...Calculus is the mathematical study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under and between curves); these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Generally, modern calculus is considered to have been developed in the 17th century by Isaac Newton and Gottfried Leibniz. Today, calculus has widespread uses in science, engineering and economics and can solve many problems that algebra alone cannot. Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus". The word "calculus" comes from Latin (calculus) and refers to a small stone used for counting. More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, calculus of variations...
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...MONEERAH INTEGRATED SCHOOL Merila, Ubaldo Laya, Iligan City S.Y. 2013- 2014 A Requirement in Mathematics IV: Calculus Controversy: Leibniz vs. Newton by Noronsalih Ali, Jra Submitted to Ms. Moneerah A. Bint- Usman Dedication I would like to dedicate this research to my adviser, teacher Monie. And to all of the people who inspired me, especially my parents for their support and to God for giving me enough knowledge to make this study successful. Acknowledgement Abstract This research explores more about the history of the two Mathematicians and how did they invent calculus with the same idea. This is a study about a controversy in Mathematics where Sir Isaac and Gottfried von Leibniz were involved. It tackles about who was the real father of calculus and who gets the credit of inventing it. Inside this paper, the researcher will also discuss a brief summary about Calculus, and short biography of the Mathematicians that were involved in this matter. Many people debates about this matter and we will also tackle some of it in this study. Introduction: So who really invented calculus first? Was it Sir Isaac Newton or Gottfried von Leibniz? Well let's do some investigation. There is no doubt about it that Newton and Leibniz made great mathematical breakthroughs but even before they began studying Calculus there were other people such as Archimedes and Euclid who discovered the infinite and infinitesimal. Much of Newton and Leibniz's work...
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...Calculus From Wikipedia, the free encyclopedia This article is about the branch of mathematics. For other uses, see Calculus (disambiguation). Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem [show]Differential calculus [show]Integral calculus [show]Vector calculus [show]Multivariable calculus Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits,functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modernmathematics education. It has two major branches,differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science,economics, and engineering and can solve many problems for which algebra alone is insufficient. Historically, calculus was called "the calculus of infinitesimals", or "infinitesimal calculus". More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus...
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...make the Philippines and the world a better place. BASIC STUDIES EDUCATIONAL OBJECTIVES MISSION a b c d 2. 3. 4. To provide students with a solid foundation in mathematics, physics, general chemistry and engineering drawing and to apply knowledge to engineering, architecture and other related disciplines. To complement the technical trairung of the students with proficiency in oral, written, and graphics communication. To instill in the students human values and cultural rehnement tbrough the humanities and social sciences. To inculcate high ethical standards in the students through its intesration in the leamins activities. COIIRSE SYLLABUS 1. 2. 3. 4, 5. 6. Course Code: Course Title: Pre-requisite: M.ath22 Calculus 2 Math 21 None 3 units Co-requisite: Credit: Course Description: This course covers topics on dehnite and indefinite integrals of algebraic and transcendental functions, tecbniques of iutegration, applications of...
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...Area is a quantity that expresses the extent of a two-dimensional surface or shape, or planar lamina, in the plane. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat.[1] It is the two-dimensional analog of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). The area of a shape can be measured by comparing the shape to squares of a fixed size.[2] In the International System of Units (SI), the standard unit of area is the square metre (written as m2), which is the area of a square whose sides are one metre long.[3] A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number. There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles.[4] For shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus.[5] For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface...
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... Calculus From Wikipedia, the free encyclopedia Jump to: navigation, search This article is about the branch of mathematics. For other uses, see Calculus (disambiguation). | It has been suggested that Infinitesimal calculus be merged into this article or section. (Discuss) Proposed since May 2011. | Topics in Calculus | Fundamental theorem Limits of functions Continuity Mean value theorem [show]Differential calculus | Derivative Change of variables Implicit differentiation Taylor's theorem Related rates Rules and identities:Power rule, Product rule, Quotient rule, Chain rule | [show]Integral calculus | IntegralLists of integrals Improper integrals Integration by: parts, disks, cylindrical shells, substitution, trigonometric substitution, partial fractions, changing order | [show]Vector calculus | Gradient Divergence Curl Laplacian Gradient theorem Green's theorem Stokes' theorem Divergence theorem | [show]Multivariable calculus | Matrix calculus Partial derivative Multiple integral Line integral Surface integral Volume integral Jacobian | | Calculus (Latin, calculus, a small stone used for counting) is a branch of mathematics focused on limits, functions, derivatives, integrals, and infinite series. This subject constitutes a major part of modern mathematics education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the...
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...Calculus is the mathematical study of change,[1] in the same way that geometry is the study of shape and algebra is the study of operations and their application to solving equations. It has two major branches, differential calculus (concerning rates of change and slopes of curves), and integral calculus (concerning accumulation of quantities and the areas under and between curves); these two branches are related to each other by the fundamental theorem of calculus. Both branches make use of the fundamental notions of convergence of infinite sequences and infinite series to a well-defined limit. Generally considered to have been founded in the 17th century by Isaac Newton and Gottfried Leibniz, today calculus has widespread uses in science, engineering and economics and can solve many problems that algebra alone cannot. Calculus is a part of modern mathematics education. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has historically been called "the calculus of infinitesimals", or "infinitesimal calculus". The word "calculus" comes from Latin (calculus) and refers to a small stone used for counting. More generally, calculus (plural calculi) refers to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, calculus of variations, lambda calculus, and...
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...the students acquainted with the concept of basic topics from Mathematics, which they need to pursue their Engineering degree in different disciplines. Course Contents: Module I: Differential Calculus Successive differentiation, Leibnitz’s theorem (without proof), Mean value theorem, Taylor’s theorem (proof), Remainder terms, Asymptote & Curvature, Partial derivatives, Chain rule, Differentiation of Implicit functions, Exact differentials, Tangents and Normals, Maxima, Approximations, Differentiation under integral sign, Jacobians and transformations of coordinates. Module II: Integral Calculus Fundamental theorems, Reduction formulae, Properties of definite integrals, Applications to length, area, volume, surface of revolution, improper integrals, Multiple Integrals-Double integrals, Applications to areas, volumes. Module III: Ordinary Differential Equations Formation of ODEs, Definition of order, degree & solutions, ODE of first order : Method of separation of variables, homogeneous and non homogeneous equations, Exactness & integrating factors, Linear equations & Bernoulli equations, General linear ODE of nth order, Solution of homogeneous equations, Operator method, Method of undetermined coefficients, Solution of simple simultaneous ODE. Module IV: Vector Calculus Scalar and Vector Field, Derivative of a Vector, Gradient, Directional Derivative, Divergence and Curl and their Physical Significance...
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...MTH 1002: Calculus 2 Spring 2014 Instructor: Dr. C. Knoll Office: Bldg 406 (Academic Quad) Email: cknoll@fit.edu Dr. A. Gibbins Bldg 406 (Academic Quad) agibbins@fit.edu Dr. D. Zaffran Bldg 405 (Academic Quad) dzaffran@fit.edu Grading Policy: Online Homework ( 50 Practice Tests ( 50 Quizzes ( 200 Tests ( 300 Final Exam ( 200 TOTAL ( 800 Grading Scale: A: 90 – 100; B: 80 – 89; C: 70 – 79; D: 60 – 69; F: below 60 Late work will not be accepted without an excused absence. Only students with excused absences will be allowed to take make-up exams, quizzes, labs, etc. There will be absolutely no exceptions (consult your student handbook). An excused absence requires official documentation, e.g. a doctor’s note (in the case of illness). ATTENDANCE IS REQUIRED and will be taken at all lectures and labs. Required Text: Single Variable Calculus: Early Transcendentals, 7th ed., by Stewart. Online Homework URL: Available through the Angel link on the FloridaTech homepage or at www.webassign.net using the Course ID: fit 9672 0423 The LectureTopics will correspond to the following sections from the textbook: 5.1: Area Between Two Curves 5.2: Volumes by Slicing & Disks and Washers 5.3: Volumes by Cylindrical Shells 7.1: Integration by Parts 7.2: Trigonometric Integrals 7.3: Trigonometric Substitution 7.4: Partial Fraction Decomposition 7.5: Strategy for Integration 7.6: Integration...
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...Kellie Aosley8 Recent Hedical school &a&ate "CALCULUS FOR THE UTTERLY CONFUSED has proven to be a wonderful review enabling me t o move forward in application of calculus and advanced topics in mathematics. I found it easy t o use and great as a reference for those darker aspects of calculus. I' Aaron Ladeville, Ekyiheeriky Student 'I1am so thankful for CALCULUS FOR THE UTTERLY CONFUSED! I started out Clueless but ended with an All' Erika Dickstein8 0usihess school Student "As a non-traditional student one thing I have learned is the Especially in importance of material supplementary t o texts. calculus it helps to have a second source, especially one as lucid and fun t o read as CALCULUS FOR THE UTTERtY CONFUSED. Anyone, whether you are a math weenie or not, will get something out of this book. With this book, your chances of survival in the calculus jungle are greatly increased.'I Brad &3~ker, Physics Student Other books i the Utterly Conhrsed Series include: n Financial Planning for the Utterly Confrcsed, Fifth Edition Job Hunting for the Utterly Confrcred Physics for the Utterly Confrred CALCULUS FOR THE UTTERLY CONFUSED Robert M. Oman Daniel M. Oman McGraw-Hill New York San Francisco Washington, D.C. Auckland Bogoth Caracas Lisbon London Madrid Mexico City Milan Montreal New Delhi San Juan Singapore Sydney Tokyo Toronto Library of Congress Cataloging-in-Publication Data Oman, Robert M. Calculus for the utterly confused / Robert M. Oman...
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...CALCULUS I Paul Dawkins Calculus I Table of Contents Preface ........................................................................................................................................... iii Outline ........................................................................................................................................... iv Review............................................................................................................................................. 2 Introduction ................................................................................................................................................ 2 Review : Functions..................................................................................................................................... 4 Review : Inverse Functions .......................................................................................................................14 Review : Trig Functions ............................................................................................................................21 Review : Solving Trig Equations ..............................................................................................................28 Review : Solving Trig Equations with Calculators, Part I ........................................................................37 Review : Solving Trig Equations with Calculators, Part II .............................................
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...Project Gutenberg EBook of Calculus Made Easy, by Silvanus Thompson This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg License included with this eBook or online at www.gutenberg.org Title: Calculus Made Easy Being a very-simplest introduction to those beautiful methods which are generally called by the terrifying names of the Differentia Author: Silvanus Thompson Release Date: October 9, 2012 [EBook #33283] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK CALCULUS MADE EASY *** Produced by Andrew D. Hwang, Brenda Lewis and the Online Distributed Proofreading Team at http://www.pgdp.net (This file was produced from images generously made available by The Internet Archive/American Libraries.) transcriber’s note Minor presentational changes, and minor typographical and numerical corrections, have been made without comment. All A textual changes are detailed in the L TEX source file. This PDF file is optimized for screen viewing, but may easily be A recompiled for printing. Please see the preamble of the L TEX source file for instructions. CALCULUS MADE EASY MACMILLAN AND CO., Limited LONDON : BOMBAY : CALCUTTA MELBOURNE THE MACMILLAN COMPANY NEW YORK : BOSTON : CHICAGO DALLAS : SAN FRANCISCO THE MACMILLAN CO. OF CANADA, Ltd. TORONTO CALCULUS MADE EASY: BEING A VERY-SIMPLEST...
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...AP CALCULUS FORMULA LIST Definition of e: [pic] ____________________________________________________________ __________________ Absolute value: [pic] ____________________________________________________________ __________________ Definition of the derivative: [pic] [pic] (Alternative form) ____________________________________________________________ ________________ Definition of continuity: f is continuous at c iff 1) f (c) is defined; 2) [pic] 3) [pic] ____________________________________________________________ _________________ [pic] ____________________________________________________________ _________________ Rolle's Theorem: If f is continuous on [a, b] and differentiable on (a, b) and if f (a) = f (b), then there is at least one number c on (a, b) such that [pic] ____________________________________________________________ _________________ Mean Value Theorem: If f is continuous on [a, b] and differentiable on (a, b), then there exists a number c on (a, b) such that [pic] ____________________________________________________________ __________________ Intermediate Value Theorem: If f is continuous on [a, b] and k is any number between f (a) and f (b), then there is at least one number c between a and b such that f (c) = k. _...
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...INTRODUCTION TO THE ESSENTIALS OF TENSOR CALCULUS ******************************************************************************** I. Basic Principles ...................................................................... 1 II. Three Dimensional Spaces ............................................................. 4 III. Physical Vectors ...................................................................... 8 IV. Examples: Cylindrical and Spherical Coordinates .................................. 9 V. Application: Special Relativity, including Electromagnetism ......................... 10 VI. Covariant Differentiation ............................................................. 17 VII. Geodesics and Lagrangians ............................................................. 21 ******************************************************************************** I. Basic Principles We shall treat only the basic ideas, which will suffice for much of physics. The objective is to analyze problems in any coordinate system, the variables of which are expressed as qj(xi) or q'j(qi) where xi : Cartesian coordinates, i = 1,2,3, ....N for any dimension N. Often N=3, but in special relativity, N=4, and the results apply in any dimension. Any well-defined set of qj will do. Some explicit requirements will be specified later. An invariant is the same in any system of coordinates. A vector, however, has components which depend upon the system chosen. To determine how the components change (transform)...
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...One of his biggest accomplishments is approximating pi, he did this by utilizing the technique known as the method of exhaustion. His approximation is still used today. He also proved that the area of a circle was equal to pi multiplied by the square of the radius of the circle. He also discovered what is called Archimedes Principle, a principle relating buoyancy to displacement. He considered his most important discoveries his discoveries on the sphere and cylinder. He realized that the volume of a cylinder is equal to 2/3 times the volume of the corresponding sphere and that the surface area of cylinder, including both ends, equals 2/3 times the surface area of the corresponding sphere. Archimedes also worked on the quadrature of the parabola, conoids and spheroids and found that the area of the parabolic segment of a parabola is equal to 3/4 times that of the triangle with the same base and height, the volume of any segment of a paraboloid is 3/2 times that of a cone with the same base and axes, and the ratio of the two segments formed by cutting a solid bounded by a paraboloid with two planes in an arbitrary way is equal to that of the squares of the lengths of their axes. He created scientific notation and it is believed that he was actually the first to have invented integral calculus, 2000 years before Newton and Leibniz. To document his multitude of findings Archimedes wrote many books. Which include On Plane Equilibria or Centres of Gravity of Planes, On the Sphere and...
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