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\huge{Week 15 --- Semester Overview} \\
\Large{MATH:114, Recitations 309 and 310} \\[2em]
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\cdotfill \ \ \ \textbf{Midterm 1} \ \ \ \cdotfill
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1. How can we use integrals to find the \textit{area between two curves}? How can we use geometry to estimate these calculations?
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2. Describe how the \textit{shell} and \textit{washer} methods work for finding volumes of solids of rotation. What geometric ideas are at play?
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3. Describe the ideas behind computing \textit{curve lengths} and \textit{surface} areas of solids of rotation. How are these related, if at all, to the shell and washer methods?
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4. What does \textit{Euler's formula} tell us?
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\cdotfill \ \ \ \textbf{Midterm 2} \ \ \ \cdotfill
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5. Talk about the ``information'' included in \textit{linear} and \textit{quadratic} approximations. How are these approximations related to \textit{Taylor polynomials}?
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6. Why do we use \textit{trigonometric substitutions} when integrating? What theorems and identities make these substitutions work?
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7. What is \textit{integration by parts}? How does it work?
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8. What makes \textit{partial fraction decomposition} a useful tool?
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9. Why do we use \textit{improper integrals}? Equivalently, what problem does an improper integral help us avoid?
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10. Discuss the ideas behind the three \textit{numerical integration} techniques: the \textit{midpoint rule}, the \textit{trapezoid rule}, and \textit{Simpson's rule}.
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11. What does it mean for an improper integral to \textit{converge} or \textit{diverge}? What techniques can we use to tell whether an improper integral converges or diverges?
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\cdotfill \ \ \ \textbf{Midterm 3} \ \ \ \cdotfill
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12. What is a \textit{sequence}? What does it mean for a sequence to \textit{converge}? Can you express this idea mathematically?
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13. What is a \textit{series}? What is the relationship between series and sequences? If a series converges, what can we say about its underlying sequence, and its sequence of partial sums?
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14. What tests can we use to determine whether a series converges or diverges? \textit{Why} do they work?
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