61. Calculus, Calculus I, Calculus II, Calculus Of A Single Variable, Multivariable calculus Labs A series of CAS technology based lab projects, Graphing Calculator Programs The calculator programs referenced in the Graphing Calculator http://college.hmco.com/mathematics/larson/calculus_analytic/8e/students/

Appendices Chapter Summaries Calculus Labs Graphing Calculator Programs ... HM mathSpace Student CD: Updated Section 2.1 Try It 6 Textbook Site for: Calculus, Calculus I, Calculus II, Calculus of a Single Variable, Multivariable Calculus Eighth Edition Ron Larson - The Pennsylvania State University, The Behrend College Robert P. Hostetler - The Pennsylvania State University, The Behrend College Bruce H. Edwards - University of Florida Appendices Additional resource material related to calculus topics Chapter Summaries Chapter Summaries are available for each chapter exclusively online. Calculus Labs A series of CAS technology based lab projects Graphing Calculator Programs The calculator programs referenced in the Graphing Calculator Guide can be downloaded from this page. Algebra Review Table Printable quick references from the book. Trigonometry Review Table Printable quick references from the book. Formulas from Geometry Printable quick references from the book. Algebra Review Summary Additional resource for review of algebra skills Derivatives and Integrals Printable quick references from the book.

62. Calculus Notes (PostScript) The first group contains notes on topics in singlevariable calculus. the Zero Limit Test, the harmonic series, p-series, the Integral Test. http://marauder.millersville.edu/~bikenaga/calculus/calcnote.html

Calculus Notes (PostScript) These are links to PostScript files containing notes for various topics in calculus. How do I view/print the notes? How may I use/distribute the notes? How did you write them? I haven't written notes for all the topics covered in calculus - so if something isn't covered here, it's probably because it hasn't been written up yet. Most of these are in rough form, with some heuristic discussion and examples (but few proofs). As I write or update my notes, I'll put copies here. If you just want worked-out problems, check out the calculus review sheets These notes are in two groups. The first group contains notes on topics in single-variable calculus. At most schools, this takes two terms; the courses are usually called Calculus I and Calculus II limintr.ps (4 pages, 92,118 bytes) : An introduction to limits; basic computations. limlr.ps (5 pages, 144,164 bytes) : Left and right-hand limits. limdef.ps (4 pages, 164,489 bytes) : The limit definition. limprop.ps (4 pages, 85,506 bytes) : Properties of limits. inflim.ps (6 pages, 176,498 bytes)

63. Topics In A Calculus II Course Ratio Test, A test for determining whether a series converges. It is used for calculating the radius of convergence for power series. http://mathworld.wolfram.com/classroom/classes/CalculusII.html

INDEX Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics ... Alphabetical Index DESTINATIONS About MathWorld About the Author Headline News ... Random Entry CONTACT Contribute an Entry Send a Message to the Team MATHWORLD - IN PRINT Order book from Amazon Topics in a Calculus II Course To learn more about a topic listed below, click the topic name to go to the corresponding MathWorld classroom page. Arc Length The length along a curve if it were straightened out. Convergent Series A series for which partial sums become arbitrarily close to some fixed number. Exponential Growth The increase in a quantity according to an exponential function. Harmonic Series The sum of the reciprocals of the positive integers. This series diverges. Maclaurin Series A Taylor series expansion of a function around zero. Power Series A sum of powers of a variable. A power series is essentially an infinite polynomial. Radius of Convergence Half the width of the interval inside which a power series converges absolutely. Ratio Test A test for determining whether a series converges. It is used for calculating the radius of convergence for power series. Surface of Revolution A surface generated by rotating a two-dimensional curve about an axis.

64. Leaving Cert. Higher Level Maths - Further Calculus And Series Index of applets from the Further calculus And series section of the TCD leaving cert higher level maths website. http://www.netsoc.tcd.ie/~jgilbert/maths_site/applets/further_calculus_and_serie

Search for: in Entire website Algebra Complex Numbers Matrices Sequences and series Differentiation Integration Circle Vectors Linear Transformations Line Geometry Trigonometry Probability Further Calculus and Series Website Home Algebra Complex Numbers Matrices ... Integration You are here: Home Category Index / Further Calculus And Series Further Calculus And Series Max/min Volume Problems - By Fergal Reid This Applet Demonstrates How Differnetial Calculus Can Quickly Solve Max/min Problems. It Provides An Illustration Of What It Is That Calculus Actually Helps Us Do, And The Power Of Calculus As A Tool For Finding Quantities Maximum Or Minimum Values, And The Conditions Under Width These Occur. [ View Applet Approximation Of Pi - By Birgit Boeckeler There Are Several Ways To Approximate Pi Mathematically, This Applet Uses The Most Illustrative One: It Draws Two Polygons And A Circle On The Screen, One Polygon Touching The Circle From The Outside, One From The Inside. The Polygons Double The Number Of Their Sides With Each Approximation, The Values Of Their Perimeters And Areas Getting More And More Close To Those Of The Circle. N.b.: The Applet Shows Just A Quarter Of The Drawing And Thus Uses A "default Zoom", As The Polygons Are Increasingly Difficult To Distinguish From The Circle. [ View Applet Maximum Area Problems - By Annie Bedford The Applet Shows The Effect Of Changing The Length And Width Of A Rectangle On The Area Of A Rectangle. The Graph Shows The Current Area's Position In Relation To The Maximum Area's Position. [

65. Leaving Cert. Higher Level Maths - Further Calculus And Series - The Ratio Test The Ratio Test is a Test to determine whether an infinite series converges towrards a point or does not. This applet allows a user to select a preset series http://www.netsoc.tcd.ie/~jgilbert/maths_site/applets/further_calculus_and_serie

Search for: in Entire website Algebra Complex Numbers Matrices Sequences and series Differentiation Integration Circle Vectors Linear Transformations Line Geometry Trigonometry Probability Further Calculus and Series Website Home Algebra Complex Numbers Matrices ... Integration You are here: Home Category Index Further Calculus And Series / The Ratio Test The Ratio Test - By Adam Bermingham How to use this applet: The three buttons in the program represent examples of the three types of result that can be obtained from the Ratio Test. These are a good starting point. It should be apparent from the graph that the converging graphs are ones which ben down and diverging graphs are those which bend up - 'neither' being in between i.e. straight. The user may also enter series. All functions must be grouped with square brackets so the program knows how to group the terms. All series must not include spaces. Operators: denotes powers denotes multiplication denotes division denotes subtract, add Here are some examples which you can use to get used to the syntax and see for yourself if they converge or not...

66. Multivariable Calculus This is a textbook for a course in multivariable calculus. Chapter Ten Sequences, series, and All That 10.1 Introduction 10.2 Sequences 10.3 series http://www.math.gatech.edu/~cain/notes/calculus.html

Multivariable Calculus George Cain James Herod This is a textbook for a course in multivariable calculus. It has been used for the past few years here at Georgia Tech. The notes are available as Adobe Acrobat documents. If you do not have an Adobe Acrobat Reader, you may down-load a copy, free of charge, from Adobe Title page and Table of Contents Table of Contents Chapter One - Euclidean Three Space 1.1 Introduction 1.2 Coordinates in Three-Space 1.3 Some Geometry 1.4 Some More GeometryLevel Sets Chapter Two - VectorsAlgebra and Geometry 2.1 Vectors 2.2 Scalar Product 2.3 Vector Product Chapter Three - Vector Functions 3.1 Relations and Functions 3.2 Vector Functions 3.3 Limits and Continuity Chapter Four - Derivatives 4.1 Derivatives 4.2 Geometry of Space CurvesCurvature 4.3 Geometry of Space CurvesTorsion 4.4 Motion Chapter Five - More Dimensions 5.1 The space R n 5.2 Functions Chapter Six - Linear Functions and Matrices 6.1 Matrices 6.2 Matrix Algebra Chapter Seven - Continuity, Derivatives, and All That 7.1 Limits and Continuity

67. Calculus - Content Standards (CA Dept Of Education) Consideration of the College Board syllabi for the calculus AB and 25.0 Students differentiate and integrate the terms of a power series in order to http://www.cde.ca.gov/be/st/ss/mthcalculus.asp

Search Advanced Site Map A-Z Index Professional Development ... Printer-friendly version Calculus Grades Eight Through Twelve - Mathematics Content Standards. Students demonstrate knowledge of both the formal definition and the graphical interpretation of limit of values of functions. This knowledge includes one-sided limits, infinite limits, and limits at infinity. Students know the definition of convergence and divergence of a function as the domain variable approaches either a number or infinity: 1.1 Students prove and use theorems evaluating the limits of sums, products, quotients, and composition of functions. 1.2 Students use graphical calculators to verify and estimate limits. 1.3 Students prove and use special limits, such as the limits of (sin(x))/x and (1-cos(x))/x as x tends to 0. Students demonstrate knowledge of both the formal definition and the graphical interpretation of continuity of a function. Students demonstrate an understanding and the application of the intermediate value theorem and the extreme value theorem.

68. Karl's Calculus Tutor: Table Of Contents Table of Contents for Karl s calculus Tutor. Select from topics Limits, More on Taylor Maclaurin series; Sample Exam Questions on Integral calculus http://www.karlscalculus.org/calculus.html

Karl's Calculus Tutor Table of Contents last update 1-Sep-2005 Donate to the Hurricane Katrina relief effort. Want to turn the tables on spammers? It's free. IMPORTANT VIEWING NOTE: If you can't see the word " here " in the line above, place your mouse-cursor on the right-hand edge of the frame, hold the left mouse button, and drag the right-hand edge of the screen to the right until you can see it. See browser notes for more details. click here Section Index 1) Number Systems 2) Limits 3) Continuity 4) Derivatives ... Special Interest Pages Table of Contents Please note that Karl's Calculus Tutor is still a work in progress. Expect a new unit to come on line every month or so. Currently being drafted: Applications of Integration (Areas) And vastly improved! I have completely revamped the Online Calculator . It is now much more user friendly and powerful. Be sure to read the Read me notes before trying any calculations. Please let me know if it helps with doing any of the on line problems (clicking will spawn a separate browser window). You can also try Online Complex Calculator , which can do arithmetic of complex numbers (I have not yet made the same improvements to the complex calculator, but that's coming).

69. Calculus Lessons AP calculus LESSONS Sequences and series; Limits of Sequences; series and Convergence; Geometric series; pseries; The Ratio and Root Tests http://www.mecca.org/~halfacre/MATH/lessons.htm

AP CALCULUS LESSONS Summer Work Class Contract Limits and Continuity Derivatives ... Integration Riemann Sums Fundamental Theorem of Calculus Integration by Substitution Trapezoidal Rule Review Semester Exam a good review source Exponential,Logarithmic, and Inverse Trigonometric Functions Logarithms The Derivative of the Natural Logarithm Derivatives of Inverse Functions Derivatives of Natural Exponential Functions Integrate Exponential Functions Slope Fields Inverse Trigonometric Functions Derivatives of Inverse Trigonometric Functions Integrals Involving Inverse Trigonometric Functions Applications of Integrals Area Between Curves Volumes by disk method Volumes, using washers Volumes, using known cross-sections Volumes, using shells Arclength Work Moments and Centroids Integration Techniques Integration by Parts Trigonometric Integrals (more complex ones) Trigonometric Substitution Partial Fractions Improper Integrals Review Infinite Series Sequences and Series Limits of Sequences Series and Convergence Geometric Series p -Series The Ratio and Root Tests Alternating Series Power Series Special Functions Review Parametric Equations and Polar Coordinates Vectors Functions in Two Variables Limits Cobwebs Review Go to Calculus Page

70. Mastering Calculus Series - Grades 11-12 The Mastering calculus series covers five topics of an introductory calculus course. Each program contains a powerful, yet flexible and easyto-use http://www.wkbradford.com/mastcalc.html

Grades 9-12 Mastering Calculus Series - Grades 11-12 Developed by: NECTAR Foundation Titles: Trigonometry Curve Sketching Limits Derivatives The Mastering Calculus Series covers five topics of an introductory Calculus course. Each program contains a powerful, yet flexible and easy-to-use interactive tutorial with lessons and questions. The series provides for self-directed, self-paced, individualized learning. The programs quickly and easily isolate student strengths and weaknesses and identify and prescribe the specific remediation required. Mastering Calculus lessons foster student responsibility for learning - students progress at their own rate. Post tests provide detailed analysis that is cross-referenced to the tutorial material. Each module consists of three software components that: evaluate prerequisite skill levels, present interactive tutorials, and provide summative assessment. Mastering Calculus allows you to easily establish whether or not a student has all of the necessary skills prior to starting a new unit of study. The first component of each module performs a diagnosis of the student's knowledge of prerequisite skills. Results indicate if the student is ready for the unit, and if not, what specific remediation is required. The tutorials combine text, graphics, animation, sample problems, and student exercises to allow students to progress at their own rate. Randomly generated questions with step by step solutions are available to students at a variety of cognitive levels. This component of each module encourages student responsibility for learning.

71. Calculus Videos Topics include calculus 1, the first title in the calculus series, A continuation of calculus 2 in the calculus series, presents more difficult http://math.about.com/cs/calculus/tp/calculusvideos.htm

var zLb=1; var zIoa1 = new Array('Related Guide Picks','Calculus Resources and Tutorials','/cs/calculus/index.htm','Top Pick Calculus Books','http://math.about.com/cs/calculus/tp/calculustp.htm'); zJs=10 zJs=11 zJs=12 zJs=13 zc(5,'jsc',zJs,9999999,'') About Homework Help Mathematics Homework Help ... Help zau(256,140,140,'el','http://z.about.com/0/ip/417/C.htm','');w(xb+xb+' ');zau(256,140,140,'von','http://z.about.com/0/ip/496/7.htm','');w(xb+xb); FREE Newsletter Sign Up Now for the Mathematics newsletter! See Online Courses Search Mathematics Stay up to date! Compare Prices Email to a friend ... Print this page Related Guide Picks Calculus Resources and Tutorials Top Pick Calculus Books Most Popular Area and Surface Formulas Worksheets in PDF and Word multiplication table tricks Multiplication Chart, Multiplication Table ... Facts to 20 - PDF What's Hot Exponents 11th grade math, Eleventh grade math Polygons Shape Book ... What's Needed? Related Topics Physics Chemistry Teen Advice Homework / Study Tips ... Homeschooling Guide Picks From Deb Russell Your Guide to Mathematics FREE Newsletter.

72. UBC Calculus Online Course Notes Definite Integrals and the Fundamental Theorem of calculus Why do Taylor series work? What can we do with Taylor series? More applications of series http://www.ugrad.math.ubc.ca/coursedoc/math101/notes/

Course Notes Here is an interactive text to accompany the course. We invite you to take advantage of the many demonstrations to explore Calculus more deeply. Definite Integrals and the Fundamental Theorem of Calculus Introduction Overview of calculus from a historical perspective Some special sums How Archimedes found the area of a circle ... How to use the Fundamental Theorem Applications of the Definite Integral Acceleration, Velocity, and Position Average value of a function Calculating Simple Volumes Arc Length and Surface Area ... Work Techniques for Antidifferentiation Indefinite Integrals Change of Variables Integration by Parts More Applications Differential Equations Separable Differential Equations The Logistic Equation and Integration by Partial Fractions The Logistic Equation with Harvesting and Qualitative Methods More about Qualitative Methods for Differential Equations ... An Application: Can cats control a rat population? Weighted Averages Centers of Mass Probability Densities Means, Medians, and Averages Moments of a Probability Distribution ... The Normal distribution More Techniques for Integration Numerical Integration Improper Integrals Taylor polynomials and series Introduction to series Convergence of series Finding Taylor Series Why do Taylor series work?

73. Canisius College - Canisius College - Series Four Courses - Dr. Sarada Rajeev MAT 314 Neither Newton nor Leibnitz The Pre-History of calculus and Celestial They knew of the theory of infinite series, notions of convergence, http://www.canisius.edu/topos/rajeev.asp

Undergraduate Admissions Graduate/Masters Admissions Transfer Students International Students Residence Life Campus Ministry Campus Programming and Leadership Development Student Affairs Student Involvement Support Resources Computer Resources Undergraduate Majors/Programs Graduate/Masters Programs Academic Calendar Internship Opportunities Faculty Service Learning Academic Integrity Teams Facilities Calendar of Events News Archives Commencement Information Reunions Shop Canisius Register for Classes Class and Exam Schedules Class Cancellations Tuition Payment Program Home Introduction Special Events Series Four ... (Fall 2004) Quicklinks About Buffalo Blackboard Bookstore Financial Aid GriffMail Jesuit Tradition Library Support Canisius MAT 314: Neither Newton nor Leibnitz - The Pre-History of Calculus and Celestial Mechanics in Medieval Kerala 7 — 11 March 2005 Old Main 403 Canisius College: 5:00 — 8:00pm Daily Instructor: Dr Sarada Rajeev Professor of Physics University of Rochester Rochester, New York rajeev@pas.rochester.edu Course Archives All files below are Adobe Acrobat (.pdf). File size as indicated.

74. Video Aided Instruction Calculus Series These videos from Video Aided Instruction review students for academic educational subjects or standardized tests. http://www.videoaidedinstruction.com/calculus.html

your shopping cart home browse our products great deals! ... help Calculus Series programs on videos printed study guide included hrs. mins. total price buy the complete series! Work at your own speed! Improve your grades! Easy for non-math majors! The Video Aided Instruction Calculus Series covers the same material taught in first-year college-level calculus courses, including high school Advanced Placement calculus courses. There is no need to dread calculus: this excellent video series prepares the high school or college student for even the most difficult and challenging problems, and is an excellent learning tool for adults who want to relearn forgotten mathematics. the 4 programs in this series are: (click on each title to learn more or buy individually) Calculus 1 Calculus 2 Calculus 3 Calculus 4 related programs include: Precalculus Read our Privacy Policy and mail: 485-34 South Broadway, Hicksville, NY 11801-5071

75. Mika Seppälä: Single Variable Calculus Maple is used to illustrate various calculus concepts. Integral Test for the Convergence of series and the Harmonic series. pdf slides, pdf handout, http://webalt.net/Calculus-2004/

Single Variable Calculus Spanish translation has been completed and will be published in September 2005. Technical Assistant Matti Pauna This set of notes corresponds to black board notes that a professor might write during a lecture. In depth discussions are given to selected parts of the text. Maple is used to illustrate various calculus concepts. The 2004 development cycle of these notes is now complete. A revision of the notes will take place in 2005. In that revision live mathematics illustrations using MapleNET will be developed and integrated into the lectures. An extensive interactive set of exercises using WebALT and MapleTA will also be written 2005. The revision will benefit from the WebALT project which is supported by the European Commission. MapleTA is a trademark of Maplesoft. The revised notes will be made available at webalt.com for registered users. and how to get the password to edit the files. Best viewed by Internet Explorer 6.0 or later with MS Office 2003, MathType and Maple installed locally. Minimum software requirements: IE 6, PowerPoint 2003 Viewer and Adobe Reader Maple is needed to compute with the Maple files.

76. Index Of /Calculus/Series . DIR Parent Directory 28May-2002 1133 - 1.tex 22-Jan-2002 2124 1k 1.tex.bak......Index of /calculus/series. Name Last modified Size http://mark.math.helsinki.fi/Calculus/Series/

Index of /Calculus/Series Name Last modified Size Description ... Parent Directory 28-May-2002 11:33 - 1.tex 22-Jan-2002 21:24 1k 1.tex.bak 22-Jan-2002 21:24 1k 2.tex 22-Jan-2002 21:24 1k 2.tex.bak 22-Jan-2002 21:24 1k 3.tex 22-Jan-2002 21:24 1k 4.tex 22-Jan-2002 21:24 2k 4.tex.bak 22-Jan-2002 21:24 2k 5.tex 22-Jan-2002 21:24 1k 5.tex.bak 22-Jan-2002 21:24 1k 5x.tex 22-Jan-2002 21:24 1k 5x.tex.bak 22-Jan-2002 21:24 1k WS_FTP.LOG 23-Jan-2002 02:13 1k 23-Jan-2002 02:12 - harmonic.gif 22-Jan-2002 21:24 12k harmonic.mws 22-Jan-2002 21:24 2k Apache/1.3.33 Server at mark.math.helsinki.fi Port 80

77. Areas Of Mathematics Related To Calculus integration, series, and so on are familiar to students of elementary calculus. 40 Sequences and series are really just the most common examples of http://www.math.niu.edu/~rusin/known-math/index/tour_cal.html

Search Subject Index MathMap Tour ... Help! Calculus and Real analysis Return to start of tour Up to Mathematical Analysis Differentiation, integration, series, and so on are familiar to students of elementary calculus. But these topics lead in a number of distinct directions when pursued with greater care and in greater detail. The central location of these fields in the MathMap is indicative of the utility in other branches of mathematics, particularly throughout analysis. 26: Real functions are those studied in calculus classes; the focus here is on their derivatives and integrals, and general inequalities. This category includes familiar functions such as rational functions. This seems the most appropriate area to receive questions concerning elementary calculus. 28: Measure theory and integration is the study of lengths, surface area, and volumes in general spaces. This is a critical feature of a full development of integration theory; moreover, it provides the basic framework for probability theory. Measure theory is a meeting place between the tame applicability of real functions and the wild possibilities of set theory. This is the setting for fractals. 33: Special functions are just that: specialized functions beyond the familiar trigonometric or exponential functions. The ones studied (hypergeometric functions, orthogonal polynomials, and so on) arise very naturally in areas of analysis, number theory, Lie groups, and combinatorics. Very detailed information is often available.

78. Calculus II: Lesson 20: Taylor Series - Maple Application Center - Maplesoft Conduct a search simple advanced calculus II Lesson 20 Taylor series In this worksheet, we look at Taylor series. http://www.maplesoft.com/applications/app_center_view.aspx?AID=1837&CID=14&SCID=

79. Calculus II: Lesson 16: Introduction To Infinite Series - Maple Application Cent Conduct a search simple advanced calculus II Lesson 16 Introduction to Infinite series This worksheet introduces infinite series. http://www.maplesoft.com/applications/app_center_view.aspx?AID=1833&CID=14&SCID=

80. A Divergent Alternating Series Whose Terms Go To Zero Next The commutative law doesn t Up Second semester calculus Previous Second This series also diverges. The divergent harmonic series overpowers http://www.math.tamu.edu/~tom.vogel/gallery/node9.html

Next: The commutative law doesn't Up: Second semester calculus Previous: Second semester calculus A divergent alternating series whose terms go to zero From the alternating series test, you know that if and if decreases monotonically to zero, then converges. However, it is not enough to have having a limit of zero, you also need decreasing, as the following example shows. Take your favorite convergent series with positive terms, say , and take your favorite divergent positive term series whose terms go to zero, say . Now ``shuffle'' these together to form the following series: This alternates, the terms go to zero, but the terms are not decreasing monotonely to zero. This series also diverges. The divergent harmonic series overpowers to force the sum off to . (This can be made rigorous by looking at partial sums). Tom Vogel Mon May 5 12:53:33 CDT 1997

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