Discipline: Mathematics
Originator: Ernesto Reyes

Riverside Community College District
Integrated Course Outline of Record

Mathematics 1B
MAT-1B : Calculus II
College:
Lecture Hours: 72.000
Lab Hours: 18.000
Outside-of-Class Hours: 144.000
Units: 4.00
Grading Methods: Pass/No Pass
Letter Grade
Course Description
Prerequisite: MAT-1A
Course Credit Recommendation: Degree Credit

Techniques of integration, applications of integration, improper integrals, parametric equations, polar coordinates, infinite sequences and series. 72 hours lecture and 18 hours laboratory. (Letter Grade, or Pass/No Pass option.)
Short Description for Class Schedule
Integration, applications of integration, parametric equations, polar coordinates and series.
Entrance Skills:
Before entering the course, students should be able to demonstrate the following skills:
  1. Evaluate limits of functions using various techniques.
    • MAT-1A - Compute the limit of a function.
  2. Find the derivative of a function using rules of differentiation.
    • MAT-1A - Find the derivative of a function.
  3. Integrate functions using Riemann Sums and the Fundamental Theorem of Calculus.
    • MAT-1A - Evaluate integrals.
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities:
  1. Evaluate definite and indefinite integrals using a variety of integration formulas and techniques.
  2. Apply integration to areas and volumes, and other applications including work and length of a curve.
  3. Evaluate improper integrals.
  4. Graph, differentiate and integrate functions in polar and parametric form.
  5. Apply convergence tests to sequences and series.
  6. Represent functions as power series and apply power series to differentiation and integration.
Student Learning Outcomes:
Upon successful completion of the course, students should be able to demonstrate the following skills:
  1. Evaluate definite, indefinite, and improper integrals.
  2. Solve applications using integration.
    • 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. Graph, differentiate, and integrate functions in polar and parametric form.
  4. Employ the concepts of convergence and divergence of infinite sequences and series.
Course Content:
  1. Techniques of Integration
    1. Substitution
    2. Integration by Parts
    3. Trigonometric Integrals
    4. Trigonometric substitution
    5. Partial fractions
  2. Applications of Integration
    1. Area between curves
    2. Volume
    3. Volumes of revolution
    4. Work
    5. Average value of a function
    6. Arc length
    7. Surface area of revolution
    8. Separable differential equations
    9. Hydrostatic force and/or moments and center of mass
  3. Numerical Integration
    1. Midpoint Rule
    2. Trapezoidal Rule
    3. Simpson’s Rule
  4. Improper Integrals
  5. Parametric and Polar Equations
    1. Graphs
    2. Differentiation
    3. Integration
  6. Infinite Sequences and Series
    1. Sequences
    2. Series
    3. Tests for convergence and divergence
    4. Power series
    5. Interval and radius of convergence
    6. Power series representation of a function
    7. Differentiation and integration of power series
    8. Taylor and MacLaurin Series
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, and demonstrations of definite and indefinite integrals, applications of integration, convergence and divergence of infinite sequences and series, approximate polynomials of analytical functions, and 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, approximate polynomials of analytical functions, and 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 student learning outcomes using methods of evaluation which may include, but are not limited to, the following activities:
  • Written and/or computerized homework assignments designed to ensure the correct application of integration techniques and concepts of convergence and divergence of infinite sequences and series.
  • Quizzes and midterm/final examinations designed to assess students' understanding of applications of integration, approximation of analytic functions using polynomials, and differentiation and integration of functions in polar and parametric form.
  • Classroom and laboratory discovery activities for content knowledge and conceptual understanding.
Sample Assignments:
Outside-of-Class Reading Assignments
  • Read text, examples, and notes covering topics such as integration techniques and convergence and divergence of infinite series.
Outside-of-Class Writing Assignments
  • Solve applications of integration problems, including those involving area, volume, work, and arc length.  
Other Outside-of-Class Assignments
  • Problem sets that require students to evaluate definite, indefinite, and improper integrals; derive Taylor series; and graph, differentiate, and integrate functions in polar and parametric form.
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:
  • Stewart, James. Single Variable Calculus: Early Transcendentals. 8th Brooks/Cole, 2016.
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 220 MATH 900S=MAT-1A+MAT-1B
Board of Trustees Approval Date: 11/13/2018
COR Rev Date: 11/13/2018