MATH 141: Calculus I

Note: If this course is being taught this semester, more information can be found at the course home page.

Cross Listed

(none)

Prerequisites

MATH 140 or a precalculus course in high school.

This course is a prerequisite or co-requisite for

Nearly all math courses require the first year calculus sequence or equivalent (MATH 141 - 143, MATH 161 - 162, or MATH 171 - 172). Two years of calculus are required to major in mathematics. Most science courses require between one and two years of calculus. See Comparing the Calculus Sequences.

Description

  • Introduces the techniques of the differential calculus of functions.

  • Reinforces algebraic manipulation and trigonometric techniques learned in high school.

  • Provides tools for use in other disciplines, although most examples come from geometry, graphs, and the simple physics of motion.

  • Rigorous proofs, providing guarantees that the techniques always work if certain criteria are met, are left to later courses in analysis such as MATH 265.

Topics covered

Analysis of the elementary real functions: algebraic, trigonometric, exponentials and their inverses and composites. Their graphs and derivatives. Topics include limits, continuity, asymptotes, the definition of the derivative, derivatives and derivative rules for algebraic, trigonometric, exponentials, and logarithms. Implicit differentiation, related rates, linear approximation, differentials, mean value theorem, maxima and minima, curve sketching, l’Hospital’s rule.

See Comparing the Calculus Sequences.