AMATH 351 SLN 10197, MWF 10:30-11:20, AND 010
(Prerequisites: MATH 126 or MATH 136)
Introduction to Differential Equations and Applications
Instructor: |
Melissa
Vellela |
TA: Peizhe Shi |
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Course Description
Introductory survey of ordinary differential
equations. Linear and nonlinear
equations.
Textbook
P. Blanchard, R. L. Devaney, G. R. Hall, Differential
Equations (3rd Edition) Brooks/Cole, 2006
Other (optional) references:
W. E. Boyce & R. C. DiPrima, Elementary Differential Equations and Boundary
Value Problems (8th Edition) (ISBN 0-471-43338-1) John Wiley & Sons, 2004.
Syllabus
(1) First-Order Equations: Introduction to modeling. Guessing solutions,
separation of variables, integrating factors, changing variables. Slope fields
and Euler's Method. Existence and uniqueness. Equilibria and bifurcations.
(2) First-Order Systems: Modeling with systems. Phase plane analysis.
Decoupled systems and writing second order equations as systems.
(3) Linear Systems: Review of linear algebra. Solutions involving real
and complex eigenvalues. Phase plane analysis and the trace-determinant plane.
Midterm Exam
(4) Second Order Equations: Harmonic oscillators. Sinusoidal forcing, undamped
forcing and resonance. Steady state solutions. Method of variation of
parameters and series solutions.
(5) Nonlinear Equations: Equilibrium point analysis. Qualitative methods. Hamiltonian and dissipative systems.
(6) Laplace Transforms:
Final Exam
Schedule and Homework
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Homework and Exams |
Homework Due Date |
Homework Problem Sets |
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First day of classes |
Wednesday, September 26th |
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Homework #1 |
Wednesday, October 3rd |
1.1: 3,4,15,16 1.2: 3,17,25,34 1.8: 1,9,13,20 1.9: 3,7,13,19 |
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Homework #2 |
Wednesday, October 10th |
1.3: 10,15,16,17 (HPG Solver parts are optional) 1.5: 1,2,15,18 1.6: 8,9,20,21,32,43,46 1.7: 2,12,17 |
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Homework #3 |
Wednesday, October 17th |
2.1: 2,7,8,19 2.2: 9,10,11,21,23,24,25,27 2.3: 5,7,12a,19 3.1: 6,16,24 (also show that the two solutions are
linearly independent using the result of problem 32),,34 |
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Homework #4 |
Wednesday, October 24th |
3.2:
(in part c of 1-10, just plot the straight line solutions on paper)
1,3,6,7,9,10,12 3.3: 1,3,4,5,7,8,10 3.4: 3,4,5 (part e can be submitted as a printout or
copied by hand), 9, 10, 11 (parts a and b only), 15 3.5: 2,3,6,7,17,18 |
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Homework #5 |
Friday, November 2nd |
3.6: 2,3,8,9,14,15,22,23 4.1: 1,5,6,11,12,14,20,25 4.2: 1,2,7,12,15,17 NOTE: Melissa’s office hours this week are Tues.
11:30-12:30 and Thurs. 10:30-11:30, still in GUG 415L |
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Midterm Exam |
Wednesday, October 31st |
In class, covers chap. 1-3 (excluding 1.4, 2.4, 2.5,
3.7 and 3.8) Grades on midterm
and hws so far |
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Homework #6 |
Wednesday, November 7th |
This is a 1/2 homework-worth 15 pts. 4.3: 5,12,16,20,21,22 4.4: 6,7 For 10 points EXTRA credit, turn in your midterm
completely corrected (write the new solutions on the backs of the test
pages). You must have the
answers right to receive credit!
These points are added to your homework grade, not your midterm grade. |
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Homework #7 |
Wednesday, November 14th |
Appendix B: 3,6,16,18 Boyce & DiPrima: 2,13 6.1: 1,7,10,11,16,21 6.2: 1,5,11,12,16,17 |
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Homework #8 |
Monday, November 26th |
6.3: 6,11,15,27,29,32 6.4: 3,5,7,8 5.1: 2,4,5,6,8 |
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Homework #9 |
Wednesday, December 5th |
5.2: 3,5,9,14,17 5.3: 1, 4,5,9,10,14 5.4: 1,12,15,20,22 |
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Last day of quarter |
Friday, December 7th |
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Final Exam
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Monday, December 10th, 8:30-10:30 am |
Final Grades |
Grading
Your course grade will be calculated by
weighing your homework, Midterm, and Final grades in the proportions 30%,
30%,and 40% respectively.
Homework problem sets will be assigned weekly.
Homework constitutes 30% of your final grade and no assignments will be
dropped. Late assignments will NOT BE ACCEPTED unless extenuating circumstances
can be proved.
Each homework assignment is worth 25 points. Four
problems are graded thoroughly and worth 5 points each and
the remaining 5 points is for completeness.
Tutorials
Extra Help is available in the differential equations workshop run by Jonathan Claridge:
Mondays, Wednesdays, 11:30-1:30 in GUG 415L
Tuesdays, Thursdays, 5:30-7:30 in GUG 218
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Thu Jun 16 18:58:26 PDT 2005 |