Exams
This semesters exam information can be found below...
- Exam 1: 1.1-3.1, Sept 23, 2010
Major Topics:
- Graphing direction fields, graphing integral (solution) curves
- Undertermined Coefficients
- Method of integrating factors
- Seperable equations
- Critical points, stable/unstable equilibrium
- Explicit vs Implicit solutions
- Exact Equations
- Inverses, determinants, eigenvalues, eigenvectors for 2x2
matrices
Suggested Problems:
- 1.1#14,28
- 1.2#10
- 2.1#19,20,24,25,26
- 2.2#5,7,14,21
- 2.5#3,4,15
- 2.6#1-12
- 3.1#1-12#20,23,29,34
- Exam 2: 3.2-3.6,7.1-7.4,4.1-4.4, October 21, 2010
Major Topics:
- Systems of Linear ODE's (and with Constant Coefficients)
- Eigenvalues of a 2x2 matrix (various cases)
- Eigenvectors of a 2x2 matrix
- Finding critical points
- Classifying critical points
- Graphing Phase plane in the vicinity of a critical point
- Autonomous systems and stability
- Jacobian matrix
- Applications - Competing species, Predator Prey
- Applications - Mass/Spring system, Pendulum, RLC circuits
- Wronskiian
- Cauchy-Euler equations
Suggested Problems:
- 3.2#12,13,18
- 3.3#11,12,18
- 3.4#11,12
- 3.5#1,7
- 3.6#13,14,15
- 7.1#3,6
- 7.2#13,14,15
- 7.3#1,2,3
- 7.4#1,2,3,4,5
- 4.1#8,9,10
- 4.2#2,4,7,8,10
- 4.3#1,2,10
- 4.4#6,9,11,13,34,35
- Exam 3: 4.6,4.8,5.1-5.6, November 18, 2010
Major Topics:
- Method of Undetermined Coefficients
- Variation of Parameters (single second order, first order system)
- Computing Laplace transform from the definition.
- Method of partial fractions
- Finding the inverse laplace transform
- Solving differential equations with piecewise continuous, or
periodic forcing terms.
Suggested Problems:
- 4.6#3,8,18
- 4.8#3,13,14,19,30
- 5.1#17,25
- 5.2#5,9,16
- 5.3#3,6,15,23
- 5.4#19,13
- 5.5#7,14,18,22
- 5.6#8,11,12
- 5.7#1,9,11
- 5.8#6,12,17
- 2.7#2,9,14,23 [computer based]
- 2.8#2,9,16 [computer based]
- Final Exam:
Section 513 - 8:00-10:00 am, Dec. 15, 2010
Section 514 - 1:00-3:00 pm, Dec. 15, 2010