...the Cartesian coordinate system. It is a coordinate plane that is formed when a vertical scale or the y-axis goes through a horizontal scale or the x-axis that defines each point in a plane. The point in which the x-axis and y-axis meet is known as the origin or zero. The two axes divide the plane into four areas called quadrants. The top- right is the first quadrant and it continues counterclockwise in order. The Cartesian coordinate system was developed in 1637 by a French mathematician and philosopher Rene Descartes who noticed a fly crawling around on the ceiling. He watched the fly for a long time. He wanted to know how to tell someone else where the fly was. Finally he realized that he could describe the position of the fly by its distance from the walls of the room. When he got out of bed, Descartes wrote down what he had discovered. Then he tried describing the positions of points, the same way he described the position of the fly. His discovery would help paved the way for more analytical geometry. The discovery of the Cartesian coordinate system has revolutionized mathematics by providing a link between algebra and geometry. It is the foundation for analytical geometry which uses the principals of algebra and analysis. For example every point on a coordinate plane has a set of coordinates which is input (x value) and the output the (y value) known as order pairs. We can draw a line on a coordinate plane using two or more points. In analytic geometry you...
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...Before the end of the European Renaissance, math was cleanly divided into the two separate subjects of geometry and algebra. You didn't use algebraic equations in geometry, and you didn't draw any pictures in algebra. Then, around 1637, a French guy named René Descartes (pronounced "ray-NAY day-CART") came up with a way to put these two subjects together. Rene Descartes was born on March 31, 1596, in Touraine, France. He was entered into Jesuit College at the age of eight, where he studied for about eight years. Although he studied the classics, logic and philosophy, Descartes only found mathematics to be satisfactory in reaching the truth of the science of nature. He then received a law degree in 1616. Thereafter, Descartes chose to join the army and served from 1617-1621. Descartes resigned from the army and traveled extensively for five years. During this period, he continued studying pure mathematics. Finally, in 1628, he devoted his life to seeking the truth about the science of nature. At that point, he moved to Holland and remained there for twenty years, dedicating his time to philosophy and mathematics. During this time, Descartes had his work "Meditations on First Philosophy" published. It was in this work that he introduced the famous phrase "I think, therefore I am." Descartes hoped to use this statement to find truth by the use of reason. He sought to take complex ideas and break them down into simpler ones that were clear. Descartes believed that mathematics...
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...Analytic Geometry is a branch of mathematics in which problems are solved using the principles of Geometry and the processes of Algebra. He is regarded as the founder of Analytic geometry by introducing coordinates system in 1637. René Descartes The Cartesian Coordinate System * also known as Rectangular Coordinate System or xy-Coordinate System. * It is made up of two mutually perpendicular number lines with the same unit of length and intersecting at their origin. The origin of its number line is its zero point. * The number lines are called the coordinate axes. * The horizontal line is called the x-axis and the vertical line is called the y-axis. * The coordinate axes divide the whole plane into four regions called quadrants. * The plane on which these axis are constructed is called the Coordinate Plane or xy-plane. * The distance of any point P from the y-axis is called x-coordinate or abscissa of the point P. * The distance of any point P from the x-axis is called the y-coordinate or ordinate of the point P. * The pair of real numbers (x,y) is called the coordinate pair of point P. * The symbol P(x,y) is used to indicate the point P on the plane with abscissa x and ordinate y. * The signs of the coordinates determine the quadrant where the point lies. * QI: (+,+) QIII: (-,-) QII: (-,+) QIV: (+,-) Exercise 1.1 Indicate the quadrant or the axis on which the point lies. 1. A(3,-2) 6. F(5,0) 2. B(-1,5)...
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...and graphics communication pertaining to technical drawing interpretation. | √ | √ | 3. To teach and train students the importance of humanistic values and respect of cultural differences through humanities and social sciences. | √ | √ | 4. To impart high ethical standards to the students through assimilation and incorporation in the learning activities. | √ | √ | 5. To infuse students with enhanced computer concepts and expertise through incorporating competent applications and disciplines. | √ | √ | 6. To acquire the total human development according to its physical, mental, emotional, social aspects in promoting a healthy lifestyle. | √ | √ | COURSE SYLLABUS 1. Course Code : MATH 121 2. Course Title : Analytic Geometry 3. Pre-Requisite : MATH 111, MATH 112 4. Co-Requisite : MATH 122, MATH 123 5. Credit/Class Schedule : 3 units 6. Course Description : Slope of a line; distance between two...
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...TEXAS COLLEGE 2404 N GRAND AVENUE TYLER, TEXAS 75702 DIVISION OF NATURAL & COMPUTATIONAL SCIENCES MATHEMATICS DEPARTMENT RESEARCH SEMINAR IN MATHEMATICS MATH 4460 01 THE NUMBER LINE BY George L Williams III Contents * THE NUMBER LINE * Extended real number line * Drawing the number line * Line segmentation * Comparing numbers * Arithmetic Operations * Arithmetic Operations (cont.) * Algebraic properties * Cartesian Plane/Cartesian Coordinate System * An Overview * My words * Applications of the number line * Resources * THE NUMBER LINE Mathematics is one of the most useful and fascinating divisions of human knowledge. In mathematics, a real number is a value that represents a quantity along a continuous line. The real numbers include all the rational numbers, such as the integer – 5 and the fraction 4/3, and all the irrational numbers such as positive square root of 2,√2. Real numbers can be thought of as points on an infinitely long number line. In basic mathematics, a number line is a picture of a straight line on which every point is assumed to correspond to a real number and every real number to a point. Often the integers are shown as specially-marked points evenly spaced on the line. Although this image only shows the integers from −9 to 9, the line includes all real numbers, continuing forever in each direction, as shown by the arrows and also numbers not...
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...Proc. CERN Accelerator School on Measurement and Alignment of Accelerator and Detector Magnets, April 11-17, 1997, Anacapri, Italy, CERN-98-05, pp.1-26 BASIC THEORY OF MAGNETS Animesh K. Jain RHIC Project, Brookhaven National Laboratory, Upton, New York 11973-5000, USA Abstract The description of two dimensional magnetic fields of magnets used in accelerators is discussed in terms of a harmonic expansion. The expansion is derived for cylindrical components and extended to Cartesian components. The Cartesian components are also described in terms of a complex field. The rules for transformation of the expansion coefficients under various types of coordinate transformation are given. The relationship between a given current distribution and the resulting field harmonics is explored in terms of the vector and complex potentials. Explicit results are presented for some simple geometries. Finally, the harmonics allowed under various symmetries in the magnet current are discussed. 1. MULTIPOLE EXPANSION OF A TWO-DIMENSIONAL FIELD For most practical purposes related to magnetic measurements in an accelerator magnet, one is interested in the magnetic field in the aperture of the magnet, which is in vacuum and carries no current. Also, most accelerator magnets tend to be long compared to their aperture. Thus, a two dimensional description is valid for most of the magnet, except at the ends. We shall at first confine ourselves to a description of a purely two dimensional...
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...Descartes and Heidegger both set a new standard for thinking, but at completely different ends. Descartes says a subject is a thinking thing that is not extended, and the object is an extended thing which does not think. Heidegger rejects this distinction between subject and object by arguing that there is no subject distinct from the external world of things because Dasein is essentially Being-in-the-world. To Heidegger, everything has an essence, yet that essence is concealed to humans. Descartes’s philosophy placed a heavy emphasis on deductive reasoning and mathematics. He developed analytic geometry and the Cartesian coordinate system which helped scientists use mathematics to model the physical world. One of his influences on today’s world is his philosophy of mind, dualism, where the mind is a nonphysical substance. Descartes proposed that reality consists of two separate realms: a physical realm and a mental realm. The physical realm is the realm of matter and energy. Its properties can be measured and studied by science. Everything in this realm operates only by mechanical properties. Descartes included the body as part of the physical realm, viewing it as a biological machine with no free will. Descartes’s view that the body is a machine has led a mechanical approach in medicine, because Descartes views technology as separate from ethics. This idea is prevalent in today’s philosophy – computer science majors are not required to take a morality course. This means...
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...DEVICES/INSTRUMENTS USED IN SETTING OUT A BUILDING ON A CONSTRUCTION SITE Setting out of a building involves marking of a building position, size and shape in terrain to establish all the pegs, lines and levels needed for construction purposes. It can vary from the measurements of angles and distances by a theodolite to the most sophisticated total station and gps. For all this control points are needed .This essay explains how theodolite, gps and total station are used in setting out a building on a construction site. First of all the first task is to establish a base line from which the whole building can be set out. Baseline are located by setting out their terminals. If coordinated the would be set out from a traseverse. The length and width of the baseline can be measured and compared with its compound value .Altenative baseline could be set out with reference to other details such as road center lines, existing buildings etc. once the baseline has been checked , individual building can be located from it . Theodolite uses movable telescope to measure angles in both horizontal and vertical planes they are manual instruments that comes in two types , transit which rotates in full circle in the vertical plane and non-transit, rotation in half-circle.Using a theodolite at point A and sighting to the furthest end of the baseline point B ,turn off a right angle and establish a peg at C .locate a peg at E in similar fashion from B .Check the distance CE . with a theodolite...
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...ANNUAL SCHEME OF WORK MATHEMATICS FORM 2 2014 |SEM. |MONTH |WEEK |TOPIC /SUBTOPIC | |1ST |JANUARY | | | |SEMESTER | | |CHAPTER 1 – DIRECTED NUMBERS. | | | |1 | | | | | |1.1 Multiplication and Division of Integers. | | | | |1.2 Combined Operations on Integers. | | | | | | | | |2 |1.3 Positive and Negative Fractions. | | | | |1.4 Positive and Negative Decimals. | | | | | ...
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...Lecture 22. Lecture 23. Three-Dimensional Coordinate Systems . . . . . . . . . . . . . . . . . . . . . iii 1 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Lines and Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 Vector Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 Space Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 Multivariable Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 Surfaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 Partial Derivatives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Directional Derivatives and Gradients . . . . . . . . . . . . . . . . . . . . . . . 77 Tangent Planes and Normal Vectors . . . . . . . . . . . . . . . . . . . . . . . 81 Extremal Values of Multivariable Functions . . . . . . . . . . . . . . . . . . . 91 Lagrange Multipliers* . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Double Integrals over Rectangles . . . . . . . . . . . . . . . . . . . . . . . . 105 Double Integrals over General Regions . . . . . . . . . . . . . . . . . . . . . 111 Double Integrals in Polar Coordinates . . . . . . . . . . . . . . . . . . . . . . 121 Triple Integrals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Triple Integrals in Cylindrical and Spherical Coordinates . . . . . . ....
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...This page intentionally left blank Physical Constants Quantity Electron charge Electron mass Permittivity of free space Permeability of free space Velocity of light Value e = (1.602 177 33 ± 0.000 000 46) × 10−19 C m = (9.109 389 7 ± 0.000 005 4) × 10−31 kg �0 = 8.854 187 817 × 10−12 F/m µ0 = 4π10−7 H/m c = 2.997 924 58 × 108 m/s Dielectric Constant (�r� ) and Loss Tangent (� �� /� � ) Material Air Alcohol, ethyl Aluminum oxide Amber Bakelite Barium titanate Carbon dioxide Ferrite (NiZn) Germanium Glass Ice Mica Neoprene Nylon Paper Plexiglas Polyethylene Polypropylene Polystyrene Porcelain (dry process) Pyranol Pyrex glass Quartz (fused) Rubber Silica or SiO2 (fused) Silicon Snow Sodium chloride Soil (dry) Steatite Styrofoam Teflon Titanium dioxide Water (distilled) Water (sea) Water (dehydrated) Wood (dry) � r �� / � 1.0005 25 8.8 2.7 4.74 1200 1.001 12.4 16 4–7 4.2 5.4 6.6 3.5 3 3.45 2.26 2.25 2.56 6 4.4 4 3.8 2.5–3 3.8 11.8 3.3 5.9 2.8 5.8 1.03 2.1 100 80 1 1.5–4 0.1 0.000 6 0.002 0.022 0.013 0.000 25 0.002 0.05 0.000 6 0.011 0.02 0.008 0.03 0.000 2 0.000 3 0.000 05 0.014 0.000 5 0.000 6 0.000 75 0.002 0.000 75 0.5 0.000 1 0.05 0.003 0.000 1 0.000 3 0.001 5 0.04 4 0 0.01 Conductivity (� ) Material Silver Copper Gold Aluminum Tungsten Zinc Brass Nickel Iron Phosphor bronze Solder Carbon steel German silver Manganin Constantan Germanium Stainless steel , S/m 6.17 × 107 4.10 × 107 3.82 × 107 1.82 × 107 1.67 × 107 1.5 × 107 1.45 × 107 1.03...
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...SAS Global Forum 2009 Pharma, Life Sciences and Healthcare Paper 174-2009 Clinical Trial Reporting Using SAS/GRAPH® SG Procedures Susan Schwartz, SAS Institute Inc., Cary, NC ABSTRACT Graphics are a powerful way to display clinical trial data. By their very nature, clinical trials generate a large amount of information, and a concise visual presentation of the results is essential. Information about the patient population, drug dosages, clinical responses, and adverse events must be clear. Clinical laboratory results need to be presented within the context of acceptable limits, and subtle changes over time must be highlighted. This presentation will show, by example, how such graphs can easily be created using the SAS/GRAPH® SG procedures. The techniques that will be emphasized in this presentation include: • • • • • • Creation of a dose response plot by overlaying multiple plots in one graph Construction of a hematology panel using treatment regimen and visit numbers as the classification variables Presentation of a matrix of liver function tests (LFTs) for at-risk patients Aggregation of data into on-the-fly classification variables using user-defined formats Getting the axis you want using built-in best fit algorithms Generation of publication-ready graphs in color and in black and white INTRODUCTION The new SAS/GRAPH procedures—SGPLOT, SGPANEL, and SGSCATTER—provide new tools for viewing and reporting data collected during clinical trials. The SG procedures are an extension...
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...Algebra I Suggested Teaching Strategies The curriculum guide is a set of suggested teaching strategies designed to be only a starting point for innovative teaching. The teaching strategies are optional, not mandatory. A teaching strategy in this guide could be a task, activity, or suggested method that is part of an instructional unit. It should not be considered sufficient to teach the competency and the associated objective(s); the teaching strategy could be one small component of the unit. There may not be enough instructional time to utilize every strategy in the curriculum guide. The 2007 Mississippi Mathematics Framework Revised includes the Depthof-Knowledge (DOK) level for each objective. As closely as possible, each strategy addresses the DOK level specified for that objective or a higher level. Suggestions or techniques for increasing the level of thinking may be included in the strategy(ies). In addition, the process strands (problem solving, communication, connections, reasoning and proof, and representation) are included in the strategies. The purpose of the suggested teaching strategies is to assist school districts and teachers in the development of possible methods of organizing the competencies and objectives to be taught. Since the competencies and objectives require multiple assessment methods, some assessment ideas may be included in the strategy. October 2007 2007 Mississippi Mathematics Framework Revised Strategies Comp. 1 2 Obj. a g ...
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...Wellness is the integration of states of physical, mental and spiritual well-being. Wellness is composed of seven dimensions that include social, emotional, spiritual, environmental, vocational, intellectual and physical wellness. Each of these dimensions act and interact in a way that contributes to own quality of life. Some of the dimensions of wellness in my life I value higher than other, but I also value some very closely. Also, at times many of these are interconnected with one another. The dimension that I value the highest is spiritual wellness. My family has always stressed upon following the Catholic way of life and having good morals and values. The three other dimensions of wellness that I value very similarly are intellectual, physical and social wellness. I am always willing and excited to learn new concepts, improve skills and seek challenges that will allow me to become a great future Health and Physical Education teacher. As a competitive runner for Rowan University, living a healthy lifestyle and having high physical fitness are vital in order to be a successful. One of my favorite aspects of college is being able to meet new friends and organizing times to hang out do something. Under the emotional wellness I acknowledge and share feelings of love, joy and happiness with my family and friends. On some occasions I express feelings of anger, fear, sadness, or stress in a healthy manner. Being on team has allowed me to be able to understand my friends on a...
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...MATH133 Unit 5 Individual Project – A 1) Describe the transformations on the following graph of f x= log( x) . State the placement of the vertical asymptote and x-intercept after the transformation. For example, vertical shift up 2 or reflected about the x-axis are descriptions. 10 9 8 7 6 5 4 3 2 1 -1 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0 -2 -3 -4 -5 -6 -7 -8 -9 -10 Y X 1 2 3 4 5 6 7 8 9 10 a) g(x) = log(x - 5) Description of transformation: horizontal shift 5 units to the right Equation(s) for the Vertical Asymptote(s): x-5=0 x=5 x-intercept in (x, y) form: o=log(x-5) 100=x-5 6=x 6,0 b) gx=- log x+ 2 Description of transformation: Vertical shift 2 units up, reflected about the x axis Equation(s) for the Vertical Asymptote(s): x=o x-intercept in (x, y) form: -logx+2=0 -logx=-2 logx=2 x=102 x=100 (100,0) 2) Students in an English class took a final exam. They took equivalent forms of the exam at monthly intervals thereafter. The average score S(t), in percent, after t months was found to be given by S(t) = 68 - 20 log (t + 1), t ≥ 0 a) What was the average score when they initially took the test, t = 0? Answer: s0=68 Show your work in this space: s0=68-20 log (0+1)^0 20 log (0+1)^0 = 0 s0=68 b) What was the average score after 14 months? Answer: s=44.48 Show your work in this space: s14=68-20log(14+1) s14=68-20log15= s=44.48 c) After...
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