MTH162: Calculus IIA

Cross Listed:

Offered:

Fall and Spring

Prerequisites:

MTH161

This course is a prerequisite or co-requisite for:

Nearly all math courses require the first year calculus sequence or equivalent (MTH141-143, MTH161-162, or MTH171-172). Two years of calculus are required to major in mathematics. Most science courses require between one and two years of calculus.

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. (The Quest Calculus with physics course has more examples from physics than the other versions of MTH 161.)
Uses proofs to help make the techniques a coherent whole rather than a set of isolated tricks.
Rigorous proofs, providing guarantees that the techniques always work if certain criteria are met, are left to later courses in analysis such as MTH265.

(See also MTH171 and Choosing a Calculus Sequence).

Topics covered:

Inverse functions, techniques of integration, improper integrals, L'Hopital's rule, applications to simple first order differential equations, arc length, surface area, infinite series, Taylor and Mclaurin series, a brief treatment of parametric equations and partial derivatives.

Related courses:

Math 142 is the second of three courses in the first year sequence MTH141, MTH142 and MTH143. The content of MTH141-143 matches the content of MTH161-162, but is covered at a slower pace. While it depends a great deal on the individual class, the approach in MTH161-162 may be more in depth because the class is better prepared. A Quest version of MTH161 is also being taught. The latter places emphasis on understanding concepts as well as on learning techniques. Homework includes more challenging and occassionally more theoretical problems. Students contemplating majoring in mathematics as well as others desiring a strong foundation in calculus are encouraged to take this course or the honors calculus course described below. First choice for positions in this course are given to students applying during the summer through the Quest program. Quest calculus IA with physics (MTH161Q) is the section of the Quest calculus course which coordinates with the fall physics course PHY 121Q. Students with strong mathematical ability should consider taking the MTH171 calculus sequence which is an honors calculus sequence for talented students interested in mathematics. The MTH171 sequence places more emphasis on the theoretical understanding of calculus in addition to teaching technical skills. The MTH171 sequence carries 5 credit hours per semester rather than the standard 4 credit hours and covers all of the material on calculus and linear algebra contained in MTH161-MTH164 and MTH235. Students completing the MTH171 sequence have completed all of the foundation requirements for a major or minor in mathematics. Physics 121 uses many of the techniques and concepts from differential calculus taught in MTH141 and MTH161.