Fall 2008
Most recent update: Thursday, May 1
These policies and schedules are subject to revision.
Most recent update: Thursday, May 1
These policies and schedules are subject to revision.
5.1 - 5.6: Applications of the Integral. January 14 - February 1
7.1 - 7.6: Techniques of Integration. February 4 - February 21
8.1 - 8.4, 9.1 - 9.9: Indeterminate Forms, Improper Integrals, Infinite Series. February 22 - April 15
10.4 - 10.7: Parametric Curves, Polar Coordinates. April 17 - April 29
Review: May 1 - May 2
Also see the calculus sequence web site: Calculus I,II,III, which has course objectives and sample exams.
Important ideas, techniques, and terms, by section:
Section 5.1: Finding the right integral for areas of plane regions; the technique that leads us to those integrals: subdivide, approximate the pieces, and
take the limit of the approximating sums; slicing vertically or horizontally; integrals involving velocity for calculating displacement and distance
Section 5.2: Volumes of solids or three-dimensional regions by integrating the cross-sectional area; the subdivide/approximate/limit technique that leads to
the right integral formulas
Section 5.3: Volumes of solids by subdivision into cylindrical shells
Section 5.4: Integrals for arc length and for areas of surfaces of revolution, and the approximation technique behind them, use of calculator to approximate the integral values
Section 5.5: Use of subdivide/approximate/llmit technique to find integrals for work in various situations and pressure exerted by a fluid
Section 5.6: Calculation of moments and centers of mass in one and two dimensions (by integral formulas you can get from first principles), Pappus's Theorem.
Section 7.1: Review the basics of integration, use of standard forms, linearity, substitution, function identities
Section 7.2: Integration by parts, use in combination with other technques, repeated, reduction formulas
Section 7.3: Integration tricks for various combinations of trig functions
Section 7.4: Use of substitutions to roots
Section 7.5: Partial fraction decomposition and its use in integration, the logistic differential equation
Section 7.6: Perspectives on definite integrals: They are a part of our language, not always things to be evaluated. Summary of our techniques for finding indefinite
integrals. The place for and use of tables of indefinite integrals, symbolic manipulation software, numberical approximation, special functions. Integrals with variable limits.
Integrals of functions defined by tables
Section 8.1, 8.2: Use of L'Hopital's Rule to evaluate limits
Section 9.1: Sequences defined by explicit formulas or recursion, convergence and limits of sequences, theorems similar to theorems on limits involving a real variable,
conversion to problems with real variables, Monotonic Sequence Theorem
Section 8.3, 8.4: Improper integrals: definition as limit of proper definite integrals, convergence/divergence
Section 9.2: Infinite series basics: terms, partial sums, convergence/divergence, recognizing and summing geometric series, nth term test, linearity of
convergent series, grouping of terms
Section 9.3: Series of positive terms converge iff the partial sums are bounded (Bounded Sum Test, comes from Monotonic Sequence Theorem), Integral Test, p-series
Test, use of integrals to test errors in approximating infinte sums by partial sums
Section 9.4: For positive series: comparison tests, ratio test.
Section 9.5: Absolute and conditional convergence: definitions, logical relations between them, intuition behind them (total or net amount is meaningful for absolutely
convergent series), alternating series test and the associated error test, absolute ratio test, rerrangement theorem
Section 9.6: Power series, interval of convergence, radius of convergence
Section 9.7: Operations on power series: differentiation, integration, substitution, addition, subtraction, multiplication, division; recognize power series for familiar functions
Section 9.8: Taylor series, including Maclaurin series, uniqueness of the Taylor series, Taylor's Formula with Remainder, Maclaurin series for certain functions,
two approaches to finding Taylor series
Section 9.9: Taylor and Maclaurin polynomials, errors of the method and of calculation, use of Taylor's Formula with Remainder for investigating the error of the method
Section 10.4: Parametrization of curves, special cases of lines, line segments, circles, ellipses
Section 10.5: Polor coordinate system, including coordinate conversions
Section 10.6: Polar coordinate representation of curves, including special cases of lines, conic sections, limacons, cardioids, roses, lemniscates
Section 10.7: Use of polar coordinates in area, tangent line, and arclength calculations
For Midterm and Final Exam samples, also see the calculus sequence web site: Calculus I,II,III
Test One, Friday, January 25, on sections 5.1 - 5.3. Solutions
Test Two, Thursday, February 7, on sections 5.4 - 5.6. Solutions
Test Three, Departmental Midterm, Thursday, February 28, 8:00 - 9:30 PM in Coover 2245. Solutions
Test Four, Thursday, March 6, on sections 8.1, 8.2, 9.1. Solutions
Test Five, Thursday, March 27, on sections 8.3, 9.2 - 9.4. Solutions
Test Six, Thursday, April 10, on sections 8.4, 9.5, 9.6. Solutions
Test Seven, Thursday, April 24, on sections 9.7 - 9.9. Solutions
Final Exam, two hours, 200 points, Wednesday, May 7 in exam week, 4:30 - 6:30 PM in Carver 101
MyMathLab/CourseCompass: Tutorials from the textbook publisher and coordinated with the textbook.
Course name is Calculus II. Course ID is wilson95299. MML/CC
(We will not use the course management features of this software.)
Info from MyMathLab tech support: If you used MyMathLab with the same text in the past year, then
to add our class, you go to the Login page but instead of logging in, click on View your Account Summary. On the Account Summary page, use your name and password
to log in. On the page listing your courses, click Enroll in a Course.
Supplemental Instruction: Led by a good student who was successful in calculus and attends a Calculus II lecture, begins week two: SI
Math Help Room: Carver 385. Staffed by good students, mainly undergraduate. Help Room Schedule
Academic Success Center: "Creating relationships and providing services to enhance students' learning and academic success", for help with many issues: ASC