Al-Khwarizmi: The Father of Algebra Muhammed Ibn Musa al-Khwarizmi‚ was a mathematical pioneer‚ and is considered by many to be the greatest mathematician of the Islamic world‚ as well as the founder algebra. His book entitled Kitâb al-Mukhtasar fî Hisâb al-Jabr wa ’l-Muqâbala‚ which means “The Compendious Book on Calculation by Completion and Balancing‚” established algebra as an independent discipline. While his arithmetic work‚ possibly entitled Kitāb al-Jamʿ wa-l-tafrīq bi-ḥisāb al-Hind
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MIDTERM NOTES Solve Linear Equations 0. Cancel all denominators by multiplying every term by the LCD. 1. Simplify LHS and RHS. 2. Eliminate variable term on RHS. 3. Eliminate variable term on LHS. 4. Eliminate the coefficient of the variable. Solve Rational Equations 1. Find LCD. 2. Cancel all denominators by multiplying every term by the LCD. 3. Solve. 4. Omit those solutions that make LCD=0. Complex Numbers: a + bi Powers of i: i0 = 1‚ i1 = i‚ i2 = −1‚ i3 = −i in = ir where r is the
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Real number Irrational numbers π ‚ √�� Rational numbers Integers Whole Natural 3 5 1 2 4 2 2 3 Rational Like: Integers {…‚ -3‚ -2‚ -1‚ 0‚ 1‚ 2‚ 3…….} Whole {0‚ 1‚ 2‚ 3…} Natural {1‚ 2‚ 3…} ‚ ‚ ‚ Properties of real numbers 1234- Reflexive property a=a Symmetric property a = b then b = a Transitive property a = b and b = c then a = c Principle of substitution if a = b then we can substitute b for a in any expirations Commutative properties a+b=b+a ‚ a.b=b.a Associative properties
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Systems and Control Experiement 1 Title: System Dynamics and Behavior Objectives: Dynamic systems like dc-servomotors‚ financial systems‚ logistic models‚ internet systems and eco-systems can be described by a set of coupled differential equations. Based on this model‚ one can study the behavior of such a system under various external factors such as initial conditions‚ variables’ interrelation changes‚ stead state responses and stability issues. In this experiment‚ a simple Loika-Volterra
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(DiGiuseppe 420). In a chemical equilibrium‚ the point where the concentrations of the products and reactants are constant is called the equilibrium position. This can be mathematically described in an equilibrium law. It is further defined in the equation by a value called the equilibrium constant‚ Kc (DiGiuseppe 421).
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Differential Equations Solving Differential Equations: 1. Direct Integration Differential Equation Solution dy f x dx y f x dx C dy f y dx 1 dy f y dx 1 f y dy 1 f y dy d2 y f x dx 2 1 1 dx dy dx F x C y f x dx C F x C dx G x Cx D xC 2. Substitution Use the substitution v x y to find the general solution of the differential equation dy
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2002:16(a) 1 (b) Outline a procedure to compare the reactivity of this alkene with its corresponding alkane. 2002:16(b) 2 (c) Describe the results obtained from this first-hand investigation and include relevant chemical equations. 2002:16(c) 3 3 Explain why alkanes and their corresponding alkenes have similar physical properties‚ but very different chemical properties. 2002:17 3 4 Which polymer is made by the polymerisation of methyl methacrylate? CH3 H2C=
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Week 1 – Discussion 1. Counting Number : Is number we can use for counting things: 1‚ 2‚ 3‚ 4‚ 5‚ ... (and so on). Does not include zero; does not include negative numbers; does not include fraction (such as 6/7 or 9/7); does not include decimals (such as 0.87 or 1.9) Whole numbers : The numbers {0‚ 1‚ 2‚ 3‚ ...} There is no fractional or decimal part; and no negatives: 5‚ 49 and 980. Integers : Include the negative numbers AND the whole numbers. Example: {...‚ -3‚ -2‚ -1‚ 0‚ 1‚ 2‚ 3‚
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differential form curl B = J. This was later modified to add a second term when it was incorporated into Maxwell’s equations. Archimedes’ Principle A body that is submerged in a fluid is buoyed up by a force equal in magnitude to the weight of the fluid that is displaced‚ and directed upward along a line through the center of gravity of the displaced fluid. Bernoulli’s Equation In an irrotational fluid‚ the sum of the static pressure‚ the weight of the fluid per unit mass times the height
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Contents MODULE 2 1 Scatter graphs 1.1 Scatter graphs and relationships 1.2 Lines of best fit and correlation 1.3 Using lines of best fit Chapter summary Chapter review questions 1 1 5 6 10 10 4 Processing‚ representing and interpreting data 4.1 Frequency polygons 4.2 Cumulative frequency 4.3 Box plots 4.4 Comparing distributions 4.5 Frequency density and histograms Chapter summary Chapter review questions 51 51 56 64 65 68 73 73 2 Collecting and recording data 14 2.1 Introduction
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