Math 132 Calculus II
WinterSpring, 2015
Professor Wickerhauser

NEWS
 The final exam will focus on these topics from Webworks 10 and
11:
 limits of infinite sequences by L'Hopital's rule
 tests of convergence for infinite series
 error estimates for alternating series
 computing basic power series
 determining radius of convergence
 computing Taylor series
 error terms in Taylor series
 limits and approximations using Taylor series
 computing binomial series
 basic parametric curves
 slopes of tangents to parametric curves
 lengths of parametric curves
 areas enclosed by parametric curves
 basic curves in polar coordinates
 lengths of polar curves
 areas enclosed by polar curves
Techniques from earlier in the course will be useful in solving the problems.
 HW 11 opened on Friday at 9am. It will close at 9:00pm on
Monday, April 27th.

LINKS

Syllabus
Topics. Continuation of Math 131. A brief review of the
definite integral and Fundamental Theorem of Calculus. Techniques of
integration, applications of the integral, sequences and series, and
some material on differential equations.
Covered so far:
 Week 1 (1/131/17 )
 5.1 Riemann sums for area approximation
 5.2 Sigma notation
 5.3 Integrability and the definite integral
 5.4 Fundamental Theorem of Calculus
 Week 2 (1/211/23 )
 5.5 Indefinite integrals and substitution
 5.6 Areas between curves in the plane.
 Week 3 (1/261/30 )
 6.1 Volumes by crosssection
 Trig substitution
 6.2 Computing volumes of rotation by discs and washers
 Theorem of Pappas
 Week 4 (2/22/6 )
 6.2 Volumes by cylindrical shells
 6.3 Arc length of curves
 6.4 Areas of surfaces of rotation
 Week 5 (2/92/13 )
 6.5 Work
 6.6 Moments and centers of mass
 Centroids of plane regions
 Week 6 (2/1620)
 7.1 Logarithm defined as an integral
 7.2 Exponential growth and decay
 Initial value problems for y'=by
 Integrals of g'(x)/g(x)
 Week 7 (2/2327)
 7.3 Hyperbolic functions
 Strategies for integration
 8.1 Integration by parts
 Week 8 (3/26)
 8.2 Trigonometric integrals
 8.3 Trigonometric substitution
 Rational functions
 Week 8 (3/1620)
 8.4 Partial fractions
 8.5 Integral tables and CAS
 8.6 Numerical integration
 Week 9 (3/2327)
 8.6 Error estimates for trapezoid and Simpson's rules
 8.7 Improper Riemann integrals
 9.1 Sequences convergent and divergent
 Week 10 (3/304/3)
 9.2 Series convergent and divergent, including
geometric series and telescoping series
 9.3 Integral test for convergence and divergence of infinite
series
 9.4 Comparison tests, part I
 Week 11 (4/64/10)
 9.4 Comparison tests, part II
 9.5 Ratio and root tests
 9.6 Alternating series tests; absolute and conditional
convergence
 9.7 Power series; radius of convergence
 Week 11 (4/134/17)
 9.8 Taylor and Maclaurin series
 Applications of Taylor series
 Binomial series
 Parametric curves
 Week 12 (4/204/24)
 Arclength and area for parametric curves
 Surfaces of rotation defined by parametric curves
 Polar coordinates
 Arclength and area in polar coordinates
Prerequisites. Math 131 or a grade of B or better in a one
year high school calculus course.
Time. Classes meet Mondays, Wednesdays and Fridays in Busch
Hall, room 100. Section 1 meets 10:00am11:00am. Section 2 meets
11:00am12:00 noon.
Text. The lectures will generally follow
University Calculus: Early Transcendentals (Second Edition)
by Joel R. Hass, Maurice D. Weir, and George B. Thomas Jr., which was
the text used in Math 131 in Fall, 2014. You are welcome to use any
similar calculus textbook, or none at all.
Homework. Homework problems will be generated and graded weekly
on WeBWorK.
You are encouraged to collaborate on homework and to
work additional exercises from your textbook, although the
homework grade will be based only on your individual WeBWorK results.
Tests. Tests, at which attendance is required, will be
given from 7:00pm9:00pm on Wednesday February 4, Wednesday March 4
and Wednesday April 8. The final examination will be held on
Friday May 1 from 10:30am to 12:30pm.
Grading. The homework, the three tests, and the final
examination will each be assigned a score and will contribute equal
shares (20%) to the course score. Letter grades, computed from the
course score, will be at least the following:
Course score at least:  90%  80%  70%  60% 
Letter grade at least:  A  B  C  D 
Students taking the Cr/NCr or P/F options will
need a grade of D or better to pass. Students taking the Audit option
will need to attend and sign in at 37 of the 41 class meetings to
obtain a Successful Audit grade.
Computing. Students are encouraged to use their own computers or
those available in the Arts and
Sciences Computing Lab for both symbolic and numerical computations.
Office Hours. Teaching assistants, assigned to you at
registration, will be available on Tuesdays throughout the day in
various classrooms. I will be available in my office Mondays
4:005:00pm, and occasionally at other times by appointment.
Questions? Return to
M. Victor Wickerhauser's home page for contact information.