Eigen Methods Math 246, Fall 2009, Professor David Levermore Eigenpairs. Let A be a real nn matrix. A number (possibly complex) is an eigenvalue of A if there exists a nonzero vector v (possibly complex) such that (1) Av = v . Each such vector is an eigen
I. FirstOrder Ordinary Dierential Equations
7. Numerical Methods
C. David Levermore
Department of Mathematics
University of Maryland
December 30, 2013
Contents
7. Numerical Methods
7.1. Numerical Approximation
7.2. Explicit and Implicit Euler Methods
7.3
I. FirstOrder Ordinary Dierential Equations
8. Exact Dierential Forms and Integrating Factors
C. David Levermore
Department of Mathematics
University of Maryland
December 30, 2013
Contents
8. Exact Dierential Forms and Integrating Factors
8.1. Implicit G
I. FirstOrder Ordinary Dierential Equations
9. Special Equations and Substitution
C. David Levermore
Department of Mathematics
University of Maryland
December 30, 2013
Contents
9. Special Equations and Substitution (not covered)
9.1.
9.2.
9.3.
9.4.
Linea
II. HigherOrder Linear Ordinary Dierential Equations
1. Introduction to HigherOrder Linear Equations
C. David Levermore
Department of Mathematics
University of Maryland
December 30, 2013
Contents
1. Introduction to HigherOrder Linear Equations
1.1.
1.2
II. HigherOrder Linear Ordinary Dierential Equations
3. Supplement: Linear Algebraic Systems and Determinants
C. David Levermore
Department of Mathematics
University of Maryland
December 30, 2013
Contents
3. Supplement: Linear Algebraic Systems and Deter
II. HigherOrder Linear Ordinary Dierential Equations
2. Homogeneous Equations: General Methods and Theory
C. David Levermore
Department of Mathematics
University of Maryland
December 30, 2013
Contents
2. Homogeneous Equations: General Methods and Theory
II. HigherOrder Linear Ordinary Dierential Equations
4. Homogeneous Equations with Constant Coecients
C. David Levermore
Department of Mathematics
University of Maryland
December 30, 2013
Contents
4. Homogeneous Equations with Constant Coecients
4.1. Cha
Differential Equations for Scientists and Engineers
MATH math246

Spring 2014
Physics 2220 Midterm 1 Fall 2013 Draft v1
1.) Shown below is a section of an innitely long cylindrical insulator of radius (a), with
uniform volume charge density .
a
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a.) Find an expression for the potential
Differential Equations for Scientists and Engineers
MATH math246

Spring 2014
Eighties 45:? Shahs , 7 or 7 7 7 7
iNAME * Quiz #75; 1211951276
Solution Section 0102
shed.
Ham's] From the cows reference frame, is it possible for the cow to t inside
the barn? If so, what minimum speed must the cow be moving? [leave your
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Differential Equations for Scientists and Engineers
MATH math246

Spring 2014
MULTIPLECHOICE TEST #1 "\../
._3. A 5.0 kilogram object is moving in a straight line_across
Multiple Choice Test #1
simple Mechanics and Conservation Problems
1. A car travels 30 miles at an average speed of 60 miles per
hour and then travals for 30
Assignment 4
2 An amplifier has an input resistance of 2 k. Determine
the feedback resistance needed to give a voltage gain
of 100 for two different types of amplifiers, inverting
and noninverting.
3 Design a summing amplifier circuit that can take an
av
The Giver
Have you ever seen someone who went from ordinary to really important. Perhaps in the news?
Or maybe even at a job? This is what happened to an 11 year old boy named Jonas. Jonas is a
ordinary boy who lived in his town with no color, no bad emot
I. FirstOrder Ordinary Dierential Equations
3. Separable Equations
C. David Levermore
Department of Mathematics
University of Maryland
December 30, 2013
Contents
3. Separable Equations
3.1.
3.2.
3.3.
3.4.
3.5.
Recipe for Autonomous Equations
Recipe for S
I. FirstOrder Ordinary Dierential Equations
6. Applications
C. David Levermore
Department of Mathematics
University of Maryland
December 30, 2013
Contents
6. Applications
6.1.
6.2.
6.3.
6.4.
6.5.
General Guidelines
Tanks and Mixtures
Loans
Motion
Populat
I. FirstOrder Ordinary Dierential Equations
5. Graphical Methods
C. David Levermore
Department of Mathematics
University of Maryland
December 30, 2013
Contents
5. Graphical Methods
5.1.
5.2.
5.3.
5.4.
PhaseLine Portraits for Autonomous Equations
Plots o
Matrix Exponentials Math 246, Fall 2009, Professor David Levermore We now consider the homogeneous constant coecient, vectorvalued initialvalue problem dx (1) = Ax , x(tI ) = xI , dt where A is a constant nn real matrix. A special fundamental matrix ass
ORDINARY DIFFERENTIAL EQUATION: Introduction and FirstOrder Equations David Levermore Department of Mathematics University of Maryland 7 September 2009 Because the presentation of this material in class will dier somewhat from that in the book, I felt th
Math 246, Fall 2009, Professor Levermore 6. FirstOrder Equations: Numerical Methods For many firstorder differential equations analytic methods are either difficult or impossible to apply. If one is interested in understanding how a particular solution
Math 246, Fall 2009, Professor David Levermore 7. Exact Differential Forms and Integrating Factors Let us ask the following question. Given a firstorder ordinary equation in the form (7.1) dy = f (x, y) , dx when do its solutions satisfy a relation of th
HIGHERORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS I: Introduction and Homogeneous Equations David Levermore Department of Mathematics University of Maryland 30 August 2009
Because the presentation of this material in class will dier somewhat from that i
HIGHERORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS II: Nonhomogeneous Equations David Levermore Department of Mathematics University of Maryland 20 October 2009
Because the presentation of this material in class will dier from that in the book, I felt th
HIGHERORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS III: Mechanical Vibrations David Levermore Department of Mathematics University of Maryland 26 October 2009
Because the presentation of this material in class will dier from that in the book, I felt that
HIGHERORDER LINEAR ORDINARY DIFFERENTIAL EQUATIONS IV: Laplace Transform Method David Levermore Department of Mathematics University of Maryland 21 June 2009
Because the presentation of this material in class will dier from that in the book, I felt that
Linear Planar Systems Math 246, Fall 2009, Professor David Levermore We now consider linear systems of the form (1) d dt x y =A x y , where A = a11 a12 a21 a22 .
Here the entries of the coecient matrix A are real constants. Such a system is called planar
MATH 246: Exam 1 Sample 2
1. Find the interval of existence for the following initial value problem. You do not need to solve!
t
dy
dt
+ ty 9 t = 1 with y(4.5) = 3
2. Solve the differential equation explicitly by writing the left hand side as the derivati