Daily Homework. As with any math class, homework is where almost all of your learning takes place. Homework exercises to be evaluated will be collected most days in class. The homework may involve some computer exercises but will be mostly hand-written computations and explanations.
Your homework should be legible, with problem number and final answer clearly indicated. Explanations should be written in complete sentences. Random math expressions floating in space will receive no credit. Written assignments will be graded holistically as opposed to problem-by-problem , with completeness, clarity of communication including legibility! The grades for homework are largely a motivation to do the necessary work, assessing apparent effort more than mathematical understanding.
Understanding is assessed more in writing projects and exams.
MAT 146 - Calculus II
You may turn in three daily homework assignments one class meeting late without question or penalty, but no other late work will be accepted without a written excuse from the Dean of Students. Preview Activities: Each section of the textbook begins with a very short introduction, often as brief as a sentence or two, but sometimes half a page, followed by a Preview Activity.
I will indicate on the daily schedule page for the class days on which the Preview Activity is to be handed in. These will be graded on a binary 0 or 1 scale, with complete, legible, apparently earnest attempts to work through the activity earning a 1.
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If you are really stumped on a preview activity, visit my office hours or the MSSC. Failing all else, write a sentence or two about what you tried to do in working the activity, and what is confusing you about that particular part of the activity. If possible, move on to later parts. Being able to express yourself in writing is important in mathematics, as it is in any other field of endeavor.
During the semester you will be asked to write two short papers on a topic relevant to the class, generally working with a partner. Parity may dictate one group of three. Your group will turn in a single paper and, except in extraordinary circumstances, each member of the group will receive the same grade. The process of writing a paper has two major components, each of which should constitute about half the work on the paper.
The first is to work out the mathematical details of the topic that you have been assigned.
MATH 1220, Section 4, Spring 2010
The second is to make sense of those mathematical details and to organize them into a coherent narrative. The paper may very well include symbols, computations, and graphs; however, these will need to be accompanied by generous verbal explanations that explain the mathematical ideas. You will be expected to write clearly and coherently, using correct mathematical and English grammar. Academic Honesty. In general, the rules set forth in the Course of Study apply. Algebra Review Table. Printable quick references from the book. Derivatives and Integrals.
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The table below shows you how to differentiate and integrate 18 of the most common functions. As you can see, integration reverses differentiation, returning the function to its original state, up to a constant C. The Riemann Sum formula provides a precise definition of the definite integral as the limit of an infinite series.
The Riemann Sum formula is as follows :.
Increase the number of rectangles n to create a better approximation:. So here is the Riemann Sum formula for approximating an integral using n rectangles:. The DI-agonal method is basically integration by parts with a chart that helps you organize information. This method is especially useful when you need to integrate by parts more than once to solve a problem. Use the following table for integration by parts using the DI-agonal method:. When you perform integration, there are three important rules that you need to know: the Sum Rule, the Constant Multiple Rule, and the Power Rule.
Calculus II | Summer | UMass Lowell
Here it is formally:. Here it is expressed in symbols:.
The Power Rule for Integration allows you to integrate any real power of x except —1. In Calculus, you can use variable substitution to evaluate a complex integral. Declare a variable u , set it equal to an algebraic expression that appears in the integral, and then substitute u for this expression in the integral.