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IAI Major Course Description - MTH901 : Calculus I

(4-5 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 functions; 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, 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.

>>>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.

Last Updated March 2016

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