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

Riverside Community College District
Integrated Course Outline of Record

Mathematics 1B


COURSE DESCRIPTION
1B Calculus II Units: 4.00
 
Prerequisite(s): MAT 1A: Calculus I
Techniques of integration, applications of integration, improper integrals, infinite sequences and series, parametric equations, polar coordinates, and conic sections. 72 hours lecture and 18 hours laboratory.
 
SHORT DESCRIPTION FOR CLASS SCHEDULE
Integration, applications of integration, series, parametric equations, and polar coordinates.
 
ADVISORY ENTRY SKILLS
Before entering the course, students will be able to:
  1. Calculate the limit of a function.

  2. Determine the continuity of a function.

  3. Find the derivatives of algebraic and transcendental functions.

  4. Solve related rates problems.

  5. Apply the absolute and relative extrema to curve sketching and optimization problems.

  6. Use Newton’s method to approximate the roots of a function.

  7. Evaluate a definite integral using Riemann sums.
STUDENT LEARNING OUTCOMES
 Upon successful completion of the course, students should be able to:

1.  Evaluate definite and indefinite integrals using techniques of integration.

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

  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

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

  1. Critical Thinking - Generalize appropriately from specific 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

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

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Construct sound arguments and evaluate arguments of others
  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

5.  Perform differentiation and integration on parametric equations and polar forms.

  1. Critical Thinking - Analyze and solve complex problems across a range of academic and everyday contexts
  2. Critical Thinking - Integrate knowledge across a range of 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
 
COURSE CONTENT
  TOPICS
 

1.   Techniques of Integration
      a.   Substitution, integration by parts, trigonometric substitution, 
            partial fractions, and miscellaneous substitution.
2.   Applications of Integration
      a.   Areas between curves, volumes, work, force, average value of 
            a function, arc length, area a surface of revolution, and
            separable differential equations.
3.   Integration
      a.   Tables of Integrals, approximate integration, improper 
            integrals
4.   Infinite Sequences and Series
      a.   Sequences, series, test for convergence and divergence, power
            series, and Taylor and Maclaurin series.
5.   Parametric Equations and Polar Coordinates
      a.   Parametric equations, polar coordinates, tangents, areas, arc 
            length, surface area, and conic sections.

 
 
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 definite and indefinite integrals, applications of integration problems, convergence and divergence of infinite sequences and series,  the Taylor series to approximate polynomials of analytical functions, differentiation and integration of parametric equations and polar forms.
  • Drills and pattern practices utilizing hand-outs and/or computer-based tools in order to assist the students in mastering the techniques of definite and indefinite integration, applications of integration, convergence and divergence of infinite sequences and series, the Taylor series to approximate polynomials of analytical functions, differentiation and integration of parametric equations and polar forms.
  • 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 calculus principles as well as the correct use of symbols and vocabulary of calculus.
  • Quizzes and midterm/final examinations for conceptual understanding as well as correct technique and application of calculus principles, definite and indefinite integrals, applications of integration, convergence and divergence of infinite sequences and series, the Taylor series to approximate polynomials of analytical functions, differentiation and integration of parametric equations and polar forms.
  • Classroom and laboratory 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:

  • Thomas, George B., et al. Thomas’ Calculus Early Transcendentals. 11th ed. Addison-Wesley, 2005.
  • Smith, Robert and Minton, Roland. Calculus: Early Transcendental Functions. 3rd ed. McGraw Hill, 2006.
  • Stewart, James. Essential Calculus; Early Transcendentals. Brooks/Cole, 2006.
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