Discipline: Mathematics Degree Credit  [X]
Non Credit  [ ]
Nondegree Credit  [ ]
Comm Service  [ ]
 

Riverside Community College District
Integrated Course Outline of Record

Mathematics 2


COURSE DESCRIPTION
2 Differential Equations Units: 4.00
 
Prerequisite(s): MAT 1B: Calculus II
Special types of differential equations, linear first and second order differential equations, series solutions, Laplace transforms, matrix theory, and elementary applications to the physical and biological sciences. 72 hours lecture.
 
SHORT DESCRIPTION FOR CLASS SCHEDULE
Introduction to differential equations and their applications.
 
ADVISORY ENTRY SKILLS
Before entering the course, students will be able to:
  1. Evaluate definite and indefinite integrals using techniques of integration.

  2. Solve applications of integration, including those involving area, volume, work, arc length, and force.

  3. Employ the basic concepts of convergence and divergence of infinite sequences and series.

  4. Derive Taylor Series and approximate polynomials of analytic functions.

  5. Perform differentiation and integration on parametric equations and polar forms.
STUDENT LEARNING OUTCOMES
 Upon successful completion of the course, students should be able to:

1.  Recognize and solve separable, exact, and linear first-order differential equations.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  4. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

2.  Solve higher-order homogeneous and non-homogeneous linear differential equations with constant coefficients and Cauchy Euler linear differential equations.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  3. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

3.  Use the method of reduction of order and variation of parameters to solve higher-order homogeneous and non-homogeneous differential equations.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

4.  Apply differential equations to the physical and biological sciences.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

5.  Find power series solutions to differential equations about ordinary and singular points.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  3. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

6.  Find the Laplace Transform and inverse Laplace Transform of functions.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Generalize appropriately from specific contexts
  3. Critical Thinking - Integrate knowledge across a range of contexts
  4. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  5. Application of Knowledge - Maintain and transfer academic and technical skills to workplace

7.  Solve systems of linear first-order differential equations.
  

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Breadth of Knowledge - Use the symbols and vocabulary of mathematics to solve problems and communicate the results
  3. Application of Knowledge - Maintain and transfer academic and technical skills to workplace
 
COURSE CONTENT
  TOPICS
 

1.   Solving First-Order Differential Equations
      a.   Exact differential equations, integrating factors, separable
            equations
2.   Applications of First-Order Differential Equations
      a.   Orthogonal and oblique trajectories, mechanics, and rate
            problems
3.   Explicit Methods of Solving Higher-Order Differential Equations
      a.   Constant coefficients, undetermined coefficients, variation of 
            parameters, and Cauchy- Euler equations
4.   Applications of Higher-Order Linear Differential Equations with 
      Constant Coefficients
      a.   Spring problems, resonance problems, and electric circuit 
            problems
5.   Series Solutions of Differential Equations
      a.   Series solutions about ordinary and singular points
6.   Laplace Transforms
      a.   Laplace transforms, inverse Laplace transforms, convolutions,
            delta functions, and applications.
7.   Systems of Differential Equations
 
METHODS OF INSTRUCTION
 Methods of instruction used to achieve student learning outcomes may include, but are not limited to:

  • Class lectures, discussions, 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 material.
  • Pair and small group activities, discussions, and exercises in order to promote mathematics discovery and enhance problems solving skills.
 
METHODS OF EVALUATION
 Students will be evaluated for progress in and/or mastery of learning outcomes by methods of evaluation which may include, but are not limited to:

  • 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.
ASSIGNMENTS

Required Reading Assignments


Required Writing Assignments


Other Outside-of-Class Assignments
 
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:

  • Boyce and DePrima. Elementary Differential Equations and Boundary Value Problems. 8th ed. Wiley, 2004.
  • Nagel, Staff, and Snyder. Calculus; Early Transcendentals. 5th ed. Addision Wesley, 2000.
  • Zill and Cullen. Differential Equations with Boundary Value Problems. 5th ed. Brooks/Cole, 2001.
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