The following description is for the full Calculus sequence (MTH 901, MTH 902, MTH 903): 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: Calculus II with a grade of C or better.
Updated - 03/22/2024 - minor change to add "the calculus of " to "logarithmic and exponential functions;" - Effective Fall 2024Previous Update 03/24/2023 - Panel description updated to mirror the Calculus sequence with the GECC Math 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 2023
Previous Update - Panel added "Cylindrical" back to surfaces. Spring 2022 - 04/7/2022, effective fall 2022. Revision will be discussed with GECC Math panel for their calculus sequence.
Previous Revisions: Descriptions reviewed and updated in Fall 2021 (12/3/2021) - clarification "to the calculus of the trigonometric and inverse trigonometric functions;" (bolded information added).
Previous Update - March 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.