For each unit of credit, a minimum of three hours per week with one of the hours for class and two hours for studying/preparation outside of class is expected.
The Mathematics Department at Seward County Community College will enhance a student's ability to think critically using mathematical principles, ideas, and concepts in order to function in a society with ever-changing technology.
Outcome #4: Demonstrate mathematical skills by using a variety of techniques and technologies.
Outcome #5: Demonstrate the ability to think critically by gathering facts, generating insights, analyzing data, and evaluating information.
1. Interpret differential equations both analytically and graphically by identifying if a function solves a differential equation and finding a slope field corresponding to a first-order equation.
2. Solve a variety of differential equations, including both general solutions and solutions to initial value problems. This includes first-order equations that are separable, exact, equations requiring integrating factors such as first-order linear, and equations requiring a change of variables such as Bernouilli equations. This also includes higher-order equations such as homogeneous and nonhomogeneous linear equations with constant coefficients that are solved using undetermined coefficients and variation of parameters.
3. Compute and apply Laplace and inverse Laplace transforms to solve initial value problems.
4. Solve systems of differential equations that are linear with constant coefficients; convert higher order linear equations to systems of first order equations; and find approximate solutions using numerical methods such as Euler’s method and phase plane analysis.
5. Use differential equations to model an application such as logistic growth, and spring-mass systems that include underdamping versus overdamping and resonance.
- Terminology, what constitutes a solution to a differential equation, solutions.
- First Order Differential Equations: Separation of variables, substitution, exact differential equations, integrating factors, approximation methods, and applications.
- Modeling with first-order linear, nonlinear, and systems of differential equations.
- Homogeneous Linear Differential Equations: Terminology, existence theorems, general solution, reduction of order, homogenous linear equations with constant coefficients, repeated roots (both real and complex), undamped vibrations, damped vibrations.
- Non-Homogeneous Differential Equations: General approach, undetermined coefficients, differential operators, inverse differential operators, variation of parameters, applications to mechanical systems, damped forced vibrations, and electrical circuits.
- Laplace Transforms: Definition and general properties, which functions have Laplace transforms, inverse Laplace transforms, initial-valued problems and a step function.
- Systems: The method of elimination and applications.Convert higher order linear equations to systems of first-order equations. Find approximate solutions using numerical methods.
- Lecture/Discussion
- In class and out of class assignments
- Calculator and/or computer exercises
- Calculator demonstrations.
- Examinations
- Individual help
- Online Textbook--the basic classroom material.
- Online WebAssign homework assignments
- Supplemental materials prepared by the instructor which are available on Canvas.
- Computer projector, computer, and The SMART Podium is the major tool used for lecture presentation and demonstrations.
SCCC Outcome 4 will be assessed and measured by class participation, quizzes, and tests.
SCCC Outcome 5 will be assessed and measured by using assignments, tests, and non-traditional problem solving activities.
SCCC Policy
Technical support is available by contacting the SCCC IT Department at itech@sccc.edu
Canvas Help: canvashelp@sccc.edu
Under the Americans with Disabilities Act, Seward County Community College will make reasonable accommodations for students with documented disabilities. If you need support or assistance because of a disability, you may be eligible for academic accommodations. Students should identify themselves to the Mental Health Counselor at 620-417-1106 or go to the Student Success Center in the Hobble Academic building, room A149.