MTH 161: Calculus IA

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This course is a prerequisite or co-requisite for

Nearly all math courses require the first year calculus sequence or equivalent (MTH 141 - 143, MTH 161 - 162, or MTH 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 and integral calculus of functions.

• Reinforces algebraic manipulation and trig 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 MTH 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, the definite integral, the fundamental theorem of calculus, and the substitution rule for integration.