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Differential Equations
Testing Guidelines:
The following exams should be scheduled:
1. A onehour exam at the end of the First Quarter.
2. A onesession exam at the end of the Second Quarter.
3. A onehour exam at the end of the Third Quarter.
4. A one session Final Examination.
Learning Outcomes
for
MAT 2680 Differential Equations
1. Students will classify differential equations .
2. Students will solve first and second order ordinary differential equations
using various
appropriate techniques.
3. When appropriate Students will use numerical methods to approximate solutions
4. Students will apply methods of solving differential equations to answer
questions about
various systems (such as mechanical and electrical).
5. Students will use technology to assist in the above.
New York City College of Technology Policy on Academic
Integrity
Students and all others who work with information, ideas, texts, images, music,
inventions, and
other intellectual property owe their audience and sources accuracy and honesty
in using,
crediting, and citing sources. As a community of intellectual and professional
workers, the
College recognizes its responsibility for providing instruction in information
literacy and
academic integrity, offering models of good practice, and responding vigilantly
and
appropriately to infractions of academic integrity. Accordingly, academic
dishonesty is
prohibited in The City University of New York and at New York City College of
Technology
and is punishable by penalties, including failing grades, suspension, and
expulsion. The complete
text of the College policy on Academic Integrity may be found in the catalog.
Mathematics Department Policy on Lateness/Absence
A student may be absent during the semester without penalty for 10% of the class
instructional
sessions. Therefore,
If the class meets:  The allowable absence is: 
1 time per week 2 times per week 
2 absences per semester 3 absences per semester 
Students who have been excessively absent and failed the
course at the end of the semester will
receive either
• the WU grade if they have attended the course at least once . This includes
students who
stop attending without officially withdrawing from the course.
• the WN grade if they have never attended the course.
In credit bearing courses, the WU and WN grades count as an F in the computation
of the GPA.
While WU and WN grades in noncredit developmental courses do not count in the
GPA, the
WU grade does count toward the limit of 2 attempts for a developmental course.
The official Mathematics Department policy is that two latenesses (this includes
arriving late or
leaving early) is equivalent to one additional absence .
Every withdrawal (official or unofficial) can affect a student’s financial aid
status, because
withdrawal from a course will change the number of credits or equated credits
that are counted
toward financial aid.
Session  First Order  Homework 
1 
1.1 Some Basic Mathematical Models 1.2 Solutions of Some Differential Equation 
P. 16: 1,3 
2  1.3 Classification of Differential Equations  P. 24: 119 odd 
3  2.1 Linear Equations; Integrating Factors  P. 39: 1,3,1319 odd 
4  2.2 Separable Equations  P. 47: 119 odd 
5  2.2 Separable Equations (Homogeneous)  P. 47: 3037 all 
6  2.4 Difference between Linear and NonLinear Equations  P. 75: 1,3 
7 
2.4 Difference between Linear and
NonLinear Equations ( Bernoulli Equations ) 
P. 75: 2731 all 
8  2.6 Exact Equations  P. 99: 115 odd, 18 
9  Exam 1  
10  2.7 Euler’s Method  P. 109: 1,3,11,13 
Second Order  
11  3.1 Homogeneous Equations – Constant Coefficients  P. 144: 117 odd 
12  3.3 Complex Roots  P. 163 121 odd 
13  3.4 Repeated Roots  P. 171: 113 odd 
14  3.5 Nonhomogeneous Equations (Undetermined Coefficients)  P. 183 117 odd 
15  3.7 Mechanical and Electrical Vibrations  P. 202 17 odd, 12 
16  Exam 2  
17  5.2 Series Solutions  P. 259: 1,2,3,5 
18  5.2 Series Solutions  P. 259: 7,9,11,15 
Laplace Transform  
19  6.1 Laplace Transform  P. 311: 1,5 
20  6.2 Initial Value Problems (Inverse Transform)  P. 320: 19 odd 
21  6.2 Initial Value Problems (Inverse Transform)  P. 320: 1117 odd 
22  6.6 Convolution Integral (Optional)  P. 351: 5,7,9 
23  Exam 3  
Numerical Methods  
24  8.1 Euler’s Methods  P. 451: 17 odd 
25  8.2 Improved Euler’s Method  P. 458: 1,3,5 
26  8.3 RungeKutta  P. 463: 1,3,5 
27  8.4 Multistep Methods  P. 469: 1,3,5 
28  Exam 4  
29  Review  
30  Final Exam 
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