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Nydus Open Learning

Mathematics

Mathematics · Avançado · Nível 1

Calculus II

Integration by parts, reduction formulas, trigonometric integrals and substitutions, completing the square and partial fractions, with a strategy for choosing between them; area, volume by slicing and by shells, arc length, surface area, work and average value; improper integrals at an infinite limit and at a singular endpoint, with comparison; sequences, partial sums, and the divergence, integral, comparison, ratio, root and alternating series tests, with absolute and conditional convergence; power series, term-by-term calculus, Taylor series and the Lagrange remainder; and parametric and polar curves, with their slopes, lengths and areas.

Ages 18+ 30 lessons about 11.5 hours in all

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As lições

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  1. 1 Integration by parts
  2. 2 Reduction formulas and the loop
  3. 3 Integrals of powers of sine and cosine
  4. 4 Trigonometric substitution
  5. 5 Completing the square, and rationalising substitutions
  6. 6 Partial fractions
  7. 7 Choosing an integration technique
  8. 8 The area between two curves
  9. 9 Volume by slicing: discs and washers
  10. 10 Volume by cylindrical shells
  11. 11 The length of a curve
  12. 12 The area of a surface of revolution
  13. 13 Work, force and average value
  14. 14 Improper integrals over an infinite interval
  15. 15 Improper integrals at a singular endpoint
  16. 16 Comparison and limit comparison
  17. 17 Sequences and monotone convergence
  18. 18 Series, partial sums, geometric and telescoping
  19. 19 The divergence test and the integral test
  20. 20 Comparison and limit comparison for series
  21. 21 The ratio and root tests
  22. 22 The alternating series test
  23. 23 Absolute and conditional convergence
  24. 24 Power series: radius and interval of convergence
  25. 25 Differentiating and integrating a power series
  26. 26 Taylor and Maclaurin series
  27. 27 Taylor's theorem and the Lagrange remainder
  28. 28 Parametric curves: slope, speed and length
  29. 29 Polar coordinates and polar curves
  30. 30 Area and length in polar coordinates