MATHEMATICAL METHODS PARTIAL DIFFERENTIAL EQUATIONS I YEAR B.Tech By Mr. Y. Prabhaker Reddy Asst. Professor of Mathematics Guru Nanak Engineering College Ibrahimpatnam‚ Hyderabad. SYLLABUS OF MATHEMATICAL METHODS (as per JNTU Hyderabad) Name of the Unit Unit-I Solution of Linear systems Unit-II Eigen values and Eigen vectors Name of the Topic Matrices and Linear system of equations: Elementary row transformations – Rank – Echelon form‚ Normal form – Solution of Linear Systems
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Title: Kinetics: The Rate of a Chemical Reaction Objectives: 1. To study the kinetics of chemical reaction‚ 2 I- + S2 O82- I2 + 2 SO42- . 2. To study the effects of reactant concentration (persulphate‚ S2O82-‚ and iodide‚ I-) and temperature on the rate of chemical reactions. ( i) Study the effect of 0.20M (S2O82-) on the rate of chemical reaction. ( ii) Study the effect of 0.10M (S2O82-) on the rate of chemical reaction. ( iii) Study the effect
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Applications: Graphing Simultaneous Equations − − − − Relating linear graphs and simultaneous equations Analysing graphs Practical applications of linear graphs Writing algebraic equations Jane Stratton Objectives: • Use linear graphs to solve simultaneous equations • Use graphs of linear equations to solve a range of problems • Translate worded problems into graphical and algebraic form Finding the Solution to an Equation from a graph • Finding solutions to an equation when we have a graph is easy
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quadratic equation is an equation that has a second-degree term and no higher terms. A second-degree term is a variable raised to the second power‚ like x2. When you graph a quadratic equation‚ you get a parabola‚ and the solutions to the quadratic equation represent where the parabola crosses the x-axis. A quadratic equation can be written in the form: quadratic equation‚ where a‚ b‚ and c are numbers (a ≠0)‚ and x is the variable. x is a solution (or a root) if it satisfies the equation ax2 +
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27 4 d e (2) 3 (b) If the length of the rectangle is x m‚ and the area is A m2‚ express A in terms of x only. (1) (c) What are the length and width of the rectangle if the area is to be a maximum? (3) (Total 6 marks) 5. (a) Solve the equation x2 – 5x + 6 = 0. (b) Find the coordinates of the points where the graph of y = x2 – 5x + 6 intersects the x-axis. Working: Answers: (a) ………………………………………….. (b) .................................................................. (Total 4 marks)
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Systems of linear equations‚ or a set of equations with two or more variables‚ are an essential part of finding solutions with only limited information‚ which happens to be exactly what algebra is. As a required part of any algebra student’s life‚ it is best to understand how they work‚ not only so an acceptable grade is received‚ but also so one day the systems can be used to actually find desired information with ease. There are three main methods of defining a system of linear equations. One way is
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Tak Nga Secondary School 2010-2011 Mid-year Exam Form 4 Mathematics (Paper I) Time allowed: 1 hour 15 minutes Class：________ Name：__________________( ) Marks: ________/ 60 Instructions: 1. Write your name‚ class and class number in the spaces provided on this cover. 2. This paper consists of THREE sections‚ A(1)‚ A(2) and B. Each section carries 20 marks. 3. Attempt ALL questions in this paper. Write your answers in the spaces provided. Supplementary answer sheets will be supplied on request.
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Without knowing something about differential equations and methods of solving them‚ it is difficult to appreciate the history of this important branch of mathematics. Further‚ the development of differential equations is intimately interwoven with the general development of mathematics and cannot be separated from it. Nevertheless‚ to provide some historical perspective‚ we indicate here some of the major trends in the history of the subject‚ and identify the most prominent early contributors. Other
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Rate of Decomposition of Calcium Carbonate Theory Calcium carbonate‚ CaCO3‚is one of the most abundant minerals on the Earth. More than 4% of the Earth’s crust is composed of calcium carbonate. It is a major component in limestone‚ marble‚ seashells‚ bedrock‚ etc. Limestone and marble have been among the most widely used building materials for more than 5 000 years‚ from the pyramids in Egypt to the Parthenon in Greece and the Taj Mahal in India. In many places‚ limestone is also the foundation
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Lab 3: Reaction Order and Rate Laws Name: Student Lab Partners: None Date of Experiment: 16 March 2014 Location: My House Course Number: CHE112 Abstract: When combining compounds‚ there are always two roles considered in the reaction. These are reactants and products. Reactants are the initial compounds before mixing. The products are synonymous with the term byproduct‚ or what remains when the reaction occurs. For example‚ Sodium (Na+) and Chlorine (Cl-)
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