Kalamazoo Valley Community College



Kalamazoo Valley Community College

Class Assignment Schedule

Math 264

Differential Equations

Instructor: Daniel Cunningham

Office: 7470 @TTC

Office Hours: To be announced

Phone: (269) 488-4173

e-mail: dcunningham@kvcc.edu

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Textbook and other materials:

❖ Advanced Engineering Mathematics (3th edition)-Dennis Zill & Michael Cullen

❖ Graphing Calculator strongly suggested TI-83,TI-86

(TI- 92 or TI -89 will be limited)

➢ text book, working paper, and pencils are required for each class

Prerequisite:

Working knowledge of Calculus III and a recent completion of Math 260 with a grade at least 2.0

Course Description:

This is a first course in linear algebra and differential equations. Techniques of linear algebra are applied to the solution of differential equations. Topics coved include first order differential equations and applications, matrices, vector spaces, linear transformations, linear differential equations, systems of differential equations, and Laplace Transforms.

Course Objectives:

Upon successful completion of the Course, students will have knowledge of topics in differential equations and linear algebra.

1. Know fundamental concepts and symbols of differential equations

1. Identify different examples of differential equations

2. Recognize terminologies and symbols of differential equations

3. Identify families of solutions

4. List different theorems

2. Solve equations of order one

2.1 Solve equations by separation

2.2 Solve homogeneous equations

2.3 Solve exact equation

2.4 Solve linear equation

2.5 Solve Bernoulli’s equations

3. Demonstrate applications of differential equations

3.1 Use Newton’s Law of cooling

3.2 Solve velocity of escape problems

3.3 solve logistic growth problems

4. Construct Matrices for differential equations

4.1 Introduce linear systems

4.2 Show Gaussian elimination methods

4.3 Show matrix operations

4.4 Show vector space and subspace

4.5 Manipulate linear combinations and independence of vectors

5. Solve equations of higher order

5.1 Identify second order linear equation

5.2 Solve homogeneous equations with constant coefficients

5.3 Identify undetermined coefficient and variation of parameters

5.4 Identify eigenvalues

5.5 Solve Laplace transformation and inverse

6. Integrate systems of differential equations with matrices

6.1 Solve first order system and application

6.2 Introduce the eigenvalue method for linear systems

6.3 Solve for distinct eigenvalue solution

6.4 Solve for multiple eigenvalue solution

6.5 Solve for imaginary eigenvalue solution

Attendance:

Every session will be of great importance to your learning this course. However, if it is necessary to miss any class period(s), you will be responsible for any announcements made, sections covered, and assignments dropped off during your absence.

Regular attendance is essential for success in this class

Grading scale:

100%-90% = 4.0 74%-70% = 2.0

89%-85% = 3.5 69%-65% =1.5

84%-80% = 3.0 64%-60% =1.0

79%-75% = 2.5 below 0.0

Distribution of grades:

Participation 4%

Homework/in-class work 16%

Tests (4) 80%

Total 100%

Participation

Students should participate in homework discussion. Students may be asked at times to put solutions on the board from assigned homework problems.

Homework

Homework will be assigned daily and collected periodically during the course of the semester at the beginning of class (turn in assignment during class). Any problems encountered may be discussed in the class. Homework should be stapled and neat (answers circle when possible).

Late assignments will not be accepted

In-class work

Assignments that are assigned in class will count towards the homework grade.

Tests

Tests will be given about every 3 to 4 weeks. Unexcused or missed test will be counted as a ZERO. The Tests will cover only those sections that were covered during the course. Each test will cover about an hour and a half of a class period. (Take advance of each test)

Academic Dishonesty

Any use of form of unauthorized aid or obtaining any help from another individual during test is considered cheating. Any student caught cheating on a test will automatically receive a ZERO for the test. A formal report will be filed. Dishonesty in academic work is considered a serious offense by the College Community.

Tentative assignment schedule

(Material and dates may change to meet the need of the class)

Weeks Sections assignments

1

1.1 DEFN and Terminology (2,4,6,8,21,23,27,28,33,34)

1.2 Initial-Value Problem (2,3,4,7,8,12,14)

1.3 Differential Equation as Mathematical Models (summary)

2.2 Separation of Variable (2,4,5,6,7,8,10,12, 15,16,18,23,26)

2 2.3 Linear Equation (1,4,5,6,8,12,17,22,25,26,28,36)

2.4 Exact Equation(2,4,10,12,21,22,24,28,39(a))

3

5. Solution by Substitution/Bernoulli Equation

(Substition-2,3,6,7,8,11,12, Bernoulli -16,18,21,22)

4 2.7 Linear Models (Growth-1,2,4,6,10 Newton’s 13,14,15, 16**)

TEST 1

5

3.1 Linear Equation (preliminary theory) (2,4,15,16,18,21,23,25,26,30,38**)

3.3 Homogeneous Linear Equation

(1, 2,8,10,13,15,16,18,24,29,30,32,33,40,50)

6. 3.4 Undetermined Coefficients (1,2,4,8,10,13,22,27,28,29)

3.5 Variation of Parameters(DNT)(1,2,19,20)

7 3.6 Cauchy-Euler Equation (DNT) (1)

3.7 Tayor(nonlinear) (13,14,15,16)

3.8 Linear Models:IVP(3.81- 3.82) (1,3,5,6,8,9,10**)

8 3.11 Solving systems of Linear Equations (1,2,3,7,11,15)

TEST 2

9 4.1 DEFN of Laplace Transform (1,2,9,11,12,13,15,16,19,20,22,24,26,27,37*)

4.2 Inverse Transform and transform of derivatives

(1,2,4,6,12,16,18,19,28,30,31,33,36,38)

10 8.1 Matrix Algebra (12,16-26even, 27)

8.2 System of linear Algebraic Equation (1,6,7,8,11,12,16,17,20)

8.3 Rank of Matrix(5,7,8,11,12)

8.4 Determinants (10,12,14,20,22,24,29,30)

8.5 Properties of determinants (11,12,13,14,15,16,36)

11

8.6 Inverse of a Matrix (6-12 even,16,20,28,32,44,48,51)

8.8 The Eigenvalue Problem (3,4, 14-20 even)

12

13. Cryptography(1,5,9,13) - Optional - if we have time

TEST 3

13

10.1 preliminary theory (2,4,6,12,13)

10.2 Homogeneous Linear system (Distinct Real Eigenvalues) (1,2,6,8,14)

14

10.2 …continue Homogeneous Linear system (Repeated/Complex) (Repeated-20,22,26,30) Complex- (33,39,43,45)

Review

15. Final Exam

Students will need to spend a tremendous amount of time each day to complete daily assignments and to perform well in class.

My Grades: Keep a record of your grades:

Participation 4%

| | |

Total

(My total participation points- get from teacher) X 4=P

Homework: (16%) TESTS: (80%)

My points Total points My points Total points

________ ________ ________ ________

________ ________ ________ ________

________ ________ ________ ________

________ ________ ________ ________

________ ________ Total

| | |

________ ________

________ ________

________ ________ (My total quiz points/Total points possible) X 80 = T

________ ________

________ ________

________ ________

________ ________

________ ________

________ ________

________ ________ ________ ________

Total

| | |

(My total quiz points/Total points possible) X 16 = H

P+H+T = your percentage (your grade)= _____%

IF YOU ARE UNABLE TO COMPLETE THIS CLASS, PLEASE OFFICIALLY WITHDRAW. OTHERWISE, I AM OBLIGATED TO GIVE YOU A GRADE OF 0.0 WHICH BECOMES PART OF YOUR PERMANENT RECORD, INCLUDING YOUR G.P.A.

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