Discipline: Mathematics
Originator: Ernesto Reyes
Riverside Community College District
Integrated Course Outline of Record
Mathematics
1B
MAT1B : Calculus II 
College:
Lecture Hours:
72.000 Lab Hours: 18.000 OutsideofClass Hours: 144.000 Units: 4.00 Grading Methods: Pass/No Pass Letter Grade 
Course Description
Prerequisite:
MAT1A
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:
Evaluate limits of functions using various techniques.
 MAT1A  Compute the limit of a function.

Find the derivative of a function using rules of differentiation.
 MAT1A  Find the derivative of a function.

Integrate functions using Riemann Sums and the Fundamental Theorem of Calculus.
 MAT1A  Evaluate integrals.
Course Objectives:
Upon successful completion of the course, students should be able to demonstrate the following activities: Evaluate definite and indefinite integrals using a variety of integration formulas and techniques.
 Apply integration to areas and volumes, and other applications including work and length of a curve.
 Evaluate improper integrals.
 Graph, differentiate and integrate functions in polar and parametric form.
 Apply convergence tests to sequences and series.
 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: Evaluate definite, indefinite, and improper integrals.
 Solve applications using integration.
 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.
 Graph, differentiate, and integrate functions in polar and parametric form.
 Employ the concepts of convergence and divergence of infinite sequences and series.
Course Content:
 Techniques of Integration
 Substitution
 Integration by Parts
 Trigonometric Integrals
 Trigonometric substitution
 Partial fractions
 Applications
of Integration
 Area between curves
 Volume
 Volumes of revolution
 Work
 Average value of a function
 Arc length
 Surface area of revolution
 Separable differential equations
 Hydrostatic force and/or moments and center of mass
 Numerical Integration
 Midpoint Rule
 Trapezoidal Rule
 Simpsonâ€™s Rule
 Improper Integrals
 Parametric and Polar Equations
 Graphs
 Differentiation
 Integration
 Infinite Sequences and Series
 Sequences
 Series
 Tests for convergence and divergence
 Power series
 Interval and radius of convergence
 Power series representation of a function
 Differentiation and integration of power series
 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 handouts and/or computerbased 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, computerbased 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:
OutsideofClass Reading Assignments
 Read text, examples, and notes covering topics such as integration techniques and convergence and divergence of infinite series.
OutsideofClass Writing Assignments
 Solve applications of integration problems, including those involving area, volume, work, and arc length.
Other OutsideofClass 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)
CID#: MATH 220 MATH 900S=MAT1A+MAT1B
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 220 MATH 900S=MAT1A+MAT1B
Board of Trustees Approval Date:
11/13/2018
COR Rev Date:
11/13/2018