MTH 178 - Calculus with Analytic Geometry I

Description
MTH 178 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.

Was previously MA 133.

Credit Hours: 5
Contact Hours: 5
Prerequisites/Other Requirements: C or Higher in one of the following courses: MTH 148 OR [MTH 122 and MTH 128] or Math Placement score of 76 or Higher
English Prerequisite(s): None
Math Prerequisite(s): None
Course Corequisite(s): None
Academic Program Prerequisite: None
Consent to Enroll in Course: No Department Consent Required
Dual Enrollment Allowed?: Yes
Course Fees: $19.00
Number of Times Course can be taken for credit: 1
Programs Where This Course is a Requirement:
Pre-Economics, A.A. (General Transfer)

General Education Requirement:
Mathematics
General Education Learner Outcomes (GELO):
3. Critical Thinking: Gather and synthesize relevant information, evaluate alternative perspectives, or understand disciplinary strategies 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)
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

Approved for Online and Hybrid Delivery?:
Yes
Instructional Strategies:
Lecture: 0-90%

Facilitated discussion: 0-80%

Mediated instruction: 0-60%

Group work: 0-60%

Mandatory Course Components:
None
Equivalent Courses:
None

Accepted GRCC Advanced Placement (AP) Exam Credit: Calculus AB, Calculus BC
AP Min. Score: 3
Name of Industry Recognize Credentials: None

Course prepares students to seek the following external certification:
No
Course-Specific Placement Test: ALEKS
Course Aligned with ARW/IRW Pairing: IRW 101 (Previously IRW 99)

Mandatory Department Assessment Measures:
None

GRCC Course Type:
General Education: Meets the specific criteria for a GRCC Distribution Requirement. The course should be designated by the requirement it fulfills.
Course Format:
Lecture - 1:1
Total Lecture Hours Per Week: 5
People Soft Course ID Number: 101081
Course CIP Code: 27.01
Maximum Course Enrollment: 35
High School Articulation Agreements exist?: No
If yes, with which high schools?: NA
Non-Credit GRCC Articulation Agreement With What Area: No
Identify the Non Credit Programs this Course is Accepted: NA

School: School of STEM
Department: Mathematics
Discipline: MA
Faculty Credential Requirements:
Master’s Degree (GRCC general requirement), Other (list below)
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.

Major Course Revisions: Prefix, Course Number Change
Last Revision Date Effective: 20260304T10:58:32
Course Review & Revision Year: 2029-2030