Course Descriptions & Syllabi

Course Descriptions & Syllabi

Search Course IDs and descriptions for:

Find complete words only

Note: some or all of the courses in the subjects marked as "Transfer" can be used towards a transfer degree: Associate of Science and Arts or Associate of Engineering Science at DACC. Transferability for specific institutions and majors varies. Consult a counselor for this information.

Areas of Study | | MATH211 syllabus




COURSE NUMBER: MATH211
COURSE TITLE:Differential Equations
DIVISION:Sciences
IAI CODE(S): EGR 904 MTH 912
SEMESTER CREDIT HOURS:3
CONTACT HOURS:45
STUDENT ENGAGEMENT HOURS:135
DELIVERY MODE:In-Person

COURSE DESCRIPTION:
This is the first course regarding the theory and application of differential equations. Students will learn graph method, numerical method, and analytical method to solve differential equations with the emphasis in the analytical method. Topics include first-order, second-order and higher-order differential equations; linear systems of differential equations, Laplace transforms, series solutions, and numerical methods. Both the understanding of theoretical concepts and the ability to use manipulative techniques are considered of prime importance.

PREREQUISITES:
MATH140 (Calculus & Analytic Geometry III, M1 900 EGR 903 MTH 903) with a grade of C or better.

NOTES: This course involves a great deal of work on the student's part and it would be nearly impossible for the student to master the content without persistently working the problems. As prerequisite, students are expected to possess the knowledge of calculus I, II, and III. Students are expected to spend an additional 3-4 hours per week outside of class to complete all assignments. To achieve the general education goals and learning outcomes, students will communicate meaningfully in writing while presenting information. Students will translate quantifiable problems into mathematical terms and solve these problems using mathematical operations. Students will construct graphs and charts, interpret them, and draw appropriate conclusions. Course activities include:
  1. Speaking assignments: students will present research individually or in groups using current technology to support the presentation; students will participate in discussions and debates related to the topics in the lessons.
  2. Case Studies: Complex situations and scenarios will be analyzed in cooperative group settings or as homework assignments.
  3. Lectures: This format will include question and answer sessions to provide interactivity between students and the instructor.
  4. Videos or Invited Speakers: Related topics will provide impetus for discussion. The class web page is updated every week, which provides supplemental information such as announcements, lecture notes, homework assignment, and students' grades.


STUDENT LEARNING OUTCOMES:
Students are expected to achieve strong critical thinking skills in terms of problem solving skills. Students are expected to be able to determine from any initial question of any of the following that apply:
  1. the meaning and importance of all given information
  2. the primary unknown for which a solution is desired
  3. all secondary unknowns that will be needed to determine the primary unknown
  4. all formulas and/or theorems that are applicable to a solution, and/or
  5. a proper understanding of the meaning/interpretation of the solution
Upon completion of this course, students will be able to:
  • Use, understand and write all required algebraic symbols and abbreviations
  • Clearly relate interpretation of solutions to standard algebraic and calculus-driven application problems
  • Clearly show work or provide clear explanation as how to setup and generate a solution for application problems
  • Correctly make use of graphing calculators as a supplemental tool and to check work through graphing technique
  • Achieve strong critical thinking skills in terms of problem solving
  • Master the standard elementary techniques for solving differential equations
  • Gain an appreciation for the key role that differential equations play in modeling natural phenomena
  • Use differential equations to formulate and solve real world problems
  • Understand what differential equations are, how they arise, why they are useful, and what they can tell us about the situations they model
  • Use correct differential equations terminology, such as the terms linear, nonlinear, order, general solution, particular solution, explicit solution, implicit solution, separable equations, ordinary differential equation, partial differential equation, existence of solutions, uniqueness of solutions, etc.
  • Verify that a given function is a solution to a differential equation, and to select a particular solution from the integral curves based on initial conditions
  • Determine the general solution to a first order linear differential equation as well as the particular solution specified by an initial condition
  • Solve first order differential equations by the standard methods of separation of variables, integrating factors, exact methods, substitutions, and transformations or show that solutions do not exist
  • Solve certain types of linear differential equations of order greater than one with various input function including discontinuous forcing function
  • Use Laplace transform and series solution methods to obtain solutions and other useful information about the differential equations to which these methods apply
  • Translate physical situations into a differential model, solve, and interpret the solutions, and to obtain other useful information about the problems that they model
  • Use technology including CPP program to solve single differential equations and to solve systems of differential equations by using numerical methods

TOPICAL OUTLINE:
MATH211 is a 16-week course. The following list is the time spent on each topic. Students who successfully complete the course will demonstrate the following outcomes by quizzes, tests and homework. The student should be able to understand and apply the following:
  • Basic definitions and terminology (Week 1 - 2)
    • Solve first-order differential equations by:Separable variables
      • Homogeneous differential equations
      • Exact equations
      • Linear differential equations
      • Equations of Bernoulli, Ricatti, and Clairaut
      • Substitutions
      • Picard's method
  • Applications of first-order differential equations: (Week 3 - 4)
    • Orthogonal trajectories
    • Applications of linear/nonlinear equations
  • Linear Differential equations of higher-order: (Week 5 - 7)
    • Initial-value and boundary-value problems
    • Linear dependence and independence
    • Solutions of linear equations
    • Constructing a second solution from and known solution
    • Homogeneous linear equation with constant coefficients:
      • Undetermined coefficients using superposition approach
      • Differential operators
      • Undetermined coefficient using annihilator approach
      • Variation of Parameters
  • Harmonic, damped, and forced motion (Week 8)
    • Electric circuits and other analogous systems
  • Differential equations with variable coefficients: (Week 9 - 10)
    • Cauchy-Euler equation
    • Power Series solutions
    • Solutions about ordinary points
    • Solutions about singular points (Frobenius)
    • Bessel's equation
    • Legendre's equation
  • Laplace transforms: (Week 11 - 12)
    • Laplace transforms
    • Inverse Laplace transform
    • Translation theorems and derivatives of a transform
    • Transforms of derivatives, integrals, and periodic functions
    • Applications
  • Systems of linear differential equations: (Week 13 - 14)
    • Operator method
    • Laplace transform method
    • Systems of linear first-order equations
    • Introduction to matrices
      • Basic definitions and theories
      • Gaussian and Gauss-Jordan elimination methods
      • The eigenvalue problem
    • Matrices and systems of linear first-order equations
    • Homogeneous linear systems
      • Distinct real eigenvalues
      • Complex eigenvalues
      • Repeated eigenvalues
  • Numerical methods for ordinary differential equations: (Week 15 - 16)
    • Direction fields
    • The Euler methods
    • The three-term Taylor method
    • The Runge-Kutta method
    • Multistep methods
    • Errors and stability
    • Higher order equations and systems
    • Second order boundary-value problems

TEXTBOOK / SPECIAL MATERIALS:

Campbell, Haberman, Introduction to Differential Equations with Boundary Value Problems, Houghton Mifflin.

Mathematica Software, Wolfram Research, Inc., 100 Trade Center Drive, Champaign, IL 61820-7237.

A TI-83 or better calculator is recommended.

See bookstore website for current book(s) at https://www.dacc.edu/bookstore

EVALUATION:

The student will be evaluated on the degree to which student learning outcomes are achieved. A variety of methods may be used, such as tests, quizzes, class attendance and participation, reading assignments, projects, homework, presentations, and a final exam. Students are expected to completely solve problems from homework as each section is assigned. Homework grade will be assigned based on the solution procedure, results, organization, and presentation. Each solution shall be explained with all the detail and diagrams necessary for another person to review. Three major separate sources will contribute to the grade in this course: Four hourly exams are given during the semester, which are composed by solving problems selected from each chapter. These hourly exams (including quizzes and projects) determine 50% of the grade. A comprehensive final exam is given at the end of the semester, which accounts for 30% of the grade. Homework (including presentation) and/or projects using programmable calculators or computers account for 20% of the grade.

Determination of grade based upon all work completed is as follows:
A= 90%-100%
B= 80%-89.9%
C= 70%-79.9%
D= 60%-69.9%
F= < 60%
Grades will be adjusted to reflect the statistical distribution of scores within the class.

BIBLIOGRAPHY:
  • A First Course in Differential Equations with Modeling Applications by Dennis G. Zill, 8th Edition, 2004.
  • Ordinary Differential Equations Introduction and Qualitative Theory, 3rd Edition, Jane Cronin, Chapman and Hall/CRC, 2007.
STUDENT CONDUCT CODE:
Membership in the DACC community brings both rights and responsibility. As a student at DACC, you are expected to exhibit conduct compatible with the educational mission of the College. Academic dishonesty, including but not limited to, cheating and plagiarism, is not tolerated. A DACC student is also required to abide by the acceptable use policies of copyright and peer-to-peer file sharing. It is the student’s responsibility to become familiar with and adhere to the Student Code of Conduct as contained in the DACC Student Handbook. The Student Handbook is available in the Information Office in Vermilion Hall and online at: https://www.dacc.edu/student-handbook

DISABILITY SERVICES:
Any student who feels s/he may need an accommodation based on the impact of a disability should contact the Testing & Academic Services Center at 217-443-8708 (TTY 217-443-8701) or stop by Cannon Hall Room 103. Please speak with your instructor privately to discuss your specific accommodation needs in this course.

REVISION:
Spring 2019

Upcoming Events