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math104-s22:s:jdamaj [2022/02/15 04:36] jdamaj [5 Questions] |
math104-s22:s:jdamaj [2026/02/21 14:41] (current) |
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| ===== Course Journal ===== | ===== Course Journal ===== | ||
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| ==== Feb 10 ==== | ==== Feb 10 ==== | ||
| - | * Unordered List Item | + | * Series |
| + | * Summation by Parts | ||
| + | * Power Series | ||
| ==== 5 Questions ==== | ==== 5 Questions ==== | ||
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| * What properties does multiplication in limsup(a_nb_n) have in general. | * What properties does multiplication in limsup(a_nb_n) have in general. | ||
| * Is there a good way to get intuition for accumulation of infinite series, eg. the case of sum(1\n) | * Is there a good way to get intuition for accumulation of infinite series, eg. the case of sum(1\n) | ||
| + | |||
| + | ==== February 22 ==== | ||
| + | * Definition of Metric Space + examples | ||
| + | * Topology | ||
| + | * Open Sets | ||
| + | |||
| + | ==== February 24 ==== | ||
| + | * More Metric Space examples | ||
| + | * Sequences + Cauchy Criterion | ||
| + | * Closure/ Closed Sets | ||
| + | |||
| + | ==== March 1 ==== | ||
| + | * Continuous Maps (open cover def and sequential def) | ||
| + | * Inherited Topology | ||
| + | |||
| + | ==== March 3 ==== | ||
| + | * Open cover compactness | ||
| + | * Sequential compactness | ||
| + | |||
| + | ==== March 8 ==== | ||
| + | * Sequential Compactness $\to$ Open Cover Compactness | ||
| + | |||
| + | ==== March 10 ==== | ||
| + | * Connectedness | ||
| + | |||
| + | ==== March 15 ==== | ||
| + | * Continuous maps preserve compactness and connectedness | ||
| + | * Uniform Continuity | ||
| + | * Discontinuity | ||
| + | |||
| + | ==== March 17 ==== | ||
| + | * Sequences and Series of Functions | ||
| + | * Uniform Convergence | ||
| + | |||
| + | ==== March 29 ==== | ||
| + | * Differentiation | ||
| + | * Rolle' | ||
| + | |||
| + | ==== March 31 ==== | ||
| + | * Generalized Mean Value Theorem | ||
| + | * L' | ||
| + | |||
| + | ==== April 7 ==== | ||
| + | * Higher Derivatives | ||
| + | * Taylor' | ||
| + | |||
| + | ==== April 12 ==== | ||
| + | * Taylor Series | ||
| + | * Power Series | ||
| + | * Reimann Integral | ||
| + | |||
| + | ==== April 14 ==== | ||
| + | * Integration | ||
| + | * Reimann - Stieltjes Integral | ||
| + | |||
| + | ==== April 19 ==== | ||
| + | | ||
| + | |||
| + | ==== April 21 ==== | ||
| + | * Properties of Integrals | ||
| + | |||
| + | ==== April 26 ==== | ||
| + | * Uniform Convergence with Integration | ||
| + | * Uniform Convergence with Differentiation | ||
| ===== Homework ===== | ===== Homework ===== | ||
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