IAI General Education Math Course Descriptions

M1900: College-level Calculus (3-5 semester credits)

Retired [effective Fall 2004]

Notice: The panel has decided to retire M1 900. Each course under M1 900 will now be identified separately with the following IAI Codes:

• M1 900-1: Calculus I
• M1 900-2: Calculus II
• M1 900-3: Calculus III
• M1 900-B: Business Calculus

A college-level calculus course. Policies on acceptance of AP credit vary among academic programs and from institution to institution, so AP credit toward the GECC or major requirements is not guaranteed. In general, a score of 3 or higher on the AP Calculus exam may be considered as equivalent to successful completion of courses approved for M1 900. Prerequisite: C or better in college algebra.

M1900-1: College-level Calculus I (4-5 semester credits)

The following description is for the full Calculus sequence (M1900-1, M1900-2, M1900-3):

Topics include (but are not limited to) the following:

• limits and continuity;
• definition of derivative, rate of change, slope;
• derivatives of polynomial and rational functions;
• the chain rule;
• implicit differentiation;
• approximation by differentials;
• higher-order derivatives;
• Rolle's Theorem and Mean Value Theorem;
• applications of the derivative;
• antiderivatives;
• the definite integral;
• the Fundamental Theorem of Calculus;
• area, volume, other applications of the integral;
• the calculus of the trigonometric and inverse trigonometric functions;
• the calculus of logarithmic and exponential functions;
• techniques of integration, including numerical methods, substitution, integration by parts, trigonometric substitution, and partial fractions;
• indeterminate forms and L'Hôpital's rule;
• improper integrals;
• sequences and series, convergence tests, Taylor series;
• parametric equations;
• polar coordinates and equations;
• vectors in 2 and 3 dimensions, vector operations;
• lines and planes in space;
• surfaces including cylindrical and quadric surfaces;
• functions of more than one variable, partial derivatives;
• the differential, directional derivatives, gradients;
• double and triple integrals, evaluation and applications;
• cylindrical and spherical coordinates.

Prerequisite for Calculus I: College Algebra and Trigonometry with grades of C or better, or Precalculus with a grade of C or better. The panel has compared the IAI GECC M1 900-1 descriptor against the AP Calculus AB and BC exams and determined there is not a match. Feb 2016.

>>>Note: When three courses are required to convey the necessary skills in calculus to mathematics majors, it is highly advised that students complete the entire sequence at a single institution. Course content may vary widely among institutions depending on the credits assigned to each course, and completing the sequence at a single institution is the best way to assure that neither credit nor content is lost in transfer.

Updated - 03/22/2024 - minor change to add "the calculus of " to "logarithmic and exponential functions;" - Effective Fall 2024.
Previous Update - 10/27/2023 - minor punctuation changes.
Previous Update - 03/24/2023 - Panel description updated to mirror the Calculus sequence with the Math major Calculus description. Minor changes made to surfaces to allow the panel a bit flexibility in topic coverage: "surfaces including cylindrical and quadric surfaces;" versus "cylindrical surfaces, quadric surfaces;" Effective fall 2023.
Previous Updated April 2016 - Wording adopted by GECC Mathematics panel from Mathematics major panel recommendations.

M1900-2: College-level Calculus II (3-5 semester credits)

The following description is for the full Calculus sequence (M1900-1, M1900-2, M1900-3):

Topics include (but are not limited to) the following:

• limits and continuity;
• definition of derivative, rate of change, slope;
• derivatives of polynomial and rational functions;
• the chain rule;
• implicit differentiation;
• approximation by differentials;
• higher-order derivatives;
• Rolle's Theorem and Mean Value Theorem;
• applications of the derivative;
• antiderivatives;
• the definite integral;
• the Fundamental Theorem of Calculus;
• area, volume, other applications of the integral;
• the calculus of the trigonometric and inverse trigonometric functions;
• the calculus of logarithmic and exponential functions;
• techniques of integration, including numerical methods, substitution, integration by parts, trigonometric substitution, and partial fractions;
• indeterminate forms and L'Hôpital's rule;
• improper integrals;
• sequences and series, convergence tests, Taylor series;
• parametric equations;
• polar coordinates and equations;
• vectors in 2 and 3 dimensions, vector operations;
• lines and planes in space;
• surfaces including cylindrical and quadric surfaces;
• functions of more than one variable, partial derivatives;
• the differential, directional derivatives, gradients;
• double and triple integrals, evaluation and applications;
• cylindrical and spherical coordinates.

Prerequisite for Calculus II: M1900-1 (Calculus I) with a grade of "C" or better. The panel has compared the IAI GECC M1 900-1 descriptor against the AP Calculus AB and BC exams and determined there is not a match. Feb 2016

>>>Note: When three courses are required to convey the necessary skills in calculus to mathematics majors, it is highly advised that students complete the entire sequence at a single institution. Course content may vary widely among institutions depending on the credits assigned to each course, and completing the sequence at a single institution is the best way to assure that neither credit nor content is lost in transfer.

Updated - 03/22/2024 - minor change to add "the calculus of " to "logarithmic and exponential functions;" - Effective Fall 2024.
Previous Update - 10/27/2023 - minor punctuation changes.
Previous Update - 03/24/2023 - Panel description updated to mirror the Calculus sequence with the Math major Calculus description. Minor changes made to surfaces to allow the panel a bit flexibility in topic coverage: "surfaces including cylindrical and quadric surfaces;" versus "cylindrical surfaces, quadric surfaces;" Effective fall 2023.
Previous Updated April 2016 - Wording adopted by GECC Mathematics panel from Mathematics major panel recommendations.

M1900-3: College-level Calculus III (3-5 semester credits)

The following description is for the full Calculus sequence (M1900-1, M1900-2, M1900-3):

Topics include (but are not limited to) the following:

• limits and continuity;
• definition of derivative, rate of change, slope;
• derivatives of polynomial and rational functions;
• the chain rule;
• implicit differentiation;
• approximation by differentials;
• higher-order derivatives;
• Rolle's Theorem and Mean Value Theorem;
• applications of the derivative;
• antiderivatives;
• the definite integral;
• the Fundamental Theorem of Calculus;
• area, volume, other applications of the integral;
• the calculus of the trigonometric and inverse trigonometric functions;
• the calculus of logarithmic and exponential functions;
• techniques of integration, including numerical methods, substitution, integration by parts, trigonometric substitution, and partial fractions;
• indeterminate forms and L'Hôpital's rule;
• improper integrals;
• sequences and series, convergence tests, Taylor series;
• parametric equations;
• polar coordinates and equations;
• vectors in 2 and 3 dimensions, vector operations;
• lines and planes in space;
• surfaces including cylindrical and quadric surfaces;
• functions of more than one variable, partial derivatives;
• the differential, directional derivatives, gradients;
• double and triple integrals, evaluation and applications;
• cylindrical and spherical coordinates.

Prerequisite for Calculus III: M1900 - 2 (Calculus II) with grades of C or better. The panel has compared the IAI GECC M1 900-1 descriptor against the AP Calculus AB and BC exams and determined there is not a match. Feb 2016.

>>>Note: When three courses are required to convey the necessary skills in calculus to mathematics majors, it is highly advised that students complete the entire sequence at a single institution. Course content may vary widely among institutions depending on the credits assigned to each course, and completing the sequence at a single institution is the best way to assure that neither credit nor content is lost in transfer.

Updated - 03/22/2024 - minor change to add "the calculus of " to "logarithmic and exponential functions;" - Effective Fall 2024.
Previous Update - 10/27/2023 - minor punctuation changes.
Previous Update - 03/24/2023 - Panel description updated to mirror the Calculus sequence with the Math major Calculus description. Minor changes made to surfaces to allow the panel a bit flexibility in topic coverage: "surfaces including cylindrical and quadric surfaces;" versus "cylindrical surfaces, quadric surfaces;" Effective fall 2023.
Previous Updated April 2016 - Wording adopted by GECC Mathematics panel from Mathematics major panel recommendations.

M1900-B: Calculus for Business and Social Sciences (4-5 semester credits)

This calculus course is designed specifically for students in business and the social sciences and does not count toward a major or minor in mathematics. It emphasizes applications of the basic concepts of calculus rather than proofs. Topics must include limits; techniques of differentiation applied to polynomial, rational, exponential, and logarithmic functions; partial derivatives and applications involving maxima and minima of functions in more than one variable; and elementary techniques of integration including substitution and integration by parts. Business and social science applications are stressed throughout the course. Prerequisite: College Algebra with a grade of C or better. The panel has compared the IAI GECC M1 900-B descriptor against the AP Calculus AB and BC exams and determined there is not a match. Feb 2016.

IMPORTANT SPECIAL NOTE: This course's credit hours increased to 4-5 semester credit hours from 3-5 semester credits on Jan. 1, 2017.

Revised information in description regarding partial derivatives and applications – Spring 2021 – 04/23/2021 – effective Fall 2021.

M1900-O: Calculus (other) (3-5 semester credits)

Courses in this category meet the basic description of a college-level calculus course and includes the concepts of differentiation and integration as appropriate. Courses such as a Short Course in Calculus, Non-Technical Calculus, and others are assigned here. Such courses do not fulfill the description of any course in the standard calculus sequence or the description of a calculus course for business and social science.

Prerequisite: college algebra or equivalent with a grade of “C” or better. Policies on the acceptance of AP credit vary among academic programs and from institution to institution, so AP credit toward the GECC or major requirements is not guaranteed. A score of 3 or higher on the AP Calculus AB or BC exam may be considered as equivalent to successful completion of post-secondary courses approved for IAI GECC M1 900-0. Feb 2016.