Calculus 2, part 2 of 2: Sequences and series
Coupon Verified on April 5th, 2025
Course Name : Calculus 2, part 2 of 2: Sequences and series
Students : 165
Duration : 60.5 hours & 449 downloadable resources
Avg Rating : 4.5
Original Price : $119.99
Discount Price : $12
Instructor / Provider : Udemy
Course Type : Self Paced Online Course. Lifetime Access
Coupon : Click on ENROLL NOW to apply discount code
What you’ll learn
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How to solve problems concerning sequences and series (illustrated with 378 solved problems) and why these methods work.
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Various ways of defining number sequences: with help of a descriptive definition, an explicit (closed) formula, a recursive definition.
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Limits of number sequences, both finite and infinite (repetition and continuation of the topic introduced in Calc1p1).
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Arithmetic on extended reals (repetition and continuation of the topic introduced in Calc1p1).
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Dealing with indeterminate forms (repetition and continuation of the topic introduced in Calc1p1).
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Standard limits, comparing infinities (repetition and continuation of the topic introduced in Calc1p1).
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Squeeze Theorem for sequences (repetition and continuation of the topic introduced in Calc1p1).
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Weierstrass’ Theorem for sequences (repetition and continuation of the topic introduced in Calc1p1).
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Functions defined for all positive arguments and their role in examining number sequences (monotonicity, limits).
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Solving recurrence relations: closed formula for linear recurrences of order two (with or without initial conditions).
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Stolz-Cesà ro Theorem for computing limits of indeterminate forms.
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Ratio test for sequences for determining convergence or divergence.
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Cauchy Theorem (convergence of the arithmetic means of a convergent sequence).
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AM-GM inequality; convergence of the geometric means of a convergent sequence.
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Examining the differences of consecutive terms of the sequence (a_n) for determining convergence of a_n/n.
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Examining the quotients of consecutive terms of the sequence (a_n) for determining convergence of the n-th roots of a_n.
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Some applications of sequences (discretisation, approximations); sequences in other courses.
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Cauchy sequences and completeness of the set of real numbers; Bolzano-Weirestrass’ Theorem.
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Series as limits of partial sums of sequences: definition and examples.
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Convergent and divergent series: simple and advanced examples.
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Arithmetic and geometric series and their convergence.
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p-series, their relation to p-integrals; discussion of their convergence.
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Comparison criteria for series.
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Integral test for series.
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Ratio test for series.
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Root test for series.
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Sequences of real-valued functions (a very brief introduction).
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Series of real-valued functions (a very brief introduction).
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Power series and their radius of convergence.
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Taylor polynomials and Taylor series, smooth functions.
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Applications of Taylor polynomials for approximating values of functions.
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Applications of Taylor polynomials for computing limits of indeterminate forms.
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Sneak peek into the content of the next course (Real Analysis: metric spaces).
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