MTH 903 Calculus III: (3-5 Semester Credits)
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 2024
Previous 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.