  
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 facetoface contact and one hour per week using CCC Confer. Students need internet access.

Course Content (Body of knowledge)  
  Classes of Differential Equations
 First Order
 Linear
 Separable
 Exact
 Second Order
 Linear
 Constant Coefficient
 Polynomial Coefficient
 HigherOrder Linear
 Autonomous
 Homogeneous
 Nonhomogeneous
 Polynomial
 Exponential
 Sinusoid
 Other continuous functions
 Discontinuous functions
 Impulses
 Initial Value Problems
 Existence and Uniqueness Theorem
 Applications
 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 (predictorcorrector)
 Graphical analysis
 Applications selected from the following topics
 Population models
 Predatorprey models
 Thresholds and carrying capacities
 Growth and decay
 Mixing problems
 Springmass systems
 Undamped
 Damped
 Electrical circuits
 Inductorcapacitor
 Resistorinductorcapacitor
 Newton's Laws
 Falling bodies
 Pendulums
 Cooling
 Torricelli's Law
 Financial applications
 Compound interest
 Time value of money
 Annuities
 Communication models
 Spread of a rumor
 Mass marketing
 Public health models
 Epidemics
 Health care utilization

Methods of Evaluation  
  Homework
 Class Participation
 Term Paper(s)
 Presentation(s)
 Computer Lab Assignment(s)
 Term Project
 Quizzes
 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  
 Mathematics


Method of Instruction  
  Lecture
 Discussion
 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
