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Calculus

Calculus. What is it? What good is it?. What is Calculus?. A systematic method for solving problems about systems that change. A language for describing dynamic systems. A collection of ideas based on infinite processes and limits. Precalculus. Calculus. Limit Process.

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Calculus

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  1. Calculus What is it? What good is it?

  2. What is Calculus? • A systematic method for solving problems about systems that change. • A language for describing dynamic systems. • A collection of ideas based on infinite processes and limits.

  3. Precalculus Calculus Limit Process Systems that change

  4. With Calculus you can… • Calculate the slope of line… even when the shape of the line is always changing!

  5. Precalculus A B 200 Miles 4 Hours Average speed = 50 mph Calculus Instantaneous Speed = 55 mph Limit Process Systems that change

  6. With Calculus you can… • Calculate the speed of a car or a particle in space… even when the speed is always changing!

  7. Precalculus Calculus Limit Process 5 5 4 4 Systems that change Area = 20 Area = 12

  8. With Calculus you can… • Calculate the area under a curve… even when the height is always changing!

  9. Precalculus formulas: Slope of a line Average speed Area of a rectangle Calculus formulas: Slope of a curve Instantaneous speed Area under a curve A method for solving problems about systems that change

  10. Precalculus: Slope of a line Average speed Area of a rectangle Calculus: Slope Instantaneous speed Area A language for describing dynamic systems.

  11. Other things calculus can do: • Explain why the angle between an observer and a rainbow is 42 degrees. • Connect designs on a laser printer to form letters of arbitrary size. • Find the best seat in the theater for viewing a movie. • Etc.

  12. What is Calculus? • A systematic method for solving problems about systems that change. • A language for describing dynamic systems.

  13. "Velocity is the derivative of position" • The relation between velocity and position is given precisely in the language of calculus.

  14. "Force is the derivative of momentum" • Newton's second law of motion is accurately and precisely described in the language of calculus.

  15. The language of calculus shows that the relationship between velocity and position is the same as that between force and momentum.

  16. What is Calculus? • A systematic method for solving problems about systems that change. • A language for describing dynamic systems. • A collection of ideas based on infinite processes and limits.

  17. Big Ideas of Calculus Limits Differential Calculus Integral Calculus

  18. …there is an opposition in all things. If not so … righteousness could not be brought to pass; neither wickedness; neither holiness nor misery; neither good nor bad. Wherefore, all things are a compound in one. II Nephi 1:81-83 What good is calculus?

  19. Voyager II movie.

  20. Trajectory of flight Effect of gravity of Saturn & Jupiter Amount of fuel needed After 12 years of flight, Voyager II came within 41 miles of its target, 3000 miles from Neptune Calculus was used to find:

  21. Determine trajectories of airborne bombs and missiles The same calculus used to:

  22. To help solve the problems of resource and energy distribution that are necessary for peace on earth. The same calculus can be used:

  23. will be the ones who choose which problems will be solved in this generation, whether for good or for evil. Those who know the calculus

  24. To be learned is good if they hearken to the counsels of God. II Nephi 6:61 Remember…

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