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
·
52739 Views
Lecture 2: Euler's Numerical Method for y'=f(x,y) and its Generalizations
Jan 19, 2009
·
21377 Views
Lecture 3: Solving First-order Linear ODE's; Steady-state and Transient Solution...
Jan 19, 2009
·
18305 Views
Lecture 4: First-order Substitution Methods: Bernouilli and Homogeneous ODE's
Jan 19, 2009
·
13542 Views
Lecture 5: First-order Autonomous ODE's: Qualitative Methods, Applications
Jan 19, 2009
·
10463 Views
Lecture 6: Complex Numbers and Complex Exponentials
Jan 19, 2009
·
15615 Views
Lecture 7: First-order Linear with Constant Coefficients: Behavior of Solutions,...
Jan 19, 2009
·
10362 Views
Lecture 8: Continuation; Applications to Temperature, Mixing, RC-circuit, Decay...
Jan 19, 2009
·
8058 Views
Lecture 9: Solving Second-order Linear ODE's with Constant Coefficients: The Thr...
Jan 19, 2009
·
10171 Views
Lecture 10: Continuation: Complex Characteristic Roots; Undamped and Damped Osci...
Jan 19, 2009
·
8326 Views
Lecture 11: Theory of General Second-order Linear Homogeneous ODE's: Superpositi...
Jan 19, 2009
·
8122 Views
Lecture 12: Continuation: General Theory for Inhomogeneous ODE's. Stability Crit...
Jan 19, 2009
·
7535 Views
Lecture 13: Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Fo...
Jan 19, 2009
·
8131 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
·
25842 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
·
36777 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
·
10920 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
·
7315 Views
Lecture 25: Homogeneous Linear Systems with Constant Coefficients: Solution via ...
Jan 19, 2009
·
9859 Views
Lecture 26: Continuation: Repeated Real Eigenvalues, Complex Eigenvalues
Jan 19, 2009
·
7378 Views
Lecture 27: Sketching Solutions of 2x2 Homogeneous Linear System with Constant C...
Jan 19, 2009
·
7339 Views
Lecture 28: Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix...
Jan 19, 2009
·
7469 Views
Lecture 29: Matrix Exponentials; Application to Solving Systems
Jan 19, 2009
·
6269 Views
Lecture 30: Decoupling Linear Systems with Constant Coefficients
Jan 19, 2009
·
6763 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
·
16442 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
·
6151 Views
Direction Fields
Mar 05, 2013
·
3121 Views
Euler's Method
Mar 05, 2013
·
3028 Views
Linear Equations
Mar 05, 2013
·
2635 Views
Solutions of First Order Linear Equations
Mar 05, 2013
·
4202 Views
Complex Numbers and Euler's Formula
Mar 05, 2013
·
3289 Views
Sinusoidal Functions
Mar 05, 2013
·
2249 Views
First Order Constant Coefficient Linear ODE's
Mar 05, 2013
·
2407 Views
Sinusoidal Inputs
Mar 05, 2013
·
2540 Views
Autonomous Equations and Phase Lines
Mar 05, 2013
·
2408 Views
Unit II: Second Order Constant Coefficient Linear Equations
Homogeneous Constant Coefficient Equations: Real Roots
Mar 05, 2013
·
2533 Views
Homogeneous Constant Coefficient Equations: Any Roots
Mar 05, 2013
·
3077 Views
Forced Oscillations
Mar 05, 2013
·
2302 Views
Gain and Phase Lag
Mar 05, 2013
·
2321 Views
Undetermined Coefficients
Mar 05, 2013
·
2448 Views
Pure Resonance
Mar 05, 2013
·
3315 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
·
2385 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
·
2547 Views
Laplace Transform: Basics
Mar 05, 2013
·
8319 Views
Step and Delta Functions: Integration and Generalized Derivatives
Mar 05, 2013
·
3178 Views
Unit Step and Impulse Response
Mar 05, 2013
·
3022 Views
Pole Diagrams
Mar 05, 2013
·
2556 Views
IV: First-order Systems
Linear Systems: Matrix Methods
Mar 05, 2013
·
3302 Views
Matrix Exponentials
Mar 05, 2013
·
2492 Views
Phase Portraits
Mar 05, 2013
·
2747 Views
Linearization
Mar 05, 2013
·
2728 Views
Damped Harmonic Oscillators
Mar 05, 2013
·
2876 Views
Trace-Determinant Diagram
Mar 05, 2013
·
2694 Views
Linear Systems: Complex Roots
Mar 05, 2013
·
2851 Views
Linear Systems of Equations
Mar 05, 2013
·
8056 Views
Laplace: Solving ODE's
Mar 05, 2013
·
2979 Views