Mathematics 3350 – Distance Education

Descriptive Title: Higher Mathematics for Engineers and Scientists I

Prerequisites: C in 2350 (or equivalent transfer credit)

About the Course:   This course covers topics in ordinary differential equations. Topics to be covered include: first-order differential equations; modeling with first-order differential equations; higher-order differential equations; modeling with higher-order differential equations; the Laplace transform and application to solving differential equations; power series solutions of differential equations.

Text: Advanced Engineering Mathematics 4rd Edition by Dennis G. Zill and Michael R. Cullen, published by Jones & Bartlett

Computer Software and Web-based Instruction

For some students “just reading the book” will not be enough to prepare them to work homework problems and do well on exams. In such cases students are encouraged to take advantage of a number of helpful sources. We mention several such sources here.

There are some web sites that contain useful information to supplement the discussion in the book. Students are strongly encouraged to check out the information on these web sites for each block of material covered in the book.

The first is Paul’s Online Math Notes

http://tutorial.math.lamar.edu/Classes/DE/DE.aspx

The second is the SOS Mathematics Page for Differential Equations

http://www.sosmath.com/diffeq/diffeq.html

Khan Academy Videos (videos in alphabetical order, scroll down to differential equations)

Khan Academy Videos

Learning Assessment

Students will be regularly assigned online homework and tests using WeBWorK. The students are encouraged to carefully read the information on using WeBWork at the following links.

Introduction to WeBWork.pdf

Students should also read the tutorial on entering answers in WeBWork

How to Enter Answers in WeBWork.pdf 

Link to WeBWork Account

Click Here to Access your WeBWork Account

Your login name is your eraider name (lowercase) and your password  is initially set as your TTU R Number (including the R). (You should change your password to something more private)

Most of the exercises covered in this course can be easily solved using any one of a number of available Computer Algebra Systems (CAS). These include, for example, Maple and  Mathematica are commercial software and XCAS is a free CAS that runs on most modern platforms.  There is also a freely available website  Wolfram Alpha that can be accessed through a  browser.  I encourage you to become familiar with these powerful tools BUT keep in mind that the course is concerned with your learning to think, enhance and reinforce your math proficiency   and develop analytical problems solving skills.  You are welcome and encouraged to use any resources available to you in doing the homework BUT  the only  tools you are allowed on tests (and, in particular, the final) is your own brain.  You are strongly encouraged to learn how to do the problems by yourself and use these other tools for confidence reinforcement. Once you have completed the course the software tools can be very useful in practical real world situations.  Of course, there is no replacement for thinking.

Students will be expected to take a final comprehensive examination on a specific date.  The date and time of the final exam is expected to be scheduled and communicated to the students during the first two weeks of classes. Students will be required to take the final examination in a supervised environment. Depending on their geographic location, each student and instructor will need to make arrangements with a certified testing service. In case no agreeable solution can be found, the University Testing Services will be designated to administer the examination.

Determination of Final Grades

Homework ..........................  10%

Tests (3)..............................  20% each

Final Exam ........................   30%

Total ..................................   100%

Upon completion of M3350, students will be able to:

1. (A) Recognize an ordinary differential equation and determine whether it is linear or nonlinear. Understand the definition of a general solution and the solution of the initial value problem (IVP). Apply the fundamental existence and uniqueness theorem for first order IVPs.
   

2. (B)  Solve a variety of first order differential equations and IVPs including:
   

separable, first order linear, exact, Bernoulli, and homogeneous equations;

3. (C)  Compute the general solution and find the solution of the IVP for homogeneous linear differential equations including constant coefficient second and higher order equations and Euler-Cauchy equations. Learn the methods of undetermined coefficients and variation of parameters for solving non-homogenous problems;
   

4. (D)  Use Laplace transforms to solve differential and integral equations. Use of the Heaviside function, convolutions and the Dirac delta function;
   

5. (E)  Find power series solutions for non-constant coefficient linear IVPs;
   

6. (F)  Introduction to Maple with application to solving ODEs.
   

 

Course Outline

Chapter 1: (1.1, 1.2) Introduction .....................................................     2-4 hours

Chapter 2: (2.1-2.8) First-Order Differential Equations ...................... 9-18 hours

Chapter 3 : (3.1-3.6, 3.8) Higher-Order Differential Equation .........  10-20 hours

Chapter 4 : (4.1-4.5) Laplace Transforms .........................................  9-18 hours

Chapter 5 : (5.1) Series Solutions of Linear Equations .....................    4-8 hours

Total number of hours for Math 3350 ............................................... 34-68 hours

Note: The necessary time to cover the sections from the text-book and web resources depend on many factors, such as: concentration level, background, major, and individual academic skills. The necessary time for homework completion, practice tests and test-taking is not included in this estimate. For each semester-based course, students should expect to devote the amount of time necessary to understand the material and be able to work problems based on the material.