## Math 132 Calculus II Winter-Spring, 2015

### 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.

### 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 (1/13--1/17 )
• 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 (1/21--1/23 )
• 5.5 Indefinite integrals and substitution
• 5.6 Areas between curves in the plane.
• Week 3 (1/26--1/30 )
• 6.1 Volumes by cross-section
• Trig substitution
• 6.2 Computing volumes of rotation by discs and washers
• Theorem of Pappas
• Week 4 (2/2--2/6 )
• 6.2 Volumes by cylindrical shells
• 6.3 Arc length of curves
• 6.4 Areas of surfaces of rotation
• Week 5 (2/9--2/13 )
• 6.5 Work
• 6.6 Moments and centers of mass
• Centroids of plane regions
• Week 6 (2/16--20)
• 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 (2/23--27)
• 7.3 Hyperbolic functions
• Strategies for integration
• 8.1 Integration by parts
• Week 8 (3/2--6)
• 8.2 Trigonometric integrals
• 8.3 Trigonometric substitution
• Rational functions
• Week 8 (3/16--20)
• 8.4 Partial fractions
• 8.5 Integral tables and CAS
• 8.6 Numerical integration
• Week 9 (3/23--27)
• 8.6 Error estimates for trapezoid and Simpson's rules
• 8.7 Improper Riemann integrals
• 9.1 Sequences convergent and divergent
• Week 10 (3/30--4/3)
• 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 (4/6--4/10)
• 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 (4/13--4/17)
• 9.8 Taylor and Maclaurin series
• Applications of Taylor series
• Binomial series
• Parametric curves
• Week 12 (4/20-4/24)
• 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 10:00am-11:00am. Section 2 meets 11:00am-12:00 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 7:00pm-9:00pm 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: Letter grade at least: 90% 80% 70% 60% 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 4:00-5:00pm, and occasionally at other times by appointment.