Differential Equations

Screenshot of Mathlet from the d'Arbeloff Interactive Math Project.

Linear Phase Portraits Mathlet from the d'Arbeloff Interactive Math Project. (Image courtesy of Hu Hohn and Prof. Haynes Miller.)

Course Highlights

This course includes lecture notes, assignments, and a full set of video lectures.

Course Description

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.

Special Features

Video lectures

Technical Requirements

Special software is required to use some of the files in this course: .jar.

Important Notes : -

It is a collection of lectures notes not ours. Our subjective is to help students to find all engineering notes with different lectures PowerPoint slides in ppt ,pdf or html file at one place. Because we always face that we lose much time by searching in Google or yahoo like search engines to find or downloading a good lecture notes in our subject area with free. Also it is difficult to find popular authoress or books slides with free of cost. If you find any copyrighted slides or notes then please inform me immediately by comments or email as following address .I will take actions to remove it. Please click bellow to download ppt slides/ pdf notes. If you face any problem in downloading or if you find any link not correctly work or if you have any idea to improve this blog/site or if you find any written mistake or you think some subjects notes should be include then give your suggestion as comment by clicking on comment link bellow the post (bottom of page) or email us in this address engineeringppt.blogspot@gmail.com?subject=comments on engineeringppt.blogspot.com. I will must consider your comments only within 1-2 days. if you have any good class notes/lecture slides in ppt or pdf or html format then please you upload these files to rapidshare.come and send us links or all files by our email address engineeringppt.blogspot@gmail.com?subject=comments on engineeringppt.blogspot.com.

To find your notes quickly please see the contents on the right hand side of this page which is alphabetically arranged and right click on it. After clicking immediately you find all the notes ppt/pdf/html/video of your searching subjects.

It is better to search your subject notes by clicking on search button which is present at middle of right side of this web page. Then enter your subject and press enter key then you can find all of your lectures notes and click on it.

Thank you for visiting our site.........

Click Below to Download the files :-

SES #	TOPICS
I. First-order Differential Equations
L0	Simple Models and Separable Equations
L1	Direction Fields, Existence and Uniqueness of Solutions (PDF)
L2	Numerical Methods (PDF)
L3	Linear Equations: Models (PDF)
L4	Solution of Linear Equations, Variation of Parameter (PDF)
L5	Complex Numbers, Complex Exponentials (PDF)
L6	Roots of Unity; Sinusoidal Functions (PDF)
L7	Linear System Response to Exponential and Sinusoidal Input; Gain, Phase Lag (PDF)
L8	Autonomous Equations; The Phase Line, Stability (PDF) Muddy Card Responses (PDF)
L9	Linear vs. Nonlinear (PDF)
L10	Hour Exam I
II. Second-order Linear Equations
L11	The Spring-mass-dashpot Model; Superposition Characteristic Polynomial; Real Roots; Initial Conditions (PDF) Muddy Card Responses (PDF)
L12	Complex Roots; Damping Conditions (PDF)
L13	Inhomogeneous Equations, Superposition (PDF)
L14	Operators and Exponential Signals (PDF) Muddy Card Responses (PDF)
L15	Undetermined Coefficients (PDF)
L16	Frequency Response (PDF)
L17	Applications: Guest appearance by EECS Professor Jeff Lang (PDF) Supplementary Notes Driving Through the Dashpot (PDF)
L18	Exponential Shift Law; Resonance (PDF)
L19	Hour Exam II
III. Fourier Series
L20	Fourier Series (PDF)
L21	Operations on Fourier series (PDF) Muddy Card Responses (PDF)
L22	Periodic Solutions; Resonance (PDF)
IV. The Laplace Transform
L23	Step Function and delta Function (PDF)
L24	Step Response, Impulse Response (PDF)
L25	Convolution (PDF)
L26	Laplace Transform: Basic Properties (PDF) Muddy Card Responses (PDF)
L27	Application to ODEs; Partial Fractions (PDF)
L28	Completing the Square; Time Translated Functions (PDF) Muddy Card Responses (PDF)
L29	Pole Diagram (PDF)
L30	Hour Exam III
V. First Order Systems
L31	Linear Systems and Matrices (PDF)
L32	Eigenvalues, Eigenvectors (PDF)
L33	Complex or Repeated Eigenvalues (PDF)
L34	Qualitative Behavior of Linear Systems; Phase Plane (PDF)
L35	Normal Modes and the Matrix Exponential (PDF)
L36	Inhomogeneous Equations: Variation of Parameters Again (PDF) Muddy Card Responses (PDF)
L37	Nonlinear Systems (PDF)
L38	Examples of Nonlinear Systems (PDF)
L39	Chaos (PDF)
L40	Final Exam

LEC #	TOPICS
1	The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves.
2	Euler's Numerical Method for y'=f(x,y) and its Generalizations.
3	Solving First-order Linear ODE's; Steady-state and Transient Solutions.
4	First-order Substitution Methods: Bernouilli and Homogeneous ODE's.
5	First-order Autonomous ODE's: Qualitative Methods, Applications.
6	Complex Numbers and Complex Exponentials.
7	First-order Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Methods.
8	Continuation; Applications to Temperature, Mixing, RC-circuit, Decay, and Growth Models.
9	Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases.
10	Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations.
11	Theory of General Second-order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians.
12	Continuation: General Theory for Inhomogeneous ODE's. Stability Criteria for the Constant-coefficient ODE's.
13	Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Formulas Involving Ixponentials.
14	Interpretation of the Exceptional Case: Resonance.
15	Introduction to Fourier Series; Basic Formulas for Period 2(pi).
16	Continuation: More General Periods; Even and Odd Functions; Periodic Extension.
17	Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds.
19	Introduction to the Laplace Transform; Basic Formulas.
20	Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's.
21	Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems.
22	Using Laplace Transform to Solve ODE's with Discontinuous Inputs.
23	Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions.
24	Introduction to First-order Systems of ODE's; Solution by Elimination, Geometric Interpretation of a System.
25	Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case).
26	Continuation: Repeated Real Eigenvalues, Complex Eigenvalues.
27	Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients.
28	Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters.
29	Matrix Exponentials; Application to Solving Systems.
30	Decoupling Linear Systems with Constant Coefficients.
31	Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum.
32	Limit Cycles: Existence and Non-existence Criteria.
33	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.

Lecture Notes
Below are the lecture notes for every lecture session. Some lecture sessions also have supplementary files called "Muddy Card Responses." Students pick up half pages of scrap paper when they come into the classroom, jot down on them what they found to be the most confusing point in the day's lecture or the question they would have liked to ask. Responses are then made available to all students on the class Web site.

SES # TOPICS
I. First-order Differential Equations
L0 Simple Models and Separable Equations
L1 Direction Fields, Existence and Uniqueness of Solutions (PDF)
L2 Numerical Methods (PDF)
L3 Linear Equations: Models (PDF)
L4 Solution of Linear Equations, Variation of Parameter (PDF)
L5 Complex Numbers, Complex Exponentials (PDF)
L6 Roots of Unity; Sinusoidal Functions (PDF)
L7 Linear System Response to Exponential and Sinusoidal Input; Gain, Phase Lag (PDF)
L8 Autonomous Equations; The Phase Line, Stability (PDF) Muddy Card Responses (PDF)
L9 Linear vs. Nonlinear (PDF)
L10 Hour Exam I
II. Second-order Linear Equations
L11 The Spring-mass-dashpot Model; Superposition Characteristic Polynomial; Real Roots; Initial Conditions (PDF) Muddy Card Responses (PDF)
L12 Complex Roots; Damping Conditions (PDF)
L13 Inhomogeneous Equations, Superposition (PDF)
L14 Operators and Exponential Signals (PDF) Muddy Card Responses (PDF)
L15 Undetermined Coefficients (PDF)
L16 Frequency Response (PDF)
L17 Applications: Guest appearance by EECS Professor Jeff Lang (PDF) Supplementary Notes Driving Through the Dashpot (PDF)
L18 Exponential Shift Law; Resonance (PDF)
L19 Hour Exam II
III. Fourier Series
L20 Fourier Series (PDF)
L21 Operations on Fourier series (PDF) Muddy Card Responses (PDF)
L22 Periodic Solutions; Resonance (PDF)
IV. The Laplace Transform
L23 Step Function and delta Function (PDF)
L24 Step Response, Impulse Response (PDF)
L25 Convolution (PDF)
L26 Laplace Transform: Basic Properties (PDF) Muddy Card Responses (PDF)
L27 Application to ODEs; Partial Fractions (PDF)
L28 Completing the Square; Time Translated Functions (PDF) Muddy Card Responses (PDF)
L29 Pole Diagram (PDF)
L30 Hour Exam III
V. First Order Systems
L31 Linear Systems and Matrices (PDF)
L32 Eigenvalues, Eigenvectors (PDF)
L33 Complex or Repeated Eigenvalues (PDF)
L34 Qualitative Behavior of Linear Systems; Phase Plane (PDF)
L35 Normal Modes and the Matrix Exponential (PDF)
L36 Inhomogeneous Equations: Variation of Parameters Again (PDF) Muddy Card Responses (PDF)
L37 Nonlinear Systems (PDF)
L38 Examples of Nonlinear Systems (PDF)
L39 Chaos (PDF)
L40 Final Exam

Video Lectures
These video lectures of Professor Arthur Mattuck teaching 18.03 were recorded live in the Spring 2003 and do not correspond precisely to the lectures taught in the Spring of 2006. Professor Mattuck has inspired and informed generations of MIT students with his engaging lectures.
The videotaping was made possible by The d'Arbeloff Fund for Excellence in MIT Education.
Note: Lecture 18, 34, and 35 are not available.

LEC # TOPICS
1 The Geometrical View of y'=f(x,y): Direction Fields, Integral Curves.
2 Euler's Numerical Method for y'=f(x,y) and its Generalizations.
3 Solving First-order Linear ODE's; Steady-state and Transient Solutions.
4 First-order Substitution Methods: Bernouilli and Homogeneous ODE's.
5 First-order Autonomous ODE's: Qualitative Methods, Applications.
6 Complex Numbers and Complex Exponentials.
7 First-order Linear with Constant Coefficients: Behavior of Solutions, Use of Complex Methods.
8 Continuation; Applications to Temperature, Mixing, RC-circuit, Decay, and Growth Models.
9 Solving Second-order Linear ODE's with Constant Coefficients: The Three Cases.
10 Continuation: Complex Characteristic Roots; Undamped and Damped Oscillations.
11 Theory of General Second-order Linear Homogeneous ODE's: Superposition, Uniqueness, Wronskians.
12 Continuation: General Theory for Inhomogeneous ODE's. Stability Criteria for the Constant-coefficient ODE's.
13 Finding Particular Sto Inhomogeneous ODE's: Operator and Solution Formulas Involving Ixponentials.
14 Interpretation of the Exceptional Case: Resonance.
15 Introduction to Fourier Series; Basic Formulas for Period 2(pi).
16 Continuation: More General Periods; Even and Odd Functions; Periodic Extension.
17 Finding Particular Solutions via Fourier Series; Resonant Terms; Hearing Musical Sounds.
19 Introduction to the Laplace Transform; Basic Formulas.
20 Derivative Formulas; Using the Laplace Transform to Solve Linear ODE's.
21 Convolution Formula: Proof, Connection with Laplace Transform, Application to Physical Problems.
22 Using Laplace Transform to Solve ODE's with Discontinuous Inputs.
23 Use with Impulse Inputs; Dirac Delta Function, Weight and Transfer Functions.
24 Introduction to First-order Systems of ODE's; Solution by Elimination, Geometric Interpretation of a System.
25 Homogeneous Linear Systems with Constant Coefficients: Solution via Matrix Eigenvalues (Real and Distinct Case).
26 Continuation: Repeated Real Eigenvalues, Complex Eigenvalues.
27 Sketching Solutions of 2x2 Homogeneous Linear System with Constant Coefficients.
28 Matrix Methods for Inhomogeneous Systems: Theory, Fundamental Matrix, Variation of Parameters.
29 Matrix Exponentials; Application to Solving Systems.
30 Decoupling Linear Systems with Constant Coefficients.
31 Non-linear Autonomous Systems: Finding the Critical Points and Sketching Trajectories; the Non-linear Pendulum.
32 Limit Cycles: Existence and Non-existence Criteria.
33 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.

ENGINEERING PPT

Pages

Search This Blog