Application of linear algebraic equation for chemical engineering problem The chemical engineering system models often outcome of set of linear algebraic equations. These problems may range in complexity from a set of two simultaneous linear algebraic equations to a set involving 1000 or even 10‚000 equations. The solution of a set two or three linear algebraic equations can be obtained easily by the algebraic elimination of variables or by the application of cramer’s rule. However for systems involving
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Rule Introduction Cramer’s rule is a method for solving linear simultaneous equations. It makes use of determinants and so a knowledge of these is necessary before proceeding. 1. Cramer’s Rule - two equations If we are given a pair of simultaneous equations a1 x + b1 y = d1 a2 x + b2 y = d2 then x‚ and y can be found from d1 b1 d2 b2 a1 b1 a2 b2 a1 d1 a2 d2 a1 b 1 a2 b 2 x= y= Example Solve the equations 3x + 4y = −14 −2x − 3y = 11 Solution Using Cramer’s rule we can write the solution
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All Four‚ One - Linear Functions In the last activity‚ we talked about how situations‚ rules‚ x-y tables‚ and graphs all relate to each other and connect. Now‚ we’ll look at how situations‚ rules‚ x-y tables‚ and graphs relate and connect to linear functions. A linear function is a function that‚ if the points from the function were to be put on a graph and connected‚ it would form a straight line. They are used to show a constant rate of change between two variables. A very simple example
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Doctor Gary Hall Differential Equations March 2013 Differential Equations in Mechanical Engineering Often times college students question the courses they are required to take and the relevance they have to their intended career. As engineers and scientists we are taught‚ and even “wired” in a way‚ to question things through-out our lives. We question the way things work‚ such as the way the shocks in our car work to give us a smooth ride back and forth to school‚ or what really happens to an
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Systems of Differential Equations and Models in Physics‚ Engineering and Economics Coordinating professor: Valeriu Prepelita Bucharest‚ July‚ 2010 Table of Contents 1. Importance and uses of differential equations 4 1.1. Creating useful models using differential equations 4 1.2. Real-life uses of differential equations 5 2. Introduction to differential equations 6 2.1. First order equations 6 2.1.1. Homogeneous equations 6 2.1.2. Exact equations 8 2.2. Second order
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2 First-Order Differential Equations Exercises 2.1 1. y 2. y y x t x t 3. y 4. y y x x t 5. y 6. y x x 7. y 8. y x x 17 Exercises 2.1 9. y 10. y x x 11. y 12. y x x 13. y 14. y x x 15. Writing the differential equation in the form dy/dx = y(1 − y)(1 + y) we see that critical points are located at y = −1‚ y = 0‚ and y = 1. The phase portrait is shown below. -1
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MAT114 Multivariable Calculus and Differential Equations Version No. 1.00 Course Prerequisites L T P C 3 0 2 4 : 10+2 level Mathematics/ Basic Mathematics (MAT001) Objectives This Mathematics course provides requisite and relevant background necessary to understand the other important engineering mathematics courses offered for Engineers and Scientists. Three important topics of applied mathematics‚ namely the Multiple integrals‚ Vector calculus‚ Laplace transforms which require knowledge of
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Contents PART XV ANALYTICAL CHEMISTRY Chapter 63 Detecting the presence of chemical species Action of heating solid sample strongly 1 Chapter 64 Separation and purification methods Centrifugation Sublimation Partition equilibrium of a solute between two immiscible solvents Two-dimensional thin-layer chromatography 2 2 3 6 Chapter 65 Quantitative methods of analysis Detection of end point in acid-alkali titration 8 Chapter 66 Instrumental analytical methods More
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the note payable. Harley made a $900 cash withdrawal from the company. Requirements: Complete the accounting equation worksheet for the transactions. Total each worksheet column. Verify that Assets = Liabilities + Equity. In proper order and form‚ prepare and Income Statement‚ Statement of Owners’ Equity and Balance Sheet. Harley’s Cutter Accounting Equation Worksheet Assets = Liab + Equity Cash AccRec PPE Note Pay
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Cranberry. * OPC contains antioxidants properties: * 20 times more powerful than Vitamin C * 50 times more powerful than Vitamin E * OPC offers 2 approach to skin protection: * Combat and neutralize free radicals. * Free radical which known as highly reactive compound that will cause oxidative damage to skin and also will faster the aging process. * Besides that‚ environment pollutants such as alcohol‚ cigarette smoke‚ chemicals‚ stress‚ and UV rays
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