODE's
Jan 19, 2009
·
13541 Views
Lecture 5: First-order Autonomous ODE's: Qualitative Methods, Applications
Jan 19, 2009
·
10460 Views
Lecture 6: Complex Numbers and Complex Exponentials
Jan 19, 2009
·
15613 Views
Lecture 7: First-order Linear with Constant Coefficients: Behavior of Solutions,...
Jan 19, 2009
·
10357 Views
Lecture 8: Continuation; Applications to Temperature, Mixing, RC-circuit, Decay...
Jan 19, 2009
·
8056 Views
Lecture 9: Solving Second-order Linear ODE's with Constant Coefficients: The Thr...
Jan 19, 2009
·
10168 Views
Lecture 10: Continuation: Complex Characteristic Roots; Undamped and Damped Osci...
Jan 19, 2009
·
8324 Views
Lecture 11: Theory of General Second-order Linear Homogeneous ODE's: Superpositi...
Jan 19, 2009
·
8121 Views
Lecture 12: Continuation: General Theory for Inhomogeneous ODE's. Stability Crit...
Jan 19, 2009
·
7534 Views
Lecture 13: Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Fo...
Jan 19, 2009
·
8130 Views
Lecture 14: Interpretation of the Exceptional Case: Resonance
Jan 19, 2009
·
7144 Views
Lecture 15: Introduction to Fourier Series; Basic Formulas for Period 2(pi)
Jan 19, 2009
·
25841 Views
Lecture 16: Continuation: More General Periods; Even and Odd Functions; Periodic...
Jan 19, 2009
·
9415 Views
Lecture 17: Finding Particular Solutions via Fourier Series; Resonant Terms; Hea...
Jan 19, 2009
·
8273 Views
Lecture 19: Introduction to the Laplace Transform; Basic Formulas
Jan 19, 2009
·
36776 Views
Lecture 20: Derivative Formulas; Using the Laplace Transform to Solve Linear ODE...
Jan 19, 2009
·
14771 Views
Lecture 21: Convolution Formula: Proof, Connection with Laplace Transform, Appli...
Jan 19, 2009
·
15291 Views
Lecture 22: Using Laplace Transform to Solve ODE's with Discontinuous Inputs
Jan 19, 2009
·
10919 Views
Lecture 23: Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer F...
Jan 19, 2009
·
10484 Views
Lecture 24: Introduction to First-order Systems of ODE's; Solution by Eliminatio...
Jan 19, 2009
·
7312 Views
Lecture 25: Homogeneous Linear Systems with Constant Coefficients: Solution via ...
Jan 19, 2009
·
9858 Views
Lecture 26: Continuation: Repeated Real Eigenvalues, Complex Eigenvalues
Jan 19, 2009
·
7377 Views
Lecture 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant C...
Jan 19, 2009
·
7338 Views
Lecture 28: Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix...
Jan 19, 2009
·
7468 Views
Lecture 29: Matrix Exponentials; Application to Solving Systems
Jan 19, 2009
·
6268 Views
Lecture 30: Decoupling Linear Systems with Constant Coefficients
Jan 19, 2009
·
6761 Views
Lecture 31: Non-linear Autonomous Systems: Finding the Critical Points and Sketc...
Jan 19, 2009
·
9320 Views
Lecture 32: Limit Cycles: Existence and Non-existence Criteria
Jan 19, 2009
·
16431 Views
Lecture 33: Relation Between Non-linear Systems and First-order ODE's; Structura...
Jan 19, 2009
·
7633 Views
Unit I: First Order Differential Equations
Separable Equations
Mar 05, 2013
·
6150 Views
Direction Fields
Mar 05, 2013
·
3120 Views
Euler's Method
Mar 05, 2013
·
3027 Views
Linear Equations
Mar 05, 2013
·
2635 Views
Solutions of First Order Linear Equations
Mar 05, 2013
·
4201 Views
Complex Numbers and Euler's Formula
Mar 05, 2013
·
3285 Views
Sinusoidal Functions
Mar 05, 2013
·
2248 Views
First Order Constant Coefficient Linear ODE's
Mar 05, 2013
·
2405 Views
Sinusoidal Inputs
Mar 05, 2013
·
2539 Views
Autonomous Equations and Phase Lines
Mar 05, 2013
·
2406 Views
Unit II: Second Order Constant Coefficient Linear Equations
Homogeneous Constant Coefficient Equations: Real Roots
Mar 05, 2013
·
2532 Views
Homogeneous Constant Coefficient Equations: Any Roots
Mar 05, 2013
·
3075 Views
Forced Oscillations
Mar 05, 2013
·
2299 Views
Gain and Phase Lag
Mar 05, 2013
·
2321 Views
Undetermined Coefficients
Mar 05, 2013
·
2447 Views
Pure Resonance
Mar 05, 2013
·
3314 Views
Frequency Response
Mar 05, 2013
·
2272 Views
Unit III: Fourier Series and Laplace Transform
Computing Fourier Series
Mar 05, 2013
·
2781 Views
Manipulating Fourier Series
Mar 05, 2013
·
2384 Views
Linear ODE's with Periodic Input
Mar 05, 2013
·
2389 Views
Convolution and Green's Formula
Mar 05, 2013
·
2601 Views
Partial Fractions and Laplace Inverse
Mar 05, 2013
·
2546 Views
Laplace Transform: Basics
Mar 05, 2013
·
8319 Views
Step and Delta Functions: Integration and Generalized Derivatives
Mar 05, 2013
·
3176 Views
Unit Step and Impulse Response
Mar 05, 2013
·
3020 Views
Pole Diagrams
Mar 05, 2013
·
2554 Views
IV: First-order Systems
Linear Systems: Matrix Methods
Mar 05, 2013
·
3300 Views
Matrix Exponentials
Mar 05, 2013
·
2492 Views
Phase Portraits
Mar 05, 2013
·
2745 Views
Linearization
Mar 05, 2013
·
2727 Views
Damped Harmonic Oscillators
Mar 05, 2013
·
2876 Views
Trace-Determinant Diagram
Mar 05, 2013
·
2693 Views
Linear Systems: Complex Roots
Mar 05, 2013
·
2851 Views
Linear Systems of Equations
Mar 05, 2013
·
8055 Views
Laplace: Solving ODE's
Mar 05, 2013
·
2978 Views