MTH162: Calculus IIA
Course home page for this semester
- Cross Listed:
- Fall and Spring
- 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.
(See also MTH171 and
Choosing a Calculus Sequence).
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.
- 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
- 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.