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Differential Equations

Testing Guidelines:
The following exams should be scheduled:
1. A one-hour exam at the end of the First Quarter.
2. A one-session exam at the end of the Second Quarter.
3. A one-hour 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 non-credit 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: 1-19 odd
3 2.1 Linear Equations; Integrating Factors P. 39: 1,3,13-19 odd
4 2.2 Separable Equations P. 47: 1-19 odd
5 2.2 Separable Equations (Homogeneous) P. 47: 30-37 all
6 2.4 Difference between Linear and Non-Linear Equations P. 75: 1,3
7
 
2.4 Difference between Linear and Non-Linear Equations
( Bernoulli Equations )
P. 75: 27-31 all
 
8 2.6 Exact Equations P. 99: 1-15 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: 1-17 odd
12 3.3 Complex Roots P. 163 1-21 odd
13 3.4 Repeated Roots P. 171: 1-13 odd
14 3.5 Non-homogeneous Equations (Undetermined Coefficients) P. 183 1-17 odd
15 3.7 Mechanical and Electrical Vibrations P. 202 1-7 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: 1-9 odd
21 6.2 Initial Value Problems (Inverse Transform) P. 320: 11-17 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: 1-7 odd
25 8.2 Improved Euler’s Method P. 458: 1,3,5
26 8.3 Runge-Kutta 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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