Yuba Community College District
Yuba College Course Outline
Course Information
Course Number:
MATH 1B
Full Course Title:
Single Variable Calculus II  Early Transcendentals
Short Title:
Calculus II
Effective Term:
Fall 2013
Course Standards
Lecture Hours:
72.000
Total Units:
4.000
Total Hours:
72.00
Repeatable:
No
Grading Method:
Letter Grade Only
Minimum Qualifications
 Mathematics (Masters Required)
Course Description
A second course in differential and integral calculus of a single variable: integration; techniques of integration; infinite sequences and series; polar and parametric equations; applications of integration. Primarily for science, technology, engineering & mathematics majors.Conditions of Enrollment
Completion with a C or better in: MATH 1A
Advisories

Language  recommended eligibility for English 1A

Mathematics  recommended eligibility for Math 52
Content
Course Lecture Content
 Areas between curves
 Volume, volume of a solid of revolution
 Additional techniques of integration including integration by parts and trigonometric substitution
 Numerical integration; trapezoidal and Simpson's rule
 Improper integrals
 Applications of integration to areas and volumes
 Additional applications such as work, arc length, area of a surface of revolution, moments and centers of mass, separable differential equations, growth and decay
 Introduction to sequences and series
 Multiple tests for convergence of sequences and series
 Power series, radius of convergence, interval of convergence
 Differentiation and integration of power series
 Taylor series expansion of functions
 Parametric equations and calculus with parametric curves
 Polar curves and calculus in polar coordinates
Objectives

Evaluate definite and indefinite integrals using a variety of integration formulas and techniques.

Apply integration to areas and volumes, and other applications such as work or length of a curve.
**Requires Critical Thinking**

Use numerical methods of integration.

Evaluate improper integrals.

Apply convergence tests to sequences and series.

Represent functions as power series.

Graph, differentiate and integrate functions in polar and parametric form.
Student Learning Outcomes
 Computation – Demonstrate the ability to apply the appropriate technique to integration.
 Critical Thinking – Demonstrate the ability to determine the convergence of sequences and series.
Methods of Instruction

Lecture/Discussion
Assignments
Hours per week on assignments outside of the class:
Reading Assignments
Writing Assignments
Methods of Evaluation
 Exams
 Homework
 Portfolio
 Problem Solving Exercises
 Quizzes

OtherGroup or individual projects.
Course Materials
Textbooks:

Robert T. Smith and Roland B. Minton. Calculus: Early Transcendental Functions, 4th ed. McGraw Hill, 2012, ISBN: 9780073532325Equivalent text is acceptable