Calculus II (Math 1230)
Section 110, Spring 2012
Syllabus and General Information

See Also: Homework Assignments and Announcements

Instructor. David A. Richter

Course Description. A continuation of Calculus I. Techniques and applications of integration, trigonometric functions, sequences and series, indeterminate forms, improper integrals, applications to elementary differential equations. Prerequisites & Corequisites: Prerequisite: MATH 1220 (recommended) or MATH 1700.

Coordinates of Class Meetings. 10:00-10:50 on Mondays, Tuesdays, Thursdays, and Fridays in room 1110 of Rood Hall.

Basis of Evaluation.

Homework. There is at least one homework assignment for each section we cover during the semester, although not all of it is collected. Generally, you are expected to complete each assignment within a week from whence it is assigned. Each homework set is worth 2 points if substantially complete, and 1 or no points if it is substantially incomplete.

Quizzes. Quizzes count for a significant part of your grade. There is at least one quiz per week, usually given 10-15 minutes before the end of class. Be prepared to take a quiz every time you attend class.

Exams. You have three exams scheduled for February 3, March 1, and April 6. The material covered on each exam is announced at least a week in advance. The third exam may have a take-home component assigned for the evening of April 5.

Final Exam. The final exam is comprehensive over all material covered throughout the semester. Unless otherwise announced or arranged, the final exam lasts from 8:00 until 10:00 a.m. on Thursday, April 26.

Basic Skills Test. The Basic Skills Test is designed to test for your readiness to take this course. It consists of 10 differentiation problems and 2 integration problems. The problems are all routine in the sense that anyone who passes Calculus I should know how to do them quickly by hand. A score of less than 9/12 is not regarded as a pass. You are allowed three attempts to take the test. If you cannot pass the test after three attempts within the first couple weeks of the semester, then your course grade is lowered by a half of a letter grade.

Required Text. Joel Hass, Maurice D. Weir, and George B. Thomas, Jr. University Calculus, Elements with Early Transcendentals. Custom Edition for WMU. Pearson, 2009. If you wish to use the standard edition, please speak with your instructor. Bring your copy of the text to every class meeting.

Calculator. You must have a graphing calculator, know how to use it, and bring it to every class meeting. Calculators are allowed on most quizzes and exams, although exceptions are bound to arise. You are not allowed to use a device capable of radio communication on any quiz or test.

Other Technologies. Neatness is a requirement for all homework you submit. If you normally use pencil, eraser, and standard notebook paper, then this is probably not a major concern. Thus, you are advised to refrain from using ink pens, remove the rough edges if you use a spiral-bound notebook, and bind your pages with a staple or a paper clip if necessary. More suggestions are offered here.

Student Conduct. Your instructor assumes that you are enrolled in this class because, at the very least, you want to participate in the University Community. In case there is any doubt, there is a code of conduct which you must follow and which your instructor enforces. In particular, the use of any radio communication device during class violates this code (unless it's a life-or-death emergency). These policies and procedures are described at the website for the Office of Student Conduct.

Expectations. Attend and participate in every class meeting. Spend at least 10 hours per week outside of class on this subject. Attempt to improve your writing skills. Take pride in your work. Remain enthused and curious about calculus. Maintain a positive attitude. Understand your assumptions.

Course Outline. We cover some fundamentals of the calculus of functions of a single variable, especially applications of the concepts of "integral" and "derivative" to concrete problems in geometry, physics, numerical analysis, and differential equations. Roughly, this means we cover chapters 5 through 8 and 14 of the text. The following "review" serves as a more detailed outline:

Skills. You are expected to master the following:
determine the slope of a line
determine the slope of a tangent line at a given point
determine the average rate of change of a function over a given interval
determine the area of a rectangle, trapezoid, parallelogram, triangle, or circle
differentiate using the power, chain, product, and quotient rules
differentiate implicitly
integrate using substitution
integrate by parts
multiply, factor, and divide polynomials
(manually) perform long division of polynomials
obtain partial-fraction decompositions of rational functions
inverse-trigonometric substitutions
direct trigonometric substituteions
integrate rational functions
evaluate limits using limit laws
evaluate limits using L'Hospital's rule
apply trapezoidal, midpoint, and Simpson's rules
estimate error for approximate integrals
evaluate and/or estimate improper integrals
determine absolute extrema of a function on a closed interval
determine the range of a function
determine intervals of concavity and points of inflection of a function
complete the square
set up an integral in order to determine area
set up an integral in order to determine volume by discs or washers
set up an integral in order to determine volume by cylindrical shells
set up an integral in order to determine volume by cross-sections
set up an integral in order to determine arc length
set up an integral in order to determine average value of a function
set up an integral in order to determine work
set up an integral in order to determine hydrostatic force
set up the appropriate integrals in order to determine the center of mass
verify a solution to a differential equation
use Euler's method
use the method of separation of variables to solve a differential equation
recognize a separable differential equation

Vocabulary: You should know how to spell and use the following terms. In particular, you should know how and why each term arises or is useful: absolute error, absolute maximum/minimum, absolutely convergenct, acceleration, alternating series, alternator, antiderivative, approximate value, arc length, area, ball, bounded from above/below, box, center of expansion, center of mass, centroid, closed interval, concave up/down, conditionally convergent, cone, continuous at a point, continuous from the left/right, continuous on an interval, convergent integral, convergent sequence, convergent series, critical number, cube, cylinder, cylindrical shell, definite integral, derivative, differential equation, disc, divergent integral, divergent limit, domain of a function, energy, Euler's method, even function, exact value, exponential function, exponential growth/decay, extreme value, factorial function, force, function, geometric series, horizontal asymptote, improper integral, improper rational function, indefinite integral, infinite series, inflection point, initial-value problem, interval of convergence, interval, limit, line, logistic equation, mathematical induction, monotone function, nondecreasing/nonincreasing, odd function, open interval, parametric function, polynomial, power series, pressure, pyramid, radius of convergence, range of a function, rate of change, rational function, rectangle, recursive sequence, reduction formula, related rates, relative error, relative maximum/minimum, Riemann sum, separable differential equation, sequence, slant asymptote, slope, sphere, square, strictly decreasing/increasing, trapezoid, triangle, velocity, vertical asymptote, volume, washer, work,

Results. Eventually, you should find all of the following as useful:
Intermediate-Value Theorem
Mean-Value Theorem
Extreme-Value Theorem
First Derivative Test
Second Derivative Test
L'Hospital's Rule
Chain, Product, and Quotient Rules
Comparison Test for Integrals
Fundamental Theorem of Calculus
Half-Angle Identities
Mean-Value Theorem, derivative version
Mean-Value Theorem, integral version
Midpoint Rule
Product Rule
Simpson's Rule
Trapezoidal Rule
Volume Formulae for boxes, cylinders, cones, and spheres
Area Formulae for rectangles, triangles, trapezoids, parallelograms, scircle, sectors
The Principle of Cut-and-Paste
The Fencepost Rule
Divergence Test
The Sum of a Geometric Series
Integral Test
p-Series Test
Compariston Test for Infinite Series
Limit Comparison Test
Alternating Series Test
Ratio Test
Root Test

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