Discipline: Mathematics
Originator: Mary Margarita Legner

Riverside Community College District
Integrated Course Outline of Record

Mathematics 2
MAT-2 : Differential Equations
College:
Lecture Hours: 72.000
Outside-of-Class Hours: 144.000
Units: 4.00
Grading Methods: Pass/No Pass
Letter Grade
Course Description
Prerequisite: MAT-1B
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:
  1. Evaluate definite and indefinite integrals using techniques of integration.
    • MAT-1B - Evaluate definite, indefinite, and improper integrals.
  2. Represent functions as power series and apply power series to differentiation and integration.
    • MAT-1B - Employ the concepts of convergence and divergence of infinite sequences and series.
  3. Evaluate improper integrals.
    • MAT-1B - Evaluate definite, indefinite, and improper integrals.
  4. Solve applications using integration.
    • MAT-1B - Solve applications using integration.
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities:
  1. Create and analyze mathematics models physical and biological sciences using ordinary differential equations.
  2. Apply the existence and uniqueness theorems for ordinary differential equations.
  3. Identify and solve separable, exact, homogeneous, Bernoulli, and linear first-order differential equations.
  4. Recognize and solve higher-order homogeneous and non-homogeneous linear differential equations.
  5. Find power series solutions to differential equations about ordinary and singular points.
  6. Determine the Laplace Transform and inverse Laplace Transform of functions.
  7. 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:
  1. 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 higher-order 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.
  2. Apply the existence and uniqueness theorems for ordinary differential equations.
    • Critical Thinking: Students will be able to demonstrate higher-order 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.
  3. 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:
  1. Solutions of ordinary differential equations
  2. Solving first order differential equations
    1. separable
    2. linear
    3. exact
    4. homogeneous/substitution
    5. Bernoulli equations
  3. Existence and uniqueness of solutions
  4. Applications of first-order differential equations
    1. orthogonal and oblique trajectories
    2. mechanics
    3. circuits
    4. population modeling
    5. mixture problems
    6. slope fields
  5. Fundamental solutions, independence, and the Wronskian
  6. Explicit methods of solving higher-order homogeneous and nonhomogeneous differential equations
    1. reduction of order
    2. constant coefficients
    3. undetermined coefficients
    4. variation of parameters
    5. Cauchy- Euler equations
  7. Applications of higher-order linear differential equations
    1. harmonic oscillation
    2. electric circuit problems
  8. Series solutions of differential equations
    1. review of radius of convergence and interval of convergence
    2. series solutions about ordinary and singular points
  9. Laplace transforms
    1. Laplace transforms
    2. inverse Laplace transforms
    3. convolutions
    4. delta functions
    5. applications
  10. 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, first-order and higher order (homogeneous and non-homogeneous) 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 first-order linear differential equations,  and Laplace transforms / inverse Laplace transforms of functions.
  • Drills and pattern practices utilizing hand-outs and/or computer-based 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, computer-based 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:
Outside-of-Class 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.
Outside-of-Class 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 Outside-of-Class 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)
C-ID#: MATH 240
Board of Trustees Approval Date: 11/13/2018
COR Rev Date: 11/13/2018