Worksheets — Set 3

Complex variables for engineers · Conformal mapping and applications

Print and write your answers. Use diagrams to show thinking.

Warm-up

1. Model population P(t) = 140e^{0.06t}. Find P(9). ___ 2. Solve the IVP dy/dt = 6y, y(0) = 7 ___ 3. Optimize: fence a rectangle with perimeter 28. Max area? ___

_See printable PDF for diagram._

Written practice

1. Model population P(t) = 130e^{0.05t}. Find P(8). ___ 2. Solve the IVP dy/dt = 5y, y(0) = 6 ___ 3. Optimize: fence a rectangle with perimeter 26. Max area? ___ 4. Set up but do not solve: mixing 13% and 33% solutions = ___ 5. Interpret units on the slope of a regression line. 6. Check dimensional consistency in your formula. ___ 7. Model population P(t) = 160e^{0.08t}. Find P(11). ___ 8. Solve the IVP dy/dt = 8y, y(0) = 9 ___

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More written practice

1. Optimize: fence a rectangle with perimeter 32. Max area? ___ 2. Set up but do not solve: mixing 16% and 36% solutions = ___ 3. Model population P(t) = 190e^{0.11t}. Find P(14). ___ 4. Solve the IVP dy/dt = 11y, y(0) = 12 ___ 5. Optimize: fence a rectangle with perimeter 38. Max area? ___ 6. Set up but do not solve: mixing 19% and 39% solutions = ___

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Patterns and rules

1. Model population P(t) = 300e^{0.22t}. Find P(25). ___ 2. Solve the IVP dy/dt = 22y, y(0) = 23 ___ 3. Optimize: fence a rectangle with perimeter 60. Max area? ___

_See printable PDF for diagram._

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Parent tip: Define variables with units