MA 255 - Calculus with Analytic Geometry III
Description
MA 255 is the third course in the three-semester Calculus sequence, and will introduce students to two main areas of study: multivariable Calculus and vector Calculus. Topics included in the first area are partial derivatives, multiple integrals, directional derivatives and gradients, maximums and minimums, cylindrical and spherical coordinates, lines, planes, and quadric surfaces. Topics included in the second area are dot and cross products, vector-valued functions, vector fields, line and surface integrals, curl and divergence, Green’s Theorem, Stokes’ Theorem, and the Divergence Theorem.
Credit Hours: 4
Contact Hours: 4
School: School of STEM
Department: Mathematics
Discipline: MA
Major Course Revisions: N/A
Last Revision Date Effective: 20230222T14:23:52
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. Demonstrate the ability to work within 3-dimensional coordinate systems, including basic by-hand graphing skills.
2. Work with vectors as mathematical objects and as tools for solving practical problems.
3. Examine the relationship between vector-valued functions and space curves, using calculus to study their properties and applications.
4. Demonstrate the ability to compute, interpret and apply partial derivatives, directional derivatives, and gradient.
5. Demonstrate the ability to compute, interpret and apply multiple integrals in various coordinate systems.
6. Synthesize vector and calculus concepts to develop key ideas of vector calculus, and apply these to the physical world.
Approved for Online Delivery?: No
Course Outline:
I. Three-Dimensional Analytic Geometry and Vectors
A. Three-dimensional rectangular coordinate system
B. Vectors
C. Dot and cross products
D. Equations of lines and planes
E. Quadric surfaces
F. Vector-valued function
G. Space curves, arc length, and curvature
H. Velocity and acceleration in three-dimensional space
I. Other coordinate systems
II. Multivariable Differential Calculus
A. Functions of several variables
B. Limits and continuity
C. Partial derivatives
D. Differentials and tangent planes
E. Chain rule
F. Directional derivatives and the gradient vector
G. Maximums and minimums
H. Lagrange multipliers
III. Multivariable Integral Calculus
A. Double integrals in rectangular coordinates
B. Double integrals in polar coordinates
C. Triple integrals in rectangular coordinates
D. Triple integrals in cylindrical and spherical coordinates
E. Applications of double and triple integrals
IV. Vector Calculus
A. Vector fields
B. Line integrals
C. Fundamental theorem of line integrals
D. Green’s theorem
E. Curl and divergence
F. Surface integrals
G. Stokes theorem
H. Divergence theorem
Mandatory CLO Competency Assessment Measures:
None
Name of Industry Recognize Credentials: None
Instructional Strategies:
Lecture: 10-80%
Facilitated discussion: 10-80%
Group work: 5-30%
Mandatory Course Components:
None
Academic Program Prerequisite: None
Prerequisites/Other Requirements: MA 134 (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: 4
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
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: 101089
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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