Chapter 2 Lecture Notes ppt

Chapter 2 Lecture Notes ppt - In Your Career in Engineering...

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In Your Career in Engineering You will deal with the solutions to Current Engineering problems So, why do you need to know Mathematics, Specially Differential Equations??? Because, Analytical Methods of Engineering like any other Applied Science, are mostly governed by Differential Equations
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You Need to Develop your understanding of 1. Reduction of Governing Physical Principles to Differential Field Equations, and Applicable boundary and/or Initial Conditions 2. Uniqueness of solutions 3. Available solution methods to derive the required answers 4. Interpretation of your solution to the Engineering problem/solution
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Flowchart of Standard Analytical Methods in Engineering
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Generation of Differential Equations in Applied Science Motivations of Applied Scientists/Engineer To learn derivations and solution Motivations Almost all fields of theoretical and applied sciences are governed by differential equations In order ot get the solutions of physical and engineering problems, we need to solve these equations with various boundary (Space) and initial (Time) conditions Your proficiency and expertise in understanding how various engineering problems can be solved using Mathematical Methods Alternatives: None
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Types of Differential Equations: Unknown Order : Order is defined by the highest order derivatives present in the Governing Differential Equations ( ) du ku f x dx + = 2 2 ( ) + + = d u du c ku f x dx dx First Order Second Order Linear Equation 2 2 ( ) ( ) ( ) ( ) + + = d u du P x Q x R x u f x dx dx ( ) function of independent variable  u x x Note that in a linear equation the coefficients of derivatives are functions of only. Nonlinear
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Chapter 2 Lecture Notes ppt - In Your Career in Engineering...

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