Discipline: Mathematics
Originator: Mary Margarita Legner
Riverside Community College District
Integrated Course Outline of Record
Mathematics
2
MAT2 : Differential Equations 
College:
Lecture Hours:
72.000 OutsideofClass Hours: 144.000 Units: 4.00 Grading Methods: Pass/No Pass Letter Grade 
Course Description
Prerequisite:
MAT1B
Course Credit Recommendation:
Degree Credit
This is a course in differential equations including both quantitative and qualitative methods as well as applications from a variety of disciplines. Introduces the theoretical aspects of differential equations, including establishing when solution(s) exists, and techniques for obtaining solutions, including linear first and second order differential equations, series solutions, Laplace transforms, linear systems, and elementary applications to the physical and biological sciences. 72 hours lecture. (Letter Grade, or Pass/No Pass option.)
Short Description for Class Schedule
Introduction to differential equations and their applications.
Entrance Skills:
Before entering the course, students should be able to demonstrate the following skills:
Evaluate definite and indefinite integrals using techniques of integration.
 MAT1B  Evaluate definite, indefinite, and improper integrals.

Represent functions as power series and apply power series to differentiation and integration.
 MAT1B  Employ the concepts of convergence and divergence of infinite sequences and series.

Evaluate improper integrals.
 MAT1B  Evaluate definite, indefinite, and improper integrals.

Solve applications using integration.
 MAT1B  Solve applications using integration.
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities: Create and analyze mathematics models physical and biological sciences using ordinary differential equations.
 Apply the existence and uniqueness theorems for ordinary differential equations.
 Identify and solve separable, exact, homogeneous, Bernoulli, and linear firstorder differential equations.
 Recognize and solve higherorder homogeneous and nonhomogeneous linear differential equations.

Find power series solutions to differential equations about ordinary and singular points.
 Determine the Laplace Transform and inverse Laplace Transform of functions.
 Solve linear systems of ordinary differential equations.
Student Learning Outcomes:
Upon successful completion of the course, students should be able to demonstrate the following skills: Apply the appropriate analytical technique for finding the solution of first and higher order ordinary differential equations.
 Critical Thinking: Students will be able to demonstrate higherorder thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
 Apply the existence and uniqueness theorems for ordinary differential equations.
 Critical Thinking: Students will be able to demonstrate higherorder thinking skills about issues, problems, and explanations for which multiple solutions are possible. Students will be able to explore problems and, where possible, solve them. Students will be able to develop, test, and evaluate rival hypotheses. Students will be able to construct sound arguments and evaluate the arguments of others.
 Create and analyze mathematical models using ordinary differential equations.
 Communication Skills: Students will be able to communicate effectively in diverse situations. They will be able to create, express, and interpret meaning in oral, visual, and written forms. They will also be able to demonstrate quantitative literacy and the ability to use graphical, symbolic, and numerical methods to analyze, organize, and interpret data.
Course Content:
 Solutions of ordinary differential equations
 Solving first order differential equations
 separable
 linear
 exact
 homogeneous/substitution
 Bernoulli equations
 Existence and uniqueness of solutions
 Applications of firstorder differential equations
 orthogonal and oblique trajectories
 mechanics
 circuits
 population modeling
 mixture problems
 slope fields
 Fundamental solutions, independence, and the Wronskian
 Explicit methods of solving higherorder homogeneous and nonhomogeneous differential equations
 reduction of order
 constant coefficients
 undetermined coefficients
 variation of parameters
 Cauchy Euler equations
 Applications of higherorder linear differential equations
 harmonic oscillation
 electric circuit problems
 Series solutions of differential equations
 review of radius of convergence and interval of convergence
 series solutions about ordinary and singular points
 Laplace transforms
 Laplace transforms
 inverse Laplace transforms
 convolutions
 delta functions
 applications
 Systems of ordinary linear differential equations
Methods of Instruction:
Methods of instruction used to achieve student learning outcomes may include, but are not limited to, the following activities:
 Class lectures, discussions, student presentations, and demonstrations of separable, exact, firstorder and higher order (homogeneous and nonhomogeneous) linear differential equations, Cauchy Euler linear differential equations, the method of reduction of order and variation of parameters, applications of differential equations to the physical and biological sciences, power series solutions about ordinary and singular points, systems of firstorder linear differential equations, and Laplace transforms / inverse Laplace transforms of functions.
 Drills and pattern practices utilizing handouts and/or computerbased tools in order to assist the students in mastering the techniques involved in solving differential equations and systems of differential equations, visualizing applications to the physical and biological sciences, and obtaining power series solutions.
 Provision and employment of a variety of learning resources such as videos, slides, audio tapes, computerbased tools, manipulatives and worksheets in order to address multiple learning styles and to reinforce the concepts of differential equations.
 Pair and small group activities, discussions, and exercises in order to promote mathematics discovery and enhance problems solving skills in finding the solutions to differential equations.
Methods of Evaluation:
Students will be evaluated for progress in and/or mastery of student learning outcomes using methods of evaluation which may include, but are not limited to, the following activities:
 Written homework assignments and/or computerized homework assignments for correct application of the principles and techniques involved in solving differential equations and systems of differential equations, as well as the correct use of symbols and vocabulary of the subject.
 Quizzes and midterm/final examinations for conceptual understanding as well as correct technique and application of the principles of differential equations and systems of differential equations to include recognition of the appropriate method for a given problem, applications to the physical and biological sciences, power series solutions about ordinary and singular points, and the correct use of Laplace Transforms and inverse Laplace Transforms of functions.
 Classroom discovery activities for content knowledge and conceptual understanding of recognizing and solving a variety of differential equations.
Sample Assignments:
OutsideofClass Reading Assignments
 Read and analyze text, examples, and notes covering topics of differential equations, such as recognizing and solving linear and higher order differential equations and determining the existence and uniqueness of solutions.
OutsideofClass Writing Assignments
 Use the symbols and vocabulary of mathematics to solve application problems in the physical and biological sciences with the use of differential equations.
Other OutsideofClass Assignments
 Problem sets that require students to recognize the type of a differential equation and applying the appropriate method for finding the solutions.
Course Materials:
All materials used in this course will be periodically reviewed to ensure that they are appropriate for college level instruction. Possible texts include the following:
 Boyce,De Prima. Elementary Differential Equations and Boundary Value Problems. 11th Wiley, 2017.
 Trench. Elementary Differential Equations. 1.01th Open Educational Resources, 2013.
 Zill. A First Course in Differential Equation, with Modeling Applications. 11th Brooks/Cole, 2018.
 Zill. A First Course in Differential Equations, The Classic 5th Edition . 5th Brooks/Cole, 2005.
Codes/Dates:
CB03 TOP Code:
1701.00  Mathematics, General
CB05 MOV Transfer Status: Transfers to Both UC/CSU (A)
CB05 NOR Transfer Status: Transfers to Both UC/CSU (A)
CB05 RIV Transfer Status: Transfers to Both UC/CSU (A)
CID#: MATH 240
CB05 MOV Transfer Status: Transfers to Both UC/CSU (A)
CB05 NOR Transfer Status: Transfers to Both UC/CSU (A)
CB05 RIV Transfer Status: Transfers to Both UC/CSU (A)
CID#: MATH 240
Board of Trustees Approval Date:
11/13/2018
COR Rev Date:
11/13/2018