Course Abstract Details

MATH-215, Differential Equations

Credits: 4

Course Description

MATH-215, Differential Equations, includes exact solutions of common types of first-order ordinary differential equations, exact solutions of second-order equations whose coefficients are constant, power series solutions, numerical and graphical techniques, Laplace transform methods, and linear systems. Additional topics may include applications to geometry and mechanics, matrix methods, Sturm-Liouville analysis, special functions, non-linear systems, and Fourier Series Methods. Students will be required to use a graphing calculator and significant mathematical software such as Mathematica, Maple, or MATLAB throughout the course. See Mathematics Department web site for details. Prerequisites: MATH-136 with a "C" grade or better. Five hours lecture each week. Four credits. Four billable hours. Offered Spring Term every even year. GENERAL EDUCATION

Course Objectives and Grading Information

MAJOR COURSE OBJECTIVES: Upon completion of this course, the student should be able to:

1. Classify differential equations by type, order and linearity. (GE2, GE3, PG1, PG3)

2. Solve the separable, exact, linear, homogeneous, and Bernoulli first-order differential equations. (GE3, PG1, PG4)

3. Apply first-order differential equations to Orthogonal Trajectories, Growth and Decay problems, as well as RL- and RC-Circuits. (GE2, GE3, PG1, PG3, PG4)

4. Solve second-order differential equations by constructing a second solution from a known solution. (GE3, PG1, PG4)

5. Solve homogeneous linear equations of second or higher order with constant coefficients. (GE3, PG1, PG4)

6. Solve second- or higher-order differential equation by the method of undetermined coefficients and by the variation of parameters. (GE2, GE3, PG1, PG3, PG4)

7. Apply second-order differential equations to LC- and RLC-Circuits. (GE2, GE3, PG1, PG3, PG4)

8. Solve Cauchy-Euler differential equations. (GE3, PG1, PG4)

9. Solve first- and second-order differential equations with initial conditions using Laplace Transformations. (GE3, PG1, PG4)

10. Solve systems of differential equations with Laplace Transformations. (GE3, PG1, PG4)

11. Solve Eigenvalue problems. (GE3, PG1, PG4)

12. Set-up and solve application problems using technology, such as graphing calculators and mathematical software. (GE1, GE2, GE3, PG1, PG2, PG3, PG4)

REQUIRED TEXTBOOK(S)
Edwards, C.H. and Penney, D.E. Elementary Differential Equations with Boundary Value Problems, 6th edition. Pearson Education/Prentice Hall, 2008. [ISBN-10: 0-13-601828-9]

Learning Goals

The abbreviations in parentheses represent Learning Goals which have been identified for this course and program of study:

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