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Mathematics - Sequences and series

A whole semesters worth of notes on Sequences and series, seperated week by week with examples, definitions, theorems and proofs. Covering topics such as c... [Show More]

8 Items

Sequences - the algebra of limits and the sandwich theorem

Notes from the third week on my Sequences and Series module on my Mathematics course. The third week includes the algebra of limits with examples, and proo... [Show More]

Class Notes
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476

Sequences - Monotone convergence theorem

Notes from the fourth week on my Sequences and Series module on my Mathematics course. The fourth week includes the monotone convergence theorem, its appli... [Show More]

Class Notes
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829

Sequences - subsequences, bolzano weierstrass theorem, cauchy sequences

Notes from the fifth week on my Sequences and Series module on my Mathematics course. The fifth week includes subsequences, the bolzano weierstrass theorem... [Show More]

Class Notes
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472

Series - Convergent, divergent and geometric series.

Notes from the seventh week on my Sequences and Series module on my Mathematics course. The seventh week includes convergent, divergent and geometric serie... [Show More]

Class Notes
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476

Series convergence tests - Linearity of summations, null sequence, comparison, ratio and root test.

Notes from the eighth week on my Sequences and Series module on my Mathematics course. The eighth week includes the linearity of summation theorem with pro... [Show More]

Class Notes
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709

Series - Integral test, alternating series test, absolute convergence test,

Notes from the ninth week on my Sequences and Series module on my Mathematics course. The ninth week includes the Integral test and examples, alternating s... [Show More]

Class Notes
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633

Power series, calculating the radius of convergence and absolute convergence.

Notes from the tenth week on my Sequences and Series module on my Mathematics course. The tenth week includes power series, calculating the radius of conv... [Show More]

Class Notes
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690

Series- Differentiability of power series, the exponential function. Taylor and MacLaurin series.

Notes from the eleventh week on my Sequences and Series module on my Mathematics course. The eleventh week includes using power series to define the expon... [Show More]