MA 133 - Calculus with Analytic Geometry I
Description
MA 133 is the first course in the three-semester Calculus sequence. Topics include limits, continuity, and differentiation of algebraic, trigonometric, logarithmic, and exponential functions. Applications of differentiation include indeterminate forms, curve sketching, optimization and related rates. Antidifferentiation and definite integrals will be introduced. This course is intended for students majoring in STEM disciplines. Students should be very proficient in algebra and trigonometry prior to enrolling in this course.
Credit Hours: 5
Contact Hours: 5
School: School of STEM
Department: Mathematics
Discipline: MA
Major Course Revisions: General Education Review
Last Revision Date Effective: 20230222T14:23:42
Course Review & Revision Year: 2027-2028
Course Type:
General Education- Offering designed to meet the specific criteria for a GRCC Distribution Requirement. The course should be designated by the requirement it fulfills.
Course Format:
Lecture - 1:1
General Education Requirement: Mathematics
General Education Learner Outcomes (GELO):
3. Critical Thinking: Gather and synthesize relevant information, evaluate alternative perspectives, or understand inquiry as a means of creating knowledge, 7. Problem-Solving: Apply theory, calculation, or experimentation to demonstrate effective problem-solving
Course Learning Outcomes:
1. Find limits of functions using numerical, graphical and algebraic techniques, as well as L’Hospital’s Rule.
2. Discuss continuity of functions and find points of discontinuity.
3. Find tangent lines to curves and instantaneous rates of change.
4. Use differentiation formulas accurately and efficiently.
5. Solve related rate and applied optimization problems.
6. Illustrate and apply the Mean Value Theorem.
7. Find relative and absolute extrema, and intervals where functions are increasing or decreasing.
8. Use the second derivative to find inflection points and intervals of concavity.
9. Use properties of first and second derivatives to sketch graphs of functions.
10. Find general and specific antiderivatives.
11. Approximate areas under curves using Riemann Sums.
12. Evaluate definite integrals using the Fundamental Theorem of Calculus.
13. Find areas using definite integrals.
14. Translate or explain what written information means and/or how it can be used. (GELO3)
15. Complete work accurately, with attention to detail.
16. Develop a plan to implement a solution to a problem or issue. (GELO7)
Approved for Online Delivery?: Yes
Course Outline:
I. Limits and rates of change
A. Limits of functions
B. Continuity and the Intermediate Value Theorem
C. Tangents, velocities, and other rates of change
II. Derivatives
A. Definition of the derivative
B. Basic differentiation formulas
C. Derivatives of algebraic, trigonometric, inverse trigonometric, exponential and logarithmic functions
D. Chain rule
E. Implicit differentiation
F. Differentials and linear approximation
III. Applications of the derivative
A. Rates of change in the sciences
B. Related rates
C. Mean Value Theorem
D. Relative and absolute maxima and minima
E. Increasing/decreasing, concavity and points of inflection
F. L’Hospital’s Rule
G. Applied optimization problems
IV. Antidifferentiation/indefinite integrals
A. Basic antidifferentiation formulas and substitutions
B. Sigma notation and Riemann sums
C. Area under a curve
D. Definite integrals
E. Fundamental Theorem of Calculus
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: C or Higher in one of the following courses: MA 131 OR [MA 108 and MA 110] or ALEKS score of 76 or Higher
English Prerequisite(s): None
Math Prerequisite(s): None
Course Corerequisite(s): None
Course-Specific Placement Test: ALEKS
Course Aligned with IRW: IRW 99
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: Master’s degree in Mathematics or in a closely related field with at least 18 semester hours of graduate work in mathematics. Teaching experience at the college level is preferred.
General Room Request: None
Maximum Course Enrollment: 35
Equivalent Courses: None
Dual Enrollment Allowed?: Yes
Advanced Placement (AP) Exam Credit Accepted: Calculus AB; Calculus BC
AP Min. Score: 5
Number of Times Course can be taken for credit: 1
Programs Where This Courses is a Requirement:
Pre-Economics, A.A. (General Transfer)
Course Fees: $19.00
People Soft Course ID Number: 101081
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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