...algebra: Linear and quadratic equations, Solving linear and quadratic equations, Application of equations: profit, pricing, savings, revenue, sales tax, investment, bond redemption, linear inequalities, applications of inequalities: profit, renting verses purchasing, leasing versus purchasing, revenue, current ratio, investment, Maple session on solving linear, quadratic and higher degree equations, solving inequalities II. Functions and Graphs: Introduction to functions, domain and range of a function, Applications: demand, supply and profit functions, demand and supply schedule, value of business, depreciation, Special functions: polynomial, rational, piecewise defined functions, Absolute value function, and evaluation of such functions. Combination of functions. Applications: cost, investment, sales, profit, business, Graphs of functions: linear, quadratic, piecewise defined functions, graphing of quadratic functions by finding vertex, Applications on graphs: inventory, debt payment, pricing, revenue and profit, demand and supply curves, Maple session on functions and graphs III. Lines and Systems: Equation of a straight line, slope and intercept of a line, parallel and perpendicular lines, Applications: price-quantity relationship, production levels, cost, revenue, demand and supply equations, isocost line, isoprofit line, depreciation, appreciation, systems of linear equations, solution of system of linear equations, nonlinear systems: one linear one quadratic...
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...2 2.1 Introduction to Equations 2.2 Linear Equations 2.3 Introduction to Problem Solving 2.4 Formulas 2.5 Linear Inequalities Linear Equations and Inequalities Education is not the filling of a pail, but the lighting of a fire. — WILLIAM BUTLER YEATS M athematics is a unique subject that is essential for describing, or modeling, events in the real world. For example, ultraviolet light from the sun is responsible for both tanning and burning exposed skin. Mathematics lets us use numbers to describe the intensity of ultraviolet light. The table shows the maximum ultraviolet intensity measured in milliwatts per square meter for various latitudes and dates. Latitude 0 10 20 30 40 50 Mar. 21 325 311 249 179 99 57 June 21 254 275 292 248 199 143 Sept. 21 325 280 256 182 127 75 Dec. 21 272 220 143 80 34 13 ISBN 1-256-49082-2 Source: J. Williams, The USA Today Weather Almanac. If a student from Chicago, located at a latitude of 42°, spends spring break in Hawaii with a latitude of 20°, the sun’s ultraviolet rays in Hawaii will be approximately 249 2.5 99 times as intense as they are in Chicago. Equations can be used to describe, or model, the intensity of the sun at various latitudes. In this chapter we will focus on linear equations and the related concept of linear inequalities. 89 Beginning and Intermediate Algebra with Applications & Visualization, Third edition, by Gary K. Rockswold and Terry A. Krieger. Published by Addison Wesley. Copyright © 2013 by...
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...2 2.1 Introduction to Equations 2.2 Linear Equations 2.3 Introduction to Problem Solving 2.4 Formulas 2.5 Linear Inequalities Linear Equations and Inequalities Education is not the filling of a pail, but the lighting of a fire. — WILLIAM BUTLER YEATS M athematics is a unique subject that is essential for describing, or modeling, events in the real world. For example, ultraviolet light from the sun is responsible for both tanning and burning exposed skin. Mathematics lets us use numbers to describe the intensity of ultraviolet light. The table shows the maximum ultraviolet intensity measured in milliwatts per square meter for various latitudes and dates. Latitude 0 10 20 30 40 50 Mar. 21 325 311 249 179 99 57 June 21 254 275 292 248 199 143 Sept. 21 325 280 256 182 127 75 Dec. 21 272 220 143 80 34 13 ISBN 1-256-49082-2 Source: J. Williams, The USA Today Weather Almanac. If a student from Chicago, located at a latitude of 42°, spends spring break in Hawaii with a latitude of 20°, the sun’s ultraviolet rays in Hawaii will be approximately 249 2.5 99 times as intense as they are in Chicago. Equations can be used to describe, or model, the intensity of the sun at various latitudes. In this chapter we will focus on linear equations and the related concept of linear inequalities. 89 Beginning and Intermediate Algebra with Applications & Visualization, Third edition, by Gary K. Rockswold and Terry A. Krieger. Published by Addison Wesley. Copyright © 2013 by...
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...College/College of Natural Sciences | | |MAT/116 Version 7 | | |Algebra 1A | Copyright © 2010, 2009, 2007, 2006 by University of Phoenix. All rights reserved. Course Description This course introduces basic algebra concepts and assists in building skills for performing specific mathematical operations and problem solving. Students solve equations, evaluate algebraic expressions, solve and graph linear equations and linear inequalities, graph lines, and solve systems of linear equations and linear inequalities. These concepts and skills serve as a foundation for subsequent coursework. Applications to real-world problems are integrated throughout the course. This course is the first half of the college algebra sequence, which is completed in Algebra 1B. Policies Faculty and students/learners will be held responsible for understanding and adhering to all policies contained within the following two documents: • University policies: You must be logged into the student website to view this document. • Instructor policies: This document is posted in the Course Materials forum. University policies are subject to change. Be sure to read the policies at the beginning of each...
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...Chapter one 1.1 Introduction For many manufacturers the task of meeting the ever rising demand and customer expectations and lowering production cost and maximizing profit in an environment of more products, more complexity, more choice and competition is placing great stress on the effectiveness of their planning of activities in the product kind. Organizations have already adopted solutions with varying degrees of planning and scheduling capabilities. Yet, operations executive acknowledge that these same systems are becoming out dated, lacking the speed, flexibility and responsiveness to manage their increasing complex production environment. Optimization techniques are applied to find out whether resources available are effectively utilized in order to achieve optimum profit from the activities of the firm. There should be consistency in the use of various resources and the mix should be such that it brings down the cost for ensuring profit. Therefore, it is the duty of the management to exercise control over the resources and to see that the resources are effectively utilized. Similarly, organizations in general are involved in manufacturing a variety of products to cater the needs of the society and to maximize the profit. While doing so, they need to be familiar with different combinations of product mix which will maximize the profit. Or alternatively minimize the cost. The techniques such as ratio analysis, correlation and regression analyses, variance analysis...
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...MAPÚA INSTITUTE OF TECHNOLOGY Department of Mathematics COURSE SYLLABUS 1. Course Code: Math 10-3 2. Course Title: Algebra 3. Pre-requisite: none 4. Co-requisite: none 5. Credit: 3 units 6. Course Description: This course covers discussions on a wide range of topics necessary to meet the demands of college mathematics. The course discussion starts with an introductory set theories then progresses to cover the following topics: the real number system, algebraic expressions, rational expressions, rational exponents and radicals, linear and quadratic equations and their applications, inequalities, and ratio, proportion and variations. 7. Student Outcomes and Relationship to Program Educational Objectives Student Outcomes Program Educational Objectives 1 2 (a) an ability to apply knowledge of mathematics, science, and engineering √ (b) an ability to design and conduct experiments, as well as to analyze and interpret from data √ (c) an ability to design a system, component, or process to meet desired needs √ (d) an ability to function on multidisciplinary teams √ √ (e) an ability to identify, formulate, and solve engineering problems √ (f) an understanding of professional and ethical responsibility √ (g) an ability to communicate effectively √ √ (h) the broad education necessary to understand the impact of engineering solutions in the global and societal context √ √ (i) a recognition of the need for, and an ability to engage...
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...LINEAR PROGRAMING AND SIMPLEX METHOD Devharajan Rangarajan Department of Electronic Engineering National University of Ireland, Maynooth devharajan.rangarajan.2016@mumail.ie Abstract— An optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function. This pays way to a new world of constrained optimization. This paper focuses on one such optimization technique known as Linear programming and one of its method known as Simplex method in detail with examples. cTx = c1x1 + · · · + cnxn The subject of linear programming can be defined quite concisely. It is concerned with the problem of maximizing or minimizing a linear function whose variables are required to satisfy a system of linear constraints, a constraint being a linear equation or inequality. The subject might more appropriately be called linear optimization. Problems of this sort come up in a natural and quite elementary way in many contexts but especially in problems of economic planning. (or Ax ≤ b) I. INTRODUCTION Linear programming is the process of taking various linear inequalities relating to some situation, and finding the "best" value obtainable under those conditions. A typical example would be taking the limitations of materials and labour, and then determining the "best" production levels for maximal profits under those conditions. In "real life", linear...
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...DOES FINANCIAL SECTOR DEVELOPMENT INCREASE INCOME INEQUALITY? SOME ECONOMETRIC EVIDENCE FROM BANGLADESH Abu N.M. Wahid Tennessee State University Muhammad Shahbaz COMSATS Institute of Information Technology, Lahore, Pakistan Mehmood Shah University of Management and Technology, Lahore, Pakistan Mohammad Salahuddin Southeast University Banani, Dhaka, Bangladesh ABSTRACT This paper is an attempt to examine the relationship between financial development and income inequality. In doing so, we have used Bangladeshi data for the period 1985-2006. We have employed auto-regressive distributed lag (ARDL) methodology for cointegration. We have also carried out sensitivity analysis and stability tests. Our findings suggest that financial development increases income inequality. Economic growth seems to equalize income distribution. Inflation and trade openness also worsen income inequality. Finally, income inequality is being increased by social spending in the country over long run. This study provides new directions for policy makers to reduce income inequality to share the fruits of economic development among the wider spectrum of the society. Keywords: Financial sector, development, trade openness, income inequality, Bangladesh JEL Classifications: D14, D33, F1 INTRODUCTION Economic growth and its correlates have been the focus of a large number of studies over the recent past. These studies primarily put emphasis on various aspects or sources of growth. One...
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...operations and problem solving. These concepts and skills serve as a foundation for subsequent quantitative business coursework. Applications to real-world problems are emphasized throughout the course. This course is the first half of the college mathematics sequence, which is completed in MTH 209: College Mathematics II. Course Topics & Objectives Week One: Fundamentals of Expressions • Identify real and variable elements. • Classify real numbers. • Solve problems containing fractions. • Evaluate expressions. • Apply mathematical laws and order of operations principles to solve math problems. • Create expressions using real-world applications. Week Two: Linear Equations & Inequalities • Evaluate forms of linear equations. • Solve linear equations. • Use equations to solve word...
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...Capital and revenue receipts, Contingent assets and contingent liabilities, Fundamental errors including rectifications thereof. 3. Bank reconciliation Statement. 4. Inventories: Basis of inventory valuation and record keeping. 5. Depreciation Accounting: Methods, computation and accounting treatment of depreciation, Change in depreciation methods. 6. Preparation of Final Accounts for Sole Proprietors. 7. Accounting for Special Transactions: (a) Consignments, (b) Joint Ventures, (c) Bills of exchange and promissory notes, (d) Sale of goods on approval or return basis. 8. Partnership Accounts: Final accounts of partnership firms – Basic concepts of admission, retirement and death of a partner including treatment of goodwill. 9. Introduction to Company Accounts: Issue of shares and debentures, forfeiture of shares, re-issue of forfeited shares, redemption of preference shares. Section B: Mercantile Law (40 Marks) 1. The Indian Contract Act, 1872: An overview of Sections 1 to 75 covering the general nature of contract, consideration, other essential elements of a valid contract, performance of contract and breach of contract. 2. The Sale of Goods Act, 1930: Formation of the contract of sale-Conditions and Warranties-Transfer of ownership and delivery of goods-Unpaid seller and his rights. 3. The Indian Partnership Act, 1932: General Nature of Partnership-Rights and duties of partners-Registration and...
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...Chapter 2 Introduction to Optimization & Linear Programming 1. If an LP model has more than one optimal solution it has an infinite number of alternate optimal solutions. In Figure 2.8, the two extreme points at (122, 78) and (174, 0) are alternate optimal solutions, but there are an infinite number of alternate optimal solutions along the edge connecting these extreme points. This is true of all LP models with alternate optimal solutions. 2. There is no guarantee that the optimal solution to an LP problem will occur at an integer-valued extreme point of the feasible region. (An exception to this general rule is discussed in Chapter 5 on networks). 3. We can graph an inequality as if they were an equality because the condition imposed by the equality corresponds to the boundary line (or most extreme case) of the inequality. 4. The objectives are equivalent. For any values of X1 and X2, the absolute value of the objectives are the same. Thus, maximizing the value of the first objective is equivalent to minimizing the value of the second objective. 5. a. linear b. nonlinear c. linear, can be re-written as: 4 X1 - .3333 X2 = 75 d. linear, can be re-written as: 2.1 X1 + 1.1 X2 - 3.9 X3 0 e. nonlinear 6. [pic] 7. [pic] 8. [pic] 9. [pic] 10. [pic] 11. [pic] 12. [pic] 13. X1 = # of TV spots, X2 = # of magazine ads MAX 15 X1 + 25 X2 (profit) ...
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...BASIC LINEAR PROGRAMMING 18.0 LEARNING OBJECTIVES After studying this chapter, readers should be able to: Understand the concept and meaning of linear programming; Know the underlying basic assumptions; Formulate the linear programming problem; Solve linear programming problem using graphical and Simplex methods; and make appropriate and correct interpretations; and Understand the concepts of duality and shadow cost in linear programming. 18.1 INTRODUCTION This is an Operations Research technique that is popular and frequently used in industry, business and other areas of human endeavour. The major focus of Linear Programming (L.P) technique, in decisionmaking, is to optimize the use of limited available resources. That is, it is an economic allocation of scarce resources by means of mathematical modeling. The history of Operations Research tells us that George B. Dantzing developed Linear Programming technique during Second World War. His primary aim of developing the technique then was to solve some military logistics problems. But now, it is being used extensively in wide areas of human endeavours. 18.2 CONCEPT AND MEANING OF LINEAR PROGRAMMING. The term “Linear Programming” consists of two words Linear and Programming. The word “Linear” implies linear relationship among the variables in a model while the word “Programming” implies modeling and solving a problem mathematically. By the combination of these two words, it is obvious that the Linear Programming technique...
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...[pic] COURSE SYLLABUS Semester: Fall, Year: 2012 College Mission Statement Richard J. Daley College provides high-quality education which leads to academic success, career development, and personal enrichment that fulfill diverse community needs. Mathematics Department Mission Statement Our mission is to deliver excellent service and to provide learning opportunities by offering a wide range of mathematics courses, which will help our diverse student population to reach their goals in their path of preference such as baccalaureate transfer, workforce development, adult or continuing education. Our dedicated faculty will guide our students in constructing the necessary elements that will help them succeed in their math classes, and also encourage and motivate them to participate in college wide activities. We are committed to preparing our students to be productive, contributing members of their community with problem solving and critical thinking skills. We provide our students with the motivation to use the power, beauty, and utility of mathematics to successfully prepare themselves for global citizenship. |Math 99 RW | |[pic] | |“Intermediate Algebra with Geometry” ...
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...2011 FRM EXAM TRAINING SYLLABUS PART I Introduction to Financial Mathematics 1. Introduction to Financial Calculus a. Variables – Discrete and Continuous b. Univariate and Multivariate Functions – Dependent variable and Independent variable c. Physical representation of a function d. Linear and Non-Linear functions e. Limits of a function f. The number e and Natural Logarithm g. Differential Calculus – Differentiation, Interpretation - Slope of a tangent, using derivatives to calculate function values and deltas. Linear functions - 1st order derivative. Non-linear functions – 1st and higher order derivatives, interpretations and usage. Rules of derivatives. h. Functions – Differentiation and Taylor Series Expansion i. Introduction to Partial Derivatives j. Introduction to Integral Calculus 2. Introduction to Bond Mathematics a. Finance and the Time Value of Money b. Concept of Zero Coupon (Discount) Bonds and Coupon Bonds. c. Bond Characteristics d. Bond Types – Fixed Rate, Floating Rate, Inverse Floater Rate, etc. e. Interest Rates – Discrete and Continuous Compounding f. Bond Pricing – using ZCYC or YTMC with discrete compounding or continuous compounding g. Difference between bond coupon rate and bond yield h. Calculating Bond Yield (YTM, CY, MMY, ZCY/Spot, Par Yield, etc.) i. Price Yield Relationship Introduction to Financial Statistics and Econometrics 1. Introduction to Financial Statistics a. Frequency distributions b. Measures of Central Tendency/Location (Mean/Mode/Median)...
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...A Generalized Logarithm for Exponential-Linear Equations Dan Kalman Dan Kalman (kalman@email.cas.american.edu) joined the mathematics faculty at American University in 1993, following an eight year stint in the aerospace industry and earlier teaching positions in Wisconsin and South Dakota. He has won three MAA writing awards, is an Associate Editor of Mathematics Magazine, and served a term as Associate Executive Director of the MAA. His interests include matrix algebra, curriculum development, and interactive computer environments for exploring mathematics, especially using Mathwright software. How do you solve the equation 1.6x = 5054.4 − 122.35x? (1) We will refer to equations of this type, with an exponential expression on one side and a linear one on the other, as exponential-linear equations. Numerical approaches such as Newton’s method or bisection quickly lead to accurate approximate solutions of exponential-linear equations. But in terms of the elementary functions of calculus and college algebra, there is no analytic solution. One approach to remedying this situation is to introduce a special function designed to solve exponential-linear equations. Quadratic equations, by way of analogy, are √ solvable in terms of the special function x, which in turn is simply the inverse of a very special and simple quadratic function. Similarly, exponential equations are solvable in terms of the natural logarithm log, and that too is the inverse of...
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