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 2024Previous Update - 10/27/2023 - Minor punctuation changes.Previous Update 03/24/2023 - Panel description updated to mirror the Calculus sequence with the Math major Caluculus 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 2023Previous Updated April 2016 - Wording adopted by GECC Mathematics panel from Mathematics major panel recommendations.