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Experience Calculus from Daily Life

Experience Calculus from Daily Life. Making Maths Visible by Sunil Bajaj, Sr. Specialist SCERT, Haryana, Sohna Road Gurgaon. Mathematics continues to draw reverence and fear in equal measure across generations.

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Experience Calculus from Daily Life

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  1. Experience Calculus from Daily Life Making Maths Visible by Sunil Bajaj, Sr. Specialist SCERT, Haryana, Sohna Road Gurgaon

  2. Mathematics continues to draw reverence and fear in equal measure across generations. • Students studying in school seldom get opportunity to “experience” the subject.

  3. Experience Calculus from Daily Life Can we make a change by relating it to Daily Life? Let us try

  4. Experience Calculus from Daily Life • The seminal objective of this is to make the Maths concepts “visible” by ‘abstract concepts’ into a ‘concrete manifestations • Need of the concepts and their use in daily life

  5. Starting Point With the Calculus as a key, Mathematics can be successfully applied to the explanation of the course of Nature.” — WHITEHEAD

  6. Function Take a cylindrical vessel of certain volume. volume of liquid in cylinder is V =  r2h( r is constant) Let radius= 10cm V = (10)2h orV=100h cm2 Now volume is a function of variable H (height ) which can be expressed as V=f(h) If H= 7cm Domain is [0,7] then Range is [0,2200]

  7. Experience Calculus from Daily Life Derivative Rate of change speed

  8. V= f(h) =volume of water in beaker V= f(h) = r2 h If r=K ( constant ) = K2 h

  9. Rate of change of volume in beaker is r2 which is visible as oil drop spreads as of yellow color.

  10. Derivative of V w.r.t. h =f’(h) =K2 Every drop is taking the shape of circular region of radius that of beaker with area K2

  11. CD- Rack

  12. Change in volume with respect to radius

  13. Change in volume with respect to radius

  14. Volume of Cuboid Length and breadth are constant

  15. Volume of cone

  16. Volume of cone tan α =r/h where α is semi vertical angle( constant ) Hence r = h tan α. If we differentiate V = with respect to h

  17. Put r = h tan α. V = V = V

  18. On differentiating(dV )/dh=

  19. Curved Surface Area of cone

  20. Change in volume of a sphere with respect to radius

  21. USE Computer use derivatives for a lot of signal processing algorithms. The stock market uses derivatives to see how stocks are changing. Anything that relates two values at different times most likely uses a derivative process.

  22. Make open box of Maximum capacity

  23. Make open box of Maximum capacity V(x) = x (30 – 2x) (80 – 2x) = 4x3 – 220x2 + 2400x Putting V/(x) = 12x2 – 440x+ 2400=0 We get , x= 30,20/3 , reject 30 and take 20/3

  24. Why modulus function is not derivable at x=0 ?

  25. Let us try C

  26. Thanks

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