MA 134 - Calculus with Analytic Geometry II
Description
MA 134 is the second course in the three-semester Calculus sequence, emphasizing integration and series. Topics include techniques of integration, parametric equations, polar coordinates, improper integrals, infinite series, and their applications. Students should be very proficient in algebra, trigonometry, and differentiation prior to enrolling in this course.
Credit Hours: 5
Contact Hours: 5
School: School of STEM
Department: Mathematics
Discipline: MA
Major Course Revisions: N/A
Last Revision Date Effective: 20230222T14:23:45
Course Review & Revision Year: 2027-2028
Course Type:
Program Requirement- Offering designed to meet the learning needs of students in a specific GRCC program.
Course Format:
Lecture - 1:1
General Education Requirement: None
General Education Learner Outcomes (GELO):
NA
Course Learning Outcomes:
1. Apply integration to solve application problems.
2. Analyze integrals and choose appropriate evaluation techniques.
3. Apply numerical techniques to find approximate values of integrals when exact techniques are inadequate.
4. Analyze and evaluate improper integrals.
5. Analyze convergence of sequences and series through a variety of tests with attention to intervals of convergence, power series, and Taylor series.
6. Use polar coordinates to solve calculus applications.
7. Apply calculus to curves defined by parametric equations.
Approved for Online Delivery?: Yes
Course Outline:
I. The Fundamental Theorem of Calculus and applications of Integration
A. Review of definite integrals and the fundamental theorem of calculus
B. Area between two curves
C. Volume: disks, washers, shells
D. Work
E. Average value of a Function
II. Techniques of Integration
A. Review the substitution rule
B. Integration by parts
C. Basics of trigonometric integrals
D. The method of trigonometric substitution
E. The method of partial fraction
F. Strategy for integration
G. Numerical integration: Trapezoidal rule and Simpsons rule
H. Improper integrals
III. Further applications of Integration
A. Differential equation: Separation of variables
B. Arc length and surfaces of revolution
C. Moments and centers of mass
D. Hydrostatic pressure and force (optional)
E. Applications to economics and biology (optional)
IV. Infinite Sequences and Series
A. Sequences and their limits
B. Series notation
C. Methods and strategy for testing series for convergence or divergence
D. Power series
E. Representation of functions by power series
F. Taylor and Maclaurin series; Binomial series
G. Applications of Taylor polynomials
V. Parametric Equations and Polar Coordinates
A. Parametric equations and curves
B. Tangents and areas
C. Arc length and surface area
D. Polar coordinates
E. Areas and lengths in polar coordinates
Mandatory CLO Competency Assessment Measures:
None
Name of Industry Recognize Credentials: None
Instructional Strategies:
Lecture: 0-90%
Facilitated discussion: 0-80%
Mediated instruction: 0-60%
Group work: 0-60%
Mandatory Course Components:
None
Academic Program Prerequisite: None
Prerequisites/Other Requirements: MA 133 (C or Higher)
English Prerequisite(s): None
Math Prerequisite(s): None
Course Corerequisite(s): None
Course-Specific Placement Test: None
Course Aligned with IRW: N/A
Consent to Enroll in Course: No Department Consent Required
Total Lecture Hours Per Week: 5
Faculty Credential Requirements:
18 graduate credit hours in discipline being taught (HLC Requirement), Master’s Degree (GRCC general requirement)
Faculty Credential Requirement Details: Standard requirements for the Mathematics Department apply.
Maximum Course Enrollment: 30
Equivalent Courses: None
Dual Enrollment Allowed?: Yes
Advanced Placement (AP) Exam Credit Accepted: Calculus BC
AP Min. Score: 5
Number of Times Course can be taken for credit: 1
Programs Where This Courses is a Requirement:
Pre-Engineering, A.A. (General Transfer), Pre-Mathematics, A.A. (General Transfer)
Course Fees: $19.00
People Soft Course ID Number: 101082
Course CIP Code: 27.01
High School Articulation Agreements exist?: No
If yes, with which high schools?: NA
Non-Credit GRCC Agreement exist?: No
If yes, with which Departments?: NA
Corporate Articulation Agreement exist?: No
If yes, with which Companies?: NA
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