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EGR 1101 Unit 2

EGR 1101 Unit 2. Quadratic Equations in Engineering (Chapter 2 of Rattan/Klingbeil text). Mathematical Review. In linear equations, which we studied last time, the two variables ( x and y ) are both raised to the first power:

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EGR 1101 Unit 2

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  1. EGR 1101 Unit 2 Quadratic Equations in Engineering (Chapter 2 of Rattan/Klingbeil text)

  2. Mathematical Review • In linear equations, which we studied last time, the two variables (x and y) are both raised to the first power: • In a quadratic equation, the dependent variable is raised to the first power and the independent variable is raised to the second power. For example:

  3. Graphical Interpretation • The graph of a quadratic equation is a parabola. In MATLAB: > fplot('2*x^2 + 3*x + 10', [-10, 10])

  4. Two Common Questions Involving Quadratic Equations • Given a quadratic equation, find the value of y for a particular value of x. (Easy!) • Given a quadratic equation, find the value of x for a particular value of y. (Harder!)

  5. Three Methods • We’ll study three ways to answer the second type of question: • Factoring • Quadratic formula • Completing the square

  6. Today’s Examples • Height of a projectile • Power and current in a circuit • Resistors in parallel

  7. Some Symbols Used in Electrical Drawings • Resistor: • Voltage Source: • Lamp (light bulb): • Circuit containing thesethree components:

  8. Three Basic Electrical Laws • Kirchhoff’s Voltage Law (KVL): Around any closed loop in a circuit, the sum of the voltage rises is equal to the sum of the voltage drops. • Ohm’s Law: For a resistor, voltage equals current times resistance: V = IR • Power Law: For any component, power equals current times voltage: P = IV

  9. Resistors in Series or Parallel • If two resistors are connected in series (end-to-end), total resistance is the sum of the two resistances: • If two resistors are connected in parallel (connected at both ends), total resistance is given by the product-over-sum rule:

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