61. Lesson Exchange: Maxima-Minima (Differential Calculus) (Senior, Mathematics) Concepts Taught Lesson Plan for MaximaMinima (Differential calculus). Day 1 Time Management 90 minutes (Pre-calculus). Assumption Students have taken http://teachers.net/lessons/posts/2976.html

Chatboards Teachers Administrators Librarians ... Print Lesson #2976. Maxima-Minima (Differential Calculus) Mathematics, level: Senior Posted Tue Nov 18 18:48:59 PST 2003 by Michael M. Bumanlag ( bumanlagm@yahoo.com http://photos.yahoo.com/bumanlagm1 (to view other scanned documents) Eastern University of Science and Technology (EUST), Philippines (currently teaching in China) Materials Required: (See Lesson Plan below) Activity Time: 90 minutes Concepts Taught: Lesson Plan for Maxima-Minima (Differential Calculus) Day 1 Time Management: 90 minutes (Pre-Calculus) Assumption : Students have taken the topic prior to this topic. They know how to evaluate functions using differentiation. Students are in Grade 11 or 12 level. Segment 1 : 15 minutes Topic : Getting to know each other (Class Size: 15) Objectives General : At the end of the session, the students shall be able to 1. Know my personal information; 2. Know the names of classmates. Specific Cognitive : 1. Identify my name, address, telephone number; 2. Identify the names of classmates.

62. Historia Matematica Mailing List Archive: Re: [HM] Books About Differential Calc Re HM Books about differential calculus 1708 1720. Kenneth L Manders (mandersk+@pitt.edu) Fri, 23 Jul 1999 112711 -0400 (EDT) http://sunsite.utk.edu/math_archives/.http/hypermail/historia/jul99/0117.html

Re: [HM] Books about differential calculus 1708 - 1720 Kenneth L Manders mandersk+@pitt.edu Fri, 23 Jul 1999 11:27:11 -0400 (EDT) Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Julio Gonzalez Cabillon: "[HM] Christian Wolff [was: Books about differential calculus 1708-1720]" Previous message: Sergio Nobre: "Re: [HM] Books about differential calculus 1708 - 1720" Next in thread: Julio Gonzalez Cabillon: "[HM] Christian Wolff [was: Books about differential calculus 1708-1720]" I would very much like to know what Swedenborg wrote about geometrically interpreting negative results of differentiation. Most authors give two examples (Euler); but l'Hopital gave a rule. Thanks, Ken Manders Next message: Julio Gonzalez Cabillon: "[HM] Christian Wolff [was: Books about differential calculus 1708-1720]" Previous message: Sergio Nobre: "Re: [HM] Books about differential calculus 1708 - 1720" Next in thread: Julio Gonzalez Cabillon: "[HM] Christian Wolff [was: Books about differential calculus 1708-1720]"

63. Historia Matematica Mailing List Archive: Re: [HM] Books About Differential Calc Re HM Books about differential calculus 1708 1720. Staffan Rodhe (book@kubkou.se) Sun, 25 Jul 1999 181344 +0200. Messages sorted by date thread http://sunsite.utk.edu/math_archives/.http/hypermail/historia/jul99/0124.html

Re: [HM] Books about differential calculus 1708 - 1720 Staffan Rodhe book@kubkou.se Sun, 25 Jul 1999 18:13:44 +0200 Messages sorted by: [ date ] [ thread ] [ subject ] [ author ] Next message: Christian Marinus Taisbak: "Re: [HM] mathematicians and aging" Previous message: John Bibby: "[HM] Germain and Safe primes" Maybe in reply to: Staffan Rodhe: "[HM] Books about differential calculus 1708 - 1720" Ken Manders wrote: By l'Hospital's rule of negative results of differentiation I suppose you mean his discussion of how the value of the subtangent PT has an effect on which side of the origin of x the point T on the diameter is situated (Section II, Proposition I). The answer is that Swedenborg doesn't bother at all about that problem. Swedenborg is not famous for being a good mathematician, I suppose he is more well-known for his interpretation of the bible. It is though remarkable that he presents some theory about the differential- and integral-calculus. When he presents the differentials for a curve defined by polar-coordinates, he discusses three cases when the fixed point (the pole) is 1. on the curve

64. Summer At Stanford University - Undergraduate & Graduate - Mathematics & Distanc Differential calculus for functions of two or more variables. Prerequisite One quarter of multivariable differential calculus (comparable to MATH 50V http://summer.stanford.edu/programs/crsMathv.asp

Summer at Stanford High School Apply Online Photos ... FAQ Search User ID Password What's this? Marc Sanders, Director sanders@csli.stanford.edu Special application required quick jump to department Anthropological Science Biological Sciences Chemistry Classics Communication Comparative Literature Computer Science Drama Economics Electrical Engineering Engineering English History Languages Mathematics Mechanical Engineering Music Philosophy Physics Political Science Psychology Religous Studies Sociology Statistics Multivariable Differential Calculus Multivariable Integral Calculus Ordinary Differential Equations Introduction to the Theory of Functions of a Complex Variable ... Fundamental Concepts of Analysis MATH 50V Multivariable Differential Calculus 4 units This is a distance-learning class, offered by EPGY. More information about this course, and the required special application, can be found at the e-Learning home page Differential calculus for functions of two or more variables. Topics: vectors and vector-valued functions in 2-space and 3-space, tangent and normal vectors, curvature, functions of two or more variables, partial derivatives and differentiability, directional derivatives and gradients, maxima and minima, and optimization using Lagrange multipliers. Prerequisite: Two quarters of single variable calculus, or consent of instructor.

65. Read This: Briefly Noted What differential calculus is, and, in general, analysis of the infinite might be, Foundations of the Differential calculus, by Leonhard Euler, http://www.maa.org/reviews/brief_jan01.html

Search MAA Online MAA Home Read This! The MAA Online book review column Briefly Noted January 2001 John D. Blanton's new translation of the first nine chapters of Euler's Institutiones Calculi Diferentialis opens the door to a different world. Consider the opening words: "What differential calculus is, and, in general, analysis of the infinite might be, can hardly be explained to those innocent of any knowledge of it. Nor can we here offer a definition at the beginning of this dissertation as is sometimes done in other disciplines. It is not that there is no clear definition of this calculus; rather, the fact is that in order to understand the definition there are concepts that must first be understood." This is quintessential Euler: all the cards are on the table. He won't try to explain what the calculus is in his introduction, because you can only understand that by actually learning it. But keep reading, he's going to try anyway. He explains, in the next few paragraphs, that the calculus deals with changing quantities called variables , which he illustrates by considering "a shot fired from a cannon with a charge of gunpowder." This situation involves many quantities, he says, some of which are to be considered constant and others are variables. He goes on to define functions and to talk about their "vanishing increments," i.e., their differentials.

66. Applications Of Differential Calculus - Maths Online Gallery Multimedia learning units on Applications of differential calculus maths online Gallery. http://www.univie.ac.at/future.media/moe/galerie/anwdiff/anwdiff.html

Applications of differential calculus The applets are started by clicking the red buttons. How to find a function's extremum is illustrated in this applet by means of a simple example. It shall make clear why the standard procedure deals with a function and why the derivative of this function is set equal to zero. In addition to graphical vizualization, the computational strategy is outlined. The applet is started from the red button in its own window. Gallery - Table of contents Maths links online tools topics ... Welcome Page

67. World Web Math: Calculus Summary calculus has two main parts differential calculus and integral calculus. Differential calculus studies the derivative and integral calculus studies http://web.mit.edu/wwmath/calculus/summary.html

Calculus Summary Calculus has two main parts: differential calculus and integral calculus. Differential calculus studies the derivative and integral calculus studies (surprise!) the integral. The derivative and integral are linked in that they are both defined via the concept of the limit: they are inverse operations of each other (a fact sometimes known as the fundamental theorem of calculus): and they are both fundamental to much of modern science as we know it. Derivatives The limit of a function f x ) as x approaches a is equal to b if for every desired closeness to b , you can find a small interval around (but not including) a that acheives that closeness when mapped by f . Limits give us a firm mathematical basis on which to examine both the infinite and the infinitesmial. They are also easy to handle algebraically: where in the last equation, c is a constant and in the first two equations, if both limits of f and g exist. One important fact to keep in mind is that doesn't depend at all on f a ) in fact

68. Differential Calculus Differential calculus. Definition Optimization Problems. calculus can be used to solve practical problems requiring maximum or minimum values. http://ptolemy.eecs.berkeley.edu/~celaine/apcalc/topic3.htm

Next: Integral Calculus Up: Topics to Study Previous: Limits Differential Calculus Definition x and if this limit exists c x c x c Differentiation Rules General and Logarithmic Differentiation Rules cu cu' u v u' v' sum rule uv uv' vu' product rule quotient rule c u n nu n u' power rule x [ln u e u e u u' x g x g' x chain rule Derivatives of the Trigonometric Functions [sin u ] = (cos u u' [csc u ] = -(csc u cot u u' [cos u ] = -(sin u u' [sec u ] = (sec u tan u u' [tan u ] = (sec u u' [cot u ] = -(csc u u' Derivatives of the Inverse Trigonometric Functions [arcsin u [arccsc u [arccos u [arcsec u [arctan u [arccot u Implicit Differentiation Implicit differentiation is useful in cases in which you cannot easily solve for y as a function of x Exercise Find for y xy y x y xy y x y x + y x y x x y Higher Order Derivatives x x x x ). The numerical notation for higher order derivatives is represented by: n x y n The second derivative is also indicated by Exercise Find the third derivative of y x y' x y'' x y''' x Derivatives of Inverse Functions If y x ) and x y ) are differentiable inverse functions, then their derivatives are reciprocals: Logarithmic Differentiation It is often advantageous to use logarithms to differentiate certain functions.

69. Calculus Differential Leibniz Function Fundamental Isbn Newton calculus Differential Leibniz Function Fundamental Isbn Newton Economy. http://www.economicexpert.com/a/Calculus.html

var GLB_RIS='http://www.economicexpert.com';var GLB_RIR='/cincshared/external';var GLB_MMS='http://www.economicexpert.com';var GLB_MIR='/site/image';GLB_MML='/'; document.write(''); document.write(''); document.write(''); document.write(''); A1('s',':','html'); Non User A B C ... Home First Prev [ 1 Next Last Topics in Calculus Fundamental theorem Function Limits of functions ... Manifold For other uses of the term calculus see calculus (disambiguation) Calculus is a branch of mathematics , developed from algebra and geometry , involving two major complementary ideas: The first, called differential calculus is a theory about rates of change , and involves the method of differentiation ; in terms of mathematical function s, velocity acceleration , and slopes of curves at a given point can all be discussed on a common symbolic basis. The second, called integral calculus , involves the idea of integration , and uses a general idea of area bounded by the graph of a function , to include related concepts such as volume The two concepts define inverse operation s, in a sense made quite precise by the

70. Science Of Logic - Quantum Remark 2 The Purpose of the Differential calculus Deduced from its Application The whole method of the differential calculus is complete in the http://www.marxists.org/reference/archive/hegel/works/hl/hl274.htm

Quantum Remark 2: The Purpose of the Differential Calculus Deduced from its Application In the previous Remark we considered on the one hand the specific nature of the notion of the infinitesimal which is used in the differential calculus, and on the other the basis of its introduction into the calculus; both are abstract determinations and therefore in themselves also easy. The so-called application, however, presents greater difficulties, but also the more interesting side; the elements of this concrete side are to be the object of this Remark. The whole method of the differential calculus is complete in the proposition that dxn = nx n dx , or ( f x + i - fx i P , that is, is equal to the coefficient of the first term of the binomial x + d , or x + 1, developed according to the powers of dx or the first stage of the task, the finding of the said differential, analytically, i.e. purely arithmetically, by the expansion of the function of the variable after this has received the form of a binomial by the addition of an increment; how it is that the second stage can be correct, namely the omission of all the terms except the first, of the series arising from the expansion. If all that were required were only this coefficient, then with its determination all that concerns the theory would, as we have said, be settled and done with in less than half an hour and the omission of the further terms of the series (with the determination of the first function, the determination of the second, third, etc., is also accomplished) far from causing any difficulty, would not come into question since they are completely irrelevant.

71. Furman Mathematics: Course Descriptions is an introduction to the theory and methods of differential calculus. methods, and applications of differential calculus and an introduction to the http://math.furman.edu/adviceinfo/descriptions.html

Furman Mathematics Department People Resources Activities ... Advice Course Descriptions This course is an introduction to the theory and methods of differential calculus. Topics included are functions, graphs, limits, continuity and derivatives. Enrollment is by placement only. Mathematics 10 is the first of a two course sequence, Mathematics 10-11S. This sequence covers the material of a standard first term calculus course supplemented with a review of precalculus mathematics. Prerequisite: Mathematics 10 This course is an introduction to applications of the derivative and the theory and applications of the definite integral. Topics included are the trigonometric functions and their derivatives, applications of derivatives, antiderivatives, the definite integral and applications of the integral. This is the second of a two course sequence, Mathematics 10-11S. This sequence covers the material of a standard first term calculus course supplemented with a review of precalculus mathematics. Prerequisite: A sufficiently high score on the placement test The first course in the standard calculus sequence. Introduction to the theory, methods, and applications of differential calculus and an introduction to the definite integral. Topics include algebraic and trigonometric functions, limits and continuity, rules for differentiation, applications of the derivative, antiderivatives, and the definition and basic properties of the definite integral.

72. Difference Equations To Differential Equations Difference Equations to Differential Equations was written with the help of Tex, A companion multivariable calculus text, The calculus of Functions of http://math.furman.edu/~dcs/book/

Difference Equations to Differential Equations An introduction to calculus Each section of the text is available in both PostScript and Portable Document Format (PDF) formats. If you require a PostScript viewer, click here for information on obtaining and installing a PostScript viewer. If you require a PDF viewer, click here or here for information on obtaining and installing a PDF viewer. Difference Equations to Differential Equations was written with the help of Tex DVIPS xdvi PDFTeX ... Mathematica A companion multi-variable calculus text, The Calculus of Functions of Several Variables is available here Send e-mail to Dan Sloughter to report any errors. Chapter Section Applet Date PostScript PDF Sequences, limits, and difference equations Calculus: areas and tangents Area of a circle Tangent line for a parabola 154 kb 103 kb Sequences 235 kb 129 kb The sum of a sequence 128 kb 110 kb Difference equations 210 kb 113 kb Nonlinear difference equations Inhibited population growth 291 kb 106 kb Functions and and their properties Functions and their graphs 406 kb 132 kb Trigonometric functions Square wave approximation Sound wave approximation 413 kb 138 kb Limits and the notion of continuity 355 kb 141 kb Continuous functions 188 kb 103 kb Some consequences of continuity 202 kb 105 kb Best affine approximations Best affine approximations Affine approximations 206 kb 111 kb Best affine approximations, derivatives and rates of change

73. Mathematics - A.P. Intro To Differential Calculus (A) Shelby County Board of Education. Shelby County Public Schools Curriculum. Mathematics AP Intro to Differential calculus (A) http://www.shelby.k12.ky.us/Curriculum/CR15493.HTM

Index Arts/Humanities Dance Drama/Theatre ... Visual Arts Mathematics Grade K Grade 1 Grade 2 Grade 3 ... Pre-Calculus A.P. Intro to Differential Calculus (A) A.P. Intro to Integral Calculus (B) Geometry Introduction Ordering Info Made with Curriculum Designer by Scantron Corporation Shelby County Board of Education Shelby County Public Schools Curriculum Mathematics - A.P. Intro to Differential Calculus (A) Printable Version Goals and Descriptions Calculus and Pre-Calculus Functions ... Probability/Statistics Calculus and Pre-Calculus Differentiation: Find/Apply The learner will be able to find/apply the successive derivatives of a function. Differentiation: Apply The learner will be able to apply the derivative to find the slope of a curve at a given point, the equation of a tangent line to a point on the curve, and the equation of the normal line to a point on the curve. Differentiation: Apply/Relationships The learner will be able to apply the relationships between f(x), f'(x), and f''(x) to find the increasing and decreasing behavior of f(x), the critical points of f(x), the concavity of f(x) over an interval, the points of inflection of f(x), to sketch the graphs of f'(x) and f''(x) when given f(x), and sketch the graph of f(x) when given f'(x). Applying Calculus Concepts: Theorems The learner will be able to apply the Mean Value and Rolle's Theorem.

74. Differential Calculus Syllabus And Course Outline This course is designed as a continuation of calculus I. It will be conducted in a format to consist Differential Equations and Initial Value problems http://www.lsmsa.edu/dandersen/Integral.htm

Louisiana School for Math, Science, and the Arts Section Number: Course Number: MA 403 Course: Calculus II Meeting Times: Days: MWF T) Meeting Place Room 208 Credit Hours: .5 unit Instructor: David F. Andersen Office: Room # 240 (The Math Lab) Phone: 357-3174 ext 176 Office Hours: Mon Tue Wed Thu Fri Geometry Rm Precalculus Rm Geometry Rm Precalculus Rm Geometry Rm Office/Prep Math Lab Office/Prep Math Lab Office/Prep Math Lab Office/Prep Math Lab Office/Prep Math Lab Office/Prep Math Lab Office/Prep Math Lab College Algebra Rm College Algebra Rm College Algebra Rm Trigonometry Rm Office/Prep Math Lab Trigonometry Rm Math Meeting Trigonometry Rm Office/Prep Math Lab Office/Prep Math Lab Office/Prep Math Lab Cont'd Office/Prep Math Lab Prob /Stat Rm Prob /Stat Rm Office/Prep Math Lab Office/Prep Math Lab Office/Prep Math Lab Calculus II Rm Calculus II ( Rm Calculus II Rm Office/Prep Math Lab Calculus II Rm Evening Study Course Description: This course is designed as a continuation of Calculus I. It will be conducted in a format to consist of theory, techniques, and applications of Integral calculus in a combination of lecture, discussion, modeling, and discovery. In addition to the above, this course is the second of two courses in helping to prepare the student for the AB Advanced Placement Calculus Exam and the first of three courses in preparing the student for the BC Advanced Placement Calculus Exam. Prerequisite: Knowledge equivalent to Calculus I MA 303.

75. Greenfield Coalition Mathematics Courses (GCM) 2111 Differential calculus I Limits, Derivatives and Derivative Rules. Cr. 1 2121 Differential calculus II Applications of the Derivatives; Curves. http://www.bulletins.wayne.edu/ubk-output/egr28.html

Greenfield Coalition Mathematics Courses (GCM) The following courses are offered for undergraduate credit. For interpretation of numbering system, signs and abbreviations, see Course Signs and Abbreviations NOTE: All GCM courses below are open only to students in the Focus:HOPE/Greenfield Coalition BSMFT Program. 1011 Technical Mathematics: Quadratics and Functions. Cr. 1 Prereq: placement. Open only to students in Focus:HOPE/Greenfield Coalition BSMFT Program. Methods of solving quadratic equations, factorable quadratics, roots, completing the square and the quadratic formula; discriminates; complex roots, inequalities, critical values. Definitions, domain, range, relations; operations, one-to-one, inverse functions; graphing, properties of curves, interpreting graphs. (Y) 1021 Technical Mathematics: Linear Equation Systems, Logarithms, and Exponents. Cr. 1 Prereq: GCM 1011. Open only to students in Focus:HOPE/Greenfield Coalition BSMFT Program. Systems of 2 and 3 linear equations; Cramer's Rule, second and third order determinants; algebraic and graphical solutions. Graphing of exponential growth and decay; conversions, natural logarithms, basic laws of logarithms, change of base. (Y) 1031 Technical Mathematics: Analytical Geometry. Cr. 1

76. Mathematics Department Courses Differential and integral calculus of one real variable; infinite series. Same as SM121 for students with prior differential calculus experience. fall http://www.usna.edu/AcDean/courses/sm&sa.html

Mathematics and Operations Analysis Courses Mathematics Courses SM005 Pre-Calculus Mathematics (4-1-4) . Basic review of algebraic and arithmetic operations, analysis of functions and their graphs, and trigonometry. This course may be required in addition to stated graduation requirements for certain midshipmen. Prereq: permission of department chair. [fall] SM122 Calculus I SM131 Calculus I (3-0-3) . Same as SM121 for students with prior differential calculus experience. [fall] SM162 Calculus with Computers I SM212 Differential Equations (4-0-4) . Linear and simultaneous differential equations; solution by Laplace transform; partial differential equations and Fourier series. Prereq: SM221, SM223, or SM251. [fall, spring, summer] SM219 Statistics and Probability (3-0-3) . Nature of statistical methods, description of data, probability, distributions, estimation, tests of hypothesis, correlation, regression. Credit cannot be given for SM219 if credit has been given for SM230 or SM239. Prereq: SM122 or SM162. [spring] SM221 Calculus III with Vector Fields (4-0-4) . Differential and integral calculus of several real variables; vector analysis including integral theorems. Prereq: SM122 or SM162. [fall, spring]

77. CALCULUS MATH U141, Home Page Brief Summary First semester calculus, including differential calculus, Math U141 covers differential calculus (the study of rates and change), http://www.math.neu.edu/~iarrobino/MathU141HP.htm

MATH U141, CALCULUS I Home Page Brief Summary: First semester calculus, including differential calculus, some differential equations, and the beginnings of integration, with emphases on applications found in health sciences, ecology. Text, overview This course uses the text: ÓApplied CalculusÓ by Hughes-Hallett (ISBN 0471-20792-6) that includes many applications to health sciences, ecology. There is also supplementary material in a Class Pac, including max-min problems, motion, and problems involving flow and amount, as well as past quizzes and exams with solutions. Students are expected to use a graphing calculator. A feature of the course and text is the attempt to integrate graphical, numerical and symbolic approaches. Also, students are asked to interpret calculus in applied problems. Math U141 covers differential calculus (the study of rates and change), and the beginnings of integral calculus (from flow to amount, areas, fundamental theorem of calculus relating derivatives and integrals), and some differential equations. MathU141 Outline MathU141 Fall 2004 syllabus Who takes this course?

78. Differential And Integral Calculus Differential and Integral calculus. Chapter II The Fundamental Ideas of the Integral and Differential calculus. Contents http://kr.cs.ait.ac.th/~radok/math/mat6/dicchap2.htm

Differential and Integral Calculus Chapter II: The Fundamental Ideas of the Integral and Differential Calculus Contents 2.1 The definite integral 2.3.9 The Approximate Representation of Arbitrary Functions by Linear Functions. Differentiation 2.1.1 The integral as an Area 2.3.10. Remarks on Applications to the Naturali Sciences ... A2.2 The Relation between the Mean Value Theorem of the Differential Calculus and the Mean Value Theorem of the Integral Calculus

79. Differential And Integral Calculus Differential and Integral calculus. Volume 2. Chapter III Developments and Applications of the Differential calculus http://kr.cs.ait.ac.th/~radok/math/mat9/dicchap3.htm

Differential and Integral Calculus Volume 2 Chapter III Developments and Applications of the Differential Calculus 3.1 IMPLICIT FUNCTIONS 3.4 APPLICATIONS 3.1.1 General Remarks 3.4.1 Applications to the Theory of Surfaces ... A3.5 Tangential Representation of a Closed Curve

80. MAT 195 - Differential Calculus Emphasizes the use of differential calculus. Applications of techniques include extreme value problems, motion, graphing, and other topics as time allows. http://www.dtae.org/teched/standards/courses/mat195.html

Standard MAT 195 - Differential Calculus Course Description Emphasizes the use of differential calculus. Applications of techniques include extreme value problems, motion, graphing, and other topics as time allows. Topics include: derivatives and applications, differentiation of transcendental functions, and introduction to integration and applications. Competency Areas Hours Derivatives and Applications Class Differentiation of Transcendental Functions D. Lab Introduction to Integration and Applications P. Lab/O.B.I. Credit Prerequisite: MAT 193 Corequisite: Course Guide Competency After completing this section, the student will: Hours Class D.Lab P.Lab/ O.B.I. DERIVATIVES AND APPLICATIONS Limits Find the limits of equations using the four step method. Differentiation theory - slope of the tangent to a curve Relate the theory of limits to solving for the slope of the tangent to a curve. Techniques of differentiation Apply methods for differentiation - power rule, chain rule, implicit differentiation. Applications Solve word problems using derivatives.

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