MATH 310 Ordinary Differential Equations*

This course includes theory and application of ordinary differential equations including classification, initial and boundary value problems of one variable, exact equations, methods of solving higher-order linear equations, second-order equations with constant coefficients, series solutions, systems of linear equations, Laplace transforms and existence theorems.

Credits

3

Semester Contact Hours Lecture

45

General Education Competency

[GE Core type]

MATH 310Ordinary Differential Equations*

Please note: This is not a course syllabus. A course syllabus is unique to a particular section of a course by instructor. This curriculum guide provides general information about a course.

I. General Information

Department

Mathematics & Engineering

II. Course Specification

Course Type

Program Requirement

General Education Competency

[GE Core type]

Credit Hours Narrative

3

Semester Contact Hours Lecture

45

Grading Method

Letter grade

Repeatable

N

III. Catalog Course Description

This course includes theory and application of ordinary differential equations including classification, initial and boundary value problems of one variable, exact equations, methods of solving higher-order linear equations, second-order equations with constant coefficients, series solutions, systems of linear equations, Laplace transforms and existence theorems.

IV. Student Learning Outcomes

Upon completion of this course, a student will be able to:

• Analyze real-world questions and mathematically structure strategies to model the questions.
• Correctly provide solutions to the models of the questions.
• Communicate the solutions to the questions when analyzed and solved mathematically.

V. Topical Outline (Course Content)

Definitions and terminology including ODE, PDE, order, linear, nonlinear, initial values, solution, solution interval, solution curve, general solution, and particular solution Existence theorem for unique solutions Analytical geometry including direction fields and phase portraits Solution methods for first-order differential equations including separation of variables, linear methods, exact, homogeneous, and numerical methods Applications of first-order differential equations including modeling in physics, chemistry, economics, and population biology Solution methods for second-order and higher differential equations including reduction of order, homogeneous linear equations with constant coefficients, auxiliary equations with complex roots, undetermined coefficients, variation of parameters, systems of equations, and the superposition principle Existence theorems for higher-order differential equations Terminology for higher-order differential equations including linear dependence/independence, Wronskian, fundamental solution set, general solution, and particular solutions Applications of second-order differential equations including spring/mass problems and electrical circuits Series solutions for differential equations including both ordinary points and singular points Laplace transforms and their application to solving differential equations, transform and translation theorems including derivatives , exponential factors (First Translation), step functions (Second), monomial factors (Derivatives of Transforms), and periodic functions Existence theorems for Laplace transforms

VI. Delivery Methodologies