|Student Learning Outcomes -|
- Students will model continuous processes using differential equations and use the model to answer related questions.
- Students will develop conceptual understanding of mathematical modeling of continuous processes and their rates of change. They will learn to demonstrate and communicate this understanding in a variety of ways, such as: reasoning with definitions and theorems, connecting concepts, and connecting multiple representations, as appropriate.
- Students will demonstrate the ability to solve differential equations and verify their solutions analytically, numerically, graphically, and qualitatively.
|Description - |
|Differential equations and selected topics of mathematical analysis.|
|Course Objectives - |
|The student will be able to: |
- Classify differential equations by order, linearity, separability, exactness, coefficient fuctions, homogeneity, type of any nonhomogeneities, and other qualities.
- Identify appropriate analytic, numerical, and graphical techniques for solving or approximating solutions to differential equations of the particular classes specified in the expanded description of course content.
- Solve differential equations with appropriate analytic techniques.
- Approximate solutions to differential equations with appropriate numeric techniques.
- Investigate solutions to differential equations with appropriate graphical techniques.
- Verify solutions to differential equations analytically, numerically, graphically, and qualitatively.
- Write differential equations and initial value problems to model phenomena in the physical, life, and social sciences.
- Interpret solutions to differential equations and initial value problems in context.
- Discuss differential equations and their solutions in accurate mathematical language and notation.
- Investigate solutions to differential equations using at least one numerical or graphing utility.
|Special Facilities and/or Equipment - |
- Graphing calculator
- When taught hybrid: Four lecture hours per week in face-to-face contact and one hour per week using CCC Confer. Students need internet access.
|Course Content (Body of knowledge) - |
- Classes of Differential Equations
- First Order
- Second Order
- Constant Coefficient
- Polynomial Coefficient
- Higher-Order Linear
- Other continuous functions
- Discontinuous functions
- Initial Value Problems
- Existence and Uniqueness Theorem
- Systems of Linear Differential Equations
- Techniques for Solving Differential Equations
- Separation of variables
- Integrating factors
- Characteristic Equations
- Distinct real roots
- Repeated real roots
- Complex roots
- Fundamental solutions
- Superposition principle
- Undetermined coefficients
- Variation of parameters
- Annihilator method
- Reduction of order
- Laplace transforms
- Power series
- Method of Frobenius
- Matrix methods
- Euler's method
- Improved Euler's method (predictor-corrector)
- Graphical analysis
- Applications selected from the following topics
- Population models
- Predator-prey models
- Thresholds and carrying capacities
- Growth and decay
- Mixing problems
- Spring-mass systems
- Electrical circuits
- Newton's Laws
- Falling bodies
- Torricelli's Law
- Financial applications
- Compound interest
- Time value of money
- Communication models
- Spread of a rumor
- Mass marketing
- Public health models
- Health care utilization
|Methods of Evaluation - |
- Class Participation
- Term Paper(s)
- Computer Lab Assignment(s)
- Term Project
- Unit Exam(s)
- Proctored Comprehensive Final Examination
|Representative Text(s) - |
|Nagle R., Saff E., Snyder D.. Fundamentals of Differential Equations. 8th ed. Pearson, 2011. |
|Disciplines - |
|Method of Instruction - |
- Cooperative learning exercises
|Lab Content - |
|Not applicable. |
|Types and/or Examples of Required Reading, Writing and Outside of Class Assignments - |
- Homework Problems: Homework problems covering subject matter from text and related material ranging from 15 - 30 problems per week
- Students will need to employ critical thinking in order to complete assignments
- Lecture: Five hours per week of lecture covering subject matter from text and related material. Reading and study of the textbook, related materials and notes
- Projects: Student projects covering subject matter from textbook and related materials. Projects will require students to discuss mathematical problems,write solutions in accurate mathematical language and notation and interpret mathematical solutions. Projects may require the use of a computer algebra system such as Mathematica or MATLAB
- Worksheets: Problems and activities covering the subject matter. Such problems and activities will require students to think critically. Such worksheets may be completed both inside and/or outside of class