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EGR 1101: Unit 9 Lecture #1

EGR 1101: Unit 9 Lecture #1. Applications of Derivatives: Electric Circuits (Section 8.4 of Rattan/Klingbeil text). Review: Some Derivative Rules. where a , c , n , and  are constants. Two New Derivative Rules. ( Product rule ).

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EGR 1101: Unit 9 Lecture #1

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  1. EGR 1101: Unit 9Lecture #1 Applications of Derivatives: Electric Circuits (Section 8.4 of Rattan/Klingbeil text)

  2. Review: Some Derivative Rules where a, c, n, and  are constants.

  3. Two New Derivative Rules • (Product rule) • If f(g) is a function of g and g(t) is a function of t, (Chain rule)

  4. Today’s Examples • Voltage, current, & power • Current & voltage in an inductor • Current & voltage in an inductor (graphical and working backwards) • Current & voltage in a capacitor • Current & voltage in a capacitor (graphical and working backwards)

  5. Review: Some Electrical Quantities

  6. Review: More Electrical Quantities

  7. Voltage-versus-Current Relations • For resistors, • For inductors, • For capacitors,

  8. EGR 1101: Unit 9Lecture #2 Applications of Derivatives: Beams (Section 8.5 of Rattan/Klingbeil text)

  9. Some Beam Terminology • Types of beams • Simply supported • Cantilever • Types of load on a beam • Concentrated • Distributed

  10. More Beam Terminology • In addition to the type of beam and load, a beam’s behavior also depends on its geometry and the material it is made of. • Its geometry is summarized in a quantity called the second moment of area (I). • Its material is summarized in a quantity called the modulus of elasticity (E). • The product of these two (EI) is called the flexural rigidity.

  11. Some Beam Quantities

  12. Excellent Online Resource • University of Wisconsin’s online lessons on Strength of Materials: http://www3.uwstout.edu/faculty/scotta/upload/Foley-StaticsStrengths.pdf • See especially Topic 4 (Beams) and Topic 8.2 (Stress on Incline Planes).

  13. Review • Given a function f(x), the function’s local maxima occur at values of x where and • Its local minima occur at values of x where and

  14. Today’s Examples • Deflection of a cantilever beam with end load • Deflection of a simply supported beam with central load • Deflection of a simply supported beam with distributed load • Maximum stress under axial loading

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