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Nydus Open Learning

Mathematics

Mathematics · Calculus BC

Calculus BC

Integration by parts and partial fractions; improper integrals at an infinite limit and at a singular endpoint; parametric and polar curves with their slopes, lengths and areas; the convergence tests and the hypotheses each one needs; power and Taylor series with the radius and the interval they converge on; the alternating and Lagrange error bounds; and Euler's method with the logistic model.

Ages 14–18 24 lessons about 9.5 hours in all

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Las lecciones

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  1. 1 Integration by parts
  2. 2 Parts applied twice
  3. 3 Partial fractions
  4. 4 Improper integrals to infinity
  5. 5 Improper integrals at a singular endpoint
  6. 6 Slopes of parametric curves
  7. 7 Velocity, speed and acceleration
  8. 8 Arc length and distance travelled
  9. 9 Polar curves and their slopes
  10. 10 Area in polar coordinates
  11. 11 Sequences, partial sums and geometric series
  12. 12 The nth-term test
  13. 13 The integral test and p-series
  14. 14 Comparison tests
  15. 15 The ratio test
  16. 16 Alternating series, absolute and conditional
  17. 17 Power series and the radius of convergence
  18. 18 The interval of convergence
  19. 19 The standard Maclaurin series
  20. 20 New series from old
  21. 21 The alternating series error bound
  22. 22 The Lagrange error bound
  23. 23 Euler's method
  24. 24 Logistic growth