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
TOP Code: 1701.00 - Mathematics, General
Effective Term: Fall 2013

### Course Standards

Course Type: Credit - Degree Applicable
Units: 4.0
Total class hours: 216.0
Total contact hours in class: 72.0
Lecture hours: 72.0
Hours outside of class: 144.0
Repeatable: No

### Minimum Qualifications for Instructors

• 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

Satisfactory completion of: MATH 1A

• Language - recommended eligibility for English 1A
• Mathematics - recommended eligibility for Math 52

### Content

Course Lecture Content
1. Areas between curves
2. Volume, volume of a solid of revolution
3. Additional techniques of integration including integration by parts and trigonometric substitution
4. Numerical integration; trapezoidal and Simpson's rule
5. Improper integrals
6. Applications of integration to areas and volumes
7. Additional applications such as work,  arc length, area of a surface of revolution, moments and centers of mass, separable differential equations, growth and decay
8. Introduction to sequences and series
9. Multiple tests for convergence of sequences and series
10. Power series, radius of convergence, interval of convergence
11. Differentiation and integration of power series
12. Taylor series expansion of functions
13. Parametric equations and calculus with parametric curves
14. Polar curves and calculus in polar coordinates

### Objectives

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

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

3. Use numerical methods of integration.

4. Evaluate improper integrals.

5. Apply convergence tests to sequences and series.

6. Represent functions as power series.

7. Graph, differentiate and integrate functions in polar and parametric form.

### Student Learning Outcomes

1. Computation – Demonstrate the ability to apply the appropriate technique to integration.
2. Critical Thinking – Demonstrate the ability to determine the convergence of sequences and series.

### Methods of Instruction

• Lecture/Discussion

### Assignments

Writing Assignments

### Methods of Evaluation

• Exams
• Homework
• Portfolio
• Problem Solving Exercises
• Quizzes
• Other
Group or individual projects.

### Course Materials

Textbooks:
1. Robert T. Smith and Roland B. Minton. Calculus: Early Transcendental Functions, 4th ed. McGraw Hill, 2012, ISBN: 978-0-07-353232-5
Equivalent text is acceptable