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MATH 237 FINAL Niall W. MacGillivray

MATH 237 FINAL Niall W. MacGillivray. Outline. 1.1-8.2 Review 8.3 Generalizations of Taylor Polynomials 9.1 Local Extrema and Critical Points 9.2 Second Derivative Test 10.1-10.2 Extreme Values 10.3 Lagrange Multipliers

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MATH 237 FINAL Niall W. MacGillivray

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  1. MATH 237 FINAL Niall W. MacGillivray

  2. Outline 1.1-8.2 Review 8.3 Generalizations of Taylor Polynomials 9.1 Local Extrema and Critical Points 9.2 Second Derivative Test 10.1-10.2 Extreme Values 10.3 Lagrange Multipliers 11.1 Polar Coordinates 11.2 Cylindrical Coordinates 11.3 Spherical Coordinates

  3. Outline cont’d 12.1-12.2 R2 → R2 Mappings 12.3 Composite Mappings and Chain Rule 13.1-13.2 Jacobian and Inverse Mapping Theorem 13.3 Creating Mappings 14.1 Double Integrals 14.2 2-fold Iterated Integrals 14.3 Change of Variables (2D) 15.1 Triple Integrals 15.2 3-fold Iterated Integrals 15.3 Change of Variables (3D)

  4. 1.1-8.2 Review

  5. 1.1-8.2 Review

  6. 1.1-8.2 Review

  7. 1.1-8.2 Review

  8. 1.1-8.2 Review

  9. 8.3 Generalizations of Taylor Polynomials

  10. 8.3 Generalizations of Taylor Polynomials

  11. 9.1 Local Extrema and Critical Points

  12. 9.1 Local Extrema and Critical Points

  13. 9.1 Local Extrema and Critical Points

  14. 9.1 Local Extrema and Critical Points

  15. 9.2 Second Derivative Test

  16. 9.2 Second Derivative Test

  17. 9.2 Second Derivative Test

  18. 9.2 Second Derivative Test

  19. 9.2 Second Derivative Test

  20. 9.2 Second Derivative Test

  21. 9.2 Second Derivative Test

  22. 9.2 Second Derivative Test

  23. 9.2 Second Derivative Test

  24. 9.2 Second Derivative Test

  25. 10.1-10.2 Extreme Values

  26. 10.1-10.2 Extreme Values

  27. 10.1-10.2 Extreme Values

  28. 10.1-10.2 Extreme Values Algorithm

  29. 10.1-10.2 Extreme Values

  30. 10.3 Lagrange Multipliers Algorithm

  31. 10.3 Lagrange Multipliers

  32. 10.3 Lagrange Multipliers

  33. 10.3 Lagrange Multipliers

  34. 10.3 Lagrange Multipliers

  35. 11.1 Polar Coordinates • Useful when there is a symmetry about the origin • Non-unique representation of points, unless we have restrictions on the angle

  36. 11.1 Polar Coordinates

  37. 11.1 Polar Coordinates

  38. 11.1 Polar Coordinates Area in Polar Coordinates

  39. 11.2 Cylindrical Coordinates • Useful when there is a symmetry about an axis • Non-unique representation of points, unless we have restrictions on the angle

  40. 11.2 Cylindrical Coordinates

  41. 11.2 Cylindrical Coordinates

  42. 11.3 Spherical Coordinates • Useful when there is a symmetry about the origin • Non-unique representation of points, unless we have restrictions on the angle

  43. 11.3 Spherical Coordinates

  44. 11.3 Spherical Coordinates

  45. 12.1-12.2 R2 → R2 Mappings

  46. 12.1-12.2 R2 → R2 Mappings Linear Approximations

  47. 12.1-12.2 R2 → R2 Mappings

  48. 12.1-12.2 R2 → R2 Mappings

  49. 12.1-12.2 R2 → R2 Mappings Generalizations

  50. 12.1-12.2 R2 → R2 Mappings Generalizations Cont’d

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