| << *continued from page 01 | A Perishable Feature |
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Day 1: Immediately begin contemplation of Fubini's Theorem of Fundamental Calculus for double integrals. A straightforward extension of the fundamental theorem for single integrals, Fubini's theorem returns volume for implicit dual-variable functions in z, and provides simple calculations of area for complex regions when regional formulae are known. Toward the end of the hour, as Dr. Polinski applies the day's theory to the realm of triple integrals, you realize that precise note-taking is required for success in this course, especially given its intense pace. |
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( Day 1 notes ) |
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Day 2: The examination of vector fields begins with a critical evaluation of magnitude and direction within multivariable functions. Close attention is paid to distinguishing between scalar and vector measurements, with implications in n-dimensional space. After several spontaneous examples, vector-valued functions of several variables lead to in-depth discussion of future applications and related theory. Given the extremely abstract nature of this new material, you will definitely need to reference your detailed notes during future study. |
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( Day 2 notes )
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Day 3: In order to evaluate volumes for implicit z-functions over complex areas, the exploration of regional classifications for double integrals ensues. The distinction between the two central types of regional boundaries rests in the nature of their respective functional descriptions. Two continuous multivariable functions in x defined along the y-axis, with constants x=a and x=b comprising x-axis limits, determines a type I region. Conversely, an inverse regional description defined in terms of two x-functions in y, as well as limiting constants y=c and y=d, determines a type II region. Although a substantial amount of material was covered today, you managed to capture its full essence. |
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( Day 3 notes ) |
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Day 4: Just as single integrals were defined for functions of one variable, and double integrals for functions of two variables, triple integrals can be defined for functions of three variables. The definition begins with functions defined over cubical regions in R^3, continues with the elaboration of the Triple Riemann Sum, and culminates in the description of triple integrals over general bounded regions E. Despite conceptual clarity, the calculations can be confusing. |
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( Day 4 notes ) |
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| /continued *next page >> | ||||
| /return to *top of page ^^ |
| Written & Illustrated by Perishable for DLa #13 / Spring, 2002 | 050502-021105 |
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| Advanced Calculus Secrets : Revealed! ~ A Perishable Guide to Mastering Mathematics / ( page 02 ) |
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