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.
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
Credit Hours Narrative
3 Credits
Semester Contact Hours Lecture
45
Prerequisite Narrative
MATH 175
Grading Method
Letter grade
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