Throughout calculus volume 3 you will find examples and exercises that present classical ideas and techniques as well as modern applications and methods. Sequences the lists of numbers you generate using a numerical method like newtons method to get better and better approximations to the. This text comprises a threetext series on calculus. Other functions will also be regarded as sequences. Volume 3 covers parametric equations and polar coordinates, vectors, functions of several variables, multiple integration, and secondorder differential equations. Series are similar to sequences, except they add terms instead of listing them as separate elements. There is online information on the following courses.
Questions and commands are never propositions, but statements like \my buick is maroon t and \my buick is black f are propositions. These simple innovations uncover a world of fascinating functions and behavior. Page 838 sigma notation college algebra wednesday april 5. A realvalued function with domain the natural numbers n f1,2 3. Convergence of a sequence, monotone sequences in less formal terms, a sequence is a set with an order in the sense that there is a rst element, second element and so on. Thus, the first term corresponds to n 1, the second to n 2, and so on. Review sheet for calculus 2 sequences and series sequences convergence a sequence fa ngconverges if lima n exists and is nite. Sequences and series harvard mathematics department. Stewart calculus 7e solutions chapter 11 infinite sequences and series exercise 11.
The first part covers material taught in many calc 1 courses. If youd like a pdf document containing the solutions the download tab above contains links to pdf s containing the solutions for the full book, chapter and section. A sequence is a function with domain the natural numbers n1,2, 3, or the nonnegative integers, z. Series recall that a series, roughly speaking, is the sum of a sequence. Derivations and explanations are based on years of classroom experience on the part of longtime calculus professors, striving for a balance of clarity and rigor that has proven successful with their. The second text covers material often taught in calc 2.
Precalculus 11 chapter 1 sequences and series created by ms. For the love of physics walter lewin may 16, 2011 duration. Sequences examples showing convergence or divergence. Calculus 2 geometric series, pseries, ratio test, root test, alternating series, integral test duration. If a n b n for every n large enough, then the series x1 n1 a n and x1 n1 b n either both converge or both diverge. The sum of an infinite series is three times its first term. In the sequel, we will consider only sequences of real numbers. Here are a set of practice problems for the series and sequences chapter of the calculus ii notes. We can now return to the example from the previous page and a similar example. If you are required to take three semesters of calculus courses. A power series is like a polynomial of in nite degree.
Introduction to series and sequences math 121 calculus ii d joyce, spring 20 the goal. Here is a set of notes used by paul dawkins to teach his calculus iii course at lamar university. Topics covered are three dimensional space, limits of functions of multiple variables, partial derivatives, directional derivatives, identifying relative and absolute extrema of functions of multiple variables, lagrange multipliers, double cartesian and polar coordinates and triple integrals. Limits of ratios an important concern of calculus is what happens to the ratio. Sequences and series department of mathematics university of. Series, convergence, divergence mit opencourseware. Lets discuss these ways of defining sequences in more detail, and take a look at some examples. Powered by create your own unique website with customizable templates. Infinite sequences and series, vector algebra, curves. This sequence is different from the first two in the sense that it doesnt have a specific formula for each term.
Chapter 2 limits of sequences university of illinois at. A sequence fa ngis called monotonic if it is either increasing or decreasing. The terms of a sequence may be arbitrary, or they may be defined by a formula, such as s n 2n in general, n starts at 1 for sequences, but there are times when it is convenient for n to start at 0, in. A sequence is converging if its terms approach a specific value as we progress through them to infinity. Remember that we are assuming the index n starts at 1. Convergent and divergent sequences video khan academy. Definition, with examples of convergent and divergent sequences.
Other useful facts a n converges to zero if and only if ja njalso converges to zero. Deturck university of pennsylvania march 29, 2018 d. This sequence of three courses cover the single variable and multivariable calculus. If you are required to take only one semester of calculus course, go for our college calculus rl411. This is correct, and will have significant value to us in this course. Gonzalezzugasti, university of massachusetts lowell 1. Math 142 with a grade of c or better or consent of instructor. And this sort of thinking is needed to make sense of numbers like. Find the nth term rule of sequence of each sequence, and use it to determine whether or not the sequence converges. This is a summary of the main points weve dis cussed in class about the infinite sequences. Calculus 3, introduction to sequences and series youtube.
The range of the function is still allowed to be the real numbers. Represent and calculate sums of series with sigma notation. Our calculus volume 3 textbook adheres to the scope and sequence of most general calculus courses nationwide. Calculus bc and bcd drill on sequences and series by susan e. The sequence we saw in the previous paragraph is an example of whats called an arithmetic sequence. Introduction to series and sequences math 121 calculus ii.
A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. In this sequence, the pattern is that i started with a 1, and add 3 to get the next term. Catalog description math 143 calculus iii 4 units ge area b1 prerequisite. The geometric series 1 368 10 lnfinlte series 1 1 10. The main purpose of our study of series and sequences is to understand power series.
In the end, all the key functions of calculus appear as infinite polynomials except the step function. The sum of an infinite geometric series is 9 and its common ratio is 3 1. Sequences and power series kenyatta university library. Sequences and series notes for math 3100 at the university. Selection file type icon file name description size revision time user.