![]() ![]() 8.7: Taylor Polynomials A Taylor polynomial is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point.We start this new approach to series with a definition. Given a value of x, we evaluate f(x) by finding the sum of a particular series that depends on x (assuming the series converges). 8.6: Power Series So far, our study of series has examined the question of "Is the sum of these infinite terms finite?,'' i.e., "Does the series converge?'' We now approach series from a different perspective: as a function.We start with a very specific form of series, where the terms of the summation alternate between being positive and negative. 8.5: Alternating Series and Absolute Convergence In this section we explore series whose summation includes negative terms.This section introduces the Ratio and Root Tests, which determine convergence by analyzing the terms of a series to see if they approach 0 "fast enough.'' 8.4: Ratio and Root Tests The comparison tests of the previous section determine convergence by comparing terms of a series to terms of another series whose convergence is known.8.3: Integral and Comparison Tests There are many important series whose convergence cannot be determined by these theorems, though, so we introduce a set of tests that allow us to handle a broad range of series including the Integral and Comparison Tests.Most series that we encounter are not one of these types, but we are still interested in knowing whether or not they converge. 8.2: Infinite Series This section introduces us to series and defined a few special types of series whose convergence properties are well known: we know when a p-series or a geometric series converges or diverges. ![]() In mathematics, we use the word sequence to refer to an ordered set of numbers, i.e., a set of numbers that "occur one after the other.'' For instance, the numbers 2, 4, 6, 8. 8.1: Sequences We commonly refer to a set of events that occur one after the other as a sequence of events.Murali has a bachelor's degree in Engineering from IIT Madras.\) Murali has also delivered training and professional development programs for secondary science teachers and 'making' skills to "gifted students" for around 4 years. In addition to delivering Vocational Training to young adults, he is currently responsible for design, manufacturing and marketing operations at a traditional handicraft (wooden toys) enterprise near Bengaluru. Muralidhar (aka Murali) is senior mentor and course designer at GenWise with 20 years of experience in the social sector. Rachit has a Masters degree from the Centre For Electronic Design And Technology at the Indian Institute of Science, Bengaluru. He likes to spend his time on reading, understanding audio, building speakers, music, and sports. His work experience includes Cosmic Circuits and Cadence Design Systems (which acquired Cosmic Circuits), on the design of integrated circuits for audio codecs, serial interfaces, and phase locked loops amongst other things. Rachit is an electronics engineer who has been designing analog circuits for the past decade. Jayasri Bhattacharya, mother of a student Jerry is doing a great job which cannot be valued in money terms. Students will submit the assignments and their questions and will receive feedback and responses from the instructor.Įvery day Jerry assigns work his comments on the submitted assignment are so good he provides clues for moving to the next step. After each interactive session, students will work on their own to extend the problems further and frame questions for future exploration. The highly interactive sessions will involve working independently and in small groups as well as sharing and discussing your work with others. In this course, we will use visualizations, pattern analysis, and real-world scenarios to explore a variety of ways in which sequences and series help us begin to understand how the past creates the future. But there is more to them than you learn in school! Because sequences and series describe patterns and show change, we can use them to model environmental and population dynamics, determine safe and effective drug dosage schedules, and even develop financial loan schedules. They are standard topics in school mathematics courses from middle school onward. In this course, you will explore sequences and series, which are simply lists of numbers and their sums. They are observers who learn to see what the untrained eye does not notice and thinkers who use logic to look beyond the obvious. ![]() ![]() Mathematicians are not human calculators. ( This course is targeted at children entering Grades 7, 8, 9, 10 in 2020-21) ![]()
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