121. Calculus History The main ideas of calculus developed over a very long period of time. Read about some of the mathematicians who contributed to this field of mathematics. http://www-history.mcs.st-andrews.ac.uk/HistTopics/The_rise_of_calculus.html

A history of the calculus Analysis index History Topics Index Version for printing The main ideas which underpin the calculus developed over a very long period of time indeed. The first steps were taken by Greek mathematicians. To the Greeks numbers were ratios of integers so the number line had "holes" in it. They got round this difficulty by using lengths, areas and volumes in addition to numbers for, to the Greeks, not all lengths were numbers. Zeno of Elea , about 450 BC, gave a number of problems which were based on the infinite. For example he argued that motion is impossible:- If a body moves from A to B then before it reaches B it passes through the mid-point, say B of AB. Now to move to B it must first reach the mid-point B of AB . Continue this argument to see that A must move through an infinite number of distances and so cannot move. Leucippus Democritus and Antiphon all made contributions to the Greek method of exhaustion which was put on a scientific basis by Eudoxus about 370 BC. The method of exhaustion is so called because one thinks of the areas measured expanding so that they account for more and more of the required area. However Archimedes , around 225 BC, made one of the most significant of the Greek contributions. His first important advance was to show that the area of a segment of a parabola is

122. Calculus Resources Covers limits, derivatives, integration, infinite series and parametric equations. Includes resource links for multivariable calculus, differential equations and math analysis. http://www.langara.bc.ca/mathstats/resource/onWeb/calculus/

Langara College - Department of Mathematics and Statistics Internet Resources for the Calculus Student Topics in Calculus Precalculus Review Limits and Continuity Derivatives Approximation ... Other Other Internet Resources for Calculus and Analysis Tools Resource Collections, Courses and Programmes, If you have come across any good web-based calculus support materials that are not in the above listed collections, please do let us know and we may add them here. Give Feedback Return to Langara College Homepage

123. The University Of Minnesota Calculus Initiative Offers calculus application examples for the mathematical properties of a rainbow, the fundamental theorem of calculus, methods of maximizing structural beams in a building, and modeling population growth. Includes general formulas to go along with the word problems and a variety of questions in relation to each exercise. http://www.geom.uiuc.edu/education/calc-init/

Up: Course Materials The University of Minnesota Calculus Initiative The Geometry Center is assisting in the development of interactive technology-based modules for the engineering calculus sequence. These modules emphasize geometric concepts of calculus while examining applications of mathematics to the physical and life sciences. Rainbow Lab How are rainbows formed? Why do they only occur when the sun is behind the observer? If the sun is low on the horizon, at what angle in the sky should we expect to see a rainbow? This lab helps to answer these and other questions by examining a mathematical model of light passing through a water droplet. Numerical Integration Lab The fundamental theorem of calculus tells us that if we know the rate of change of some quantity, then adding up (or integrating) the rate of change over some interval will give the total change in that quantity over the same interval. But often scientists do not know a formula for a function, but can only experimentally know the value of the function at discrete times. Is it possible to "integrate" this discrete data? If so, how? Beams, Bending, and Boundary Conditions Lab

124. That's Calculus! Humorous approach to lessons , which are given using Real Player video clips. Topics cover the concept of limit, derivatives, and summation series. http://www.math.dartmouth.edu/~matc/eBookshelf/calculus/CalculusVideo/welcome.ht

"The introduction of limits causes much anxiety for many students in introductory calculus. This video is an excellent resource because it touches upon the important ideas underlying limits in a light-hearted, but correct way. It also serves a bridge enabling the instructor to pick up, review, and expand on this important concept. I highly recommend it." Richard Melka Professor of Mathematics University of Pittsburgh This humorous video review of basic calculus concepts is ideal to supplement high school or college mathematics classes, home schooling, or individual study. The series, featuring acclaimed performance artist Josh Kornbluth, was developed by Dartmouth College faculty for the Mathematics Across The Curriculum project with the support of the National Science Foundation. Episode 1: To The Limit. Josh explores the intuitive notion of limit from playground slides to food processors. Episodes 2 and 3: The Formal Limit. Josh plays the epsilon-delta game and visits the For All There Exists Cafe as he explains the formal definition of limit.

125. Advice For Calculus Students Advice provided by calculus students, at the end of the semester, for future beginning calculus students. http://shell.cas.usf.edu/~mccolm/pedagogy/CalcAdvice.html

Advice for Beginning Calculus Students This is some advice provided by Calculus students I have had, at the end of the semester, for future beginning calculus students. Prerequisites For Calculus I, the requirement should be a strong background in mathematics. This course requires that you study about ten to fifteen hours a week outside of class. Work ahead of the professor's lecture and always read the section before you go to class. Never give up, and always try your hardest. Make sure that you're in the right class (don't get stuck in the wrong class). Be prepared! Calculus is a tough course and it helps to have a strong background in precalculus algebra and trigonometry. Be sure to really know those trig functions. In Class During class, view the examples seriously, and copy them quickly in detail. Read the section before coming to class, it would help a lot. Ask lots of questions in class. Go to each and every class. If you don't understand something, try reading the book. Learn how to write good notes. Do not depend on your instructor to teach you everything.

126. Information Of Products - IES Inc. Information of Products. http://www.ies.co.jp/math/java/calc/index.html

Information of Products Information of Products

127. Brachistochrone Construction Here one can see a graph of the brachistochrone for the given endpoint. Java applet. http://home.imm.uran.ru/iagsoft/brach/BrachJ2.html

Russian version of this page Brachistochrone Construction Here one can see a graph of the brachistochrone for the given endpoint. For this, JAVA-applets must be supported. Choose the desired endpoint inside the black area, aim the mouse cursor at this point and click the mouse button. JAVA not supported! Cycloid - optimal solution of the brachistochrone problem - arc of cycloid Straight Line - straight line between startpoint and endpoint Broken Line 1 - optimal solution in the class of two-link piecewise lines with fixed x-coordinate of breakpoint ( x Broken Line 2 - optimal solution in the class of two-link piecewise lines with free breakpoint (two-parametric family) For start of the animation - press A-key For selection of the initial velocity use right scrollbar Home page iagsoft@imm.uran.ru Counter:

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