AMATH 351 SLN 10204, MWF 10:30-11:20, LOW 113
(Prerequisites: MATH 126 or MATH 136)
Introduction to Differential Equations and Applications
Instructor: |
Melissa
Vellela |
TA: Justine Gunog Seo |
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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 and Reading |
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First day of classes |
Monday, January 7th |
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Homework #1 |
Wednesday, January 16th |
1.1: 3,4,15,16 1.2: 3,17,25,34 1.8: 1,9,13,20 1.9: 3,7,13,19 Reading: sections
2.1-2.2 |
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Friday, January 18th |
Reading: sections 2.2-2.3 |
Martin Luther King Jr. Day |
Monday, January 21st |
No Class |
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Homework #2 |
Wednesday, January 23rd |
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 Reading: section 3.1 |
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Friday, January 25th |
Reading: section 3.2 |
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Monday, January 28th |
Reading: 3.3 |
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Homework #3 |
Wednesday, January 30th |
2.1: 2,7,8,19 2.2: 9,10,11,21,23,24,25,27 2.3: 5,7,12a,19 3.1: 3,6,16,24,34 HPG Solver parts are optional Reading: 3.4 |
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Friday, February 1st |
Reading: 3.5 |
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Monday, February 4th |
Reading: 3.6, 3.7 |
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Homework #4 |
Wednesday, February 6th |
3.2: 1,3,6,7,9,10,12 (HPGS optional) 3.3: 1,3,4,5,7,8,10 3.4: 3,4,5,9,10,11 (part e optional), 15 3.5: 2,3,6,7,17,18 Reading: 4.1 |
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Friday, February 8th |
Reading: 4.2 |
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Monday, February 11th |
Review for Midterm |
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Midterm Exam |
Wednesday, February 13th |
Covers Chapters 1,2 and 3 (excluding 1.4, 2.4, 2.5,
3.7, 3.8), here is last quarter’s midterm, solutions Here are the grades
so far |
Homework #5 |
Friday, February 15th |
3.6: 2,3,8,9,14,15,22,23 (It is suggested that you
do these problems BEFORE the midterm) 4.1: 1,5,6,11,12,14,20,25 4.2: 1,2,7,12,15,17 Reading: 4.3,4.4 |
President’s Day |
Monday, February 18th |
No Class |
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Homework #6 |
Wednesday, February 20th |
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 (you can write the new solutions on the back of the
pages). You must get the answers
right to receive credit. These
points will be added to your homework grade, not your midterm grade. Reading: Boyce & Diprima Handout |
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Friday, February 22nd |
Reading: 6.1 |
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Monday, February 25th |
Reading: 6.2 |
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Homework #7 |
Wednesday, February 27th |
Appendix B: 3,6,16,18 Boyce & DiPrima: 2,13 6.1: 1,7,10,11,16,21 Reading: 6.3 |
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Friday, February 29th |
Reading: 6.4 |
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Monday, March 3rd |
Reading: 5.1, 5.2 |
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Homework #8 |
Wednesday, March 5th |
6.2: 1,5,11,12,16,17 6.3: 6,11,15,27,29,32 6.4: 3,5,7,8 Reading: 5.3 |
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Friday, March 7th |
Reading: 5.4 |
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Monday, March 10th |
Review: Chapters 1-3 |
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Homework #9 |
Wednesday, March 12th |
5.1: 2,4,5,6,8 5.2: 3,5,9,14,17 5.3: 4,9,10,14 5.4: 1,15,20,22 Review: Chapters 4-6 |
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Last day of quarter |
Friday, March 14th |
MATLAB Demo |
Final Exam
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Monday, March 17th, 8:30-10:30 am |
Last quarter’s final, solution
to the final, and grades so far 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 for 5 points each and the
remaining 5 points is for completeness.
Tutorials
There are no Tutorials for this class.
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Thu Jun 16 18:58:26 PDT 2005 |