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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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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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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factoring‚ absolute value‚ rational expressions‚ equations (linear‚ quadratic‚ radical‚ rational)‚ systems of equations‚ inequalities‚ functions‚ graphs of quadratic and linear equations and inequalities in two variables‚ complex numbers and applications. 2. Learning Outcomes Upon successful completion of this course‚ students will be able to: 1. perform operations involving polynomials and factoring polynomials 2. solve and graph equations and inequalities such as linear‚ absolute value
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divisibility‚ highest common factor‚ primes‚ factorization‚ Diophantine equations and so on‚ among which I chose Diophantine equations as the specific topic I would like to go deep into. Fermat ’s Last Theorem states that if n is a positive integer greater than 2‚ then the Diophantine equation x^n+y^n=z^n has no nontrivial solutions. Diophantine equation is an equation together with the restriction that the only solutions of the equation of interest are those belonging to a specified set‚ often the
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Purpose: To find number of moles of Fe+3 which react with one mole of NH3OH+ in order to partially balance the equation: NH3OH+ + 2Fe+3 "" ? + 2Fe+2 and to find the missing product. Procedure: H2C2O4 and H2SO4 were titrated with potassium permanganate. The molarity of the permanganate was then found because the molarity of the H2C2O4 and H2SO4 were already known. Then hydroxylammonium chloride and ferric sulfate and water was titrated with known potassium permanganate to get the molarity of the
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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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