Saltar para o conteúdo
Nydus Open Learning

Mathematics

Mathematics · Avançado · Nível 2

Calculus III

Vectors in space with the dot, cross and scalar triple products, and the lines, planes and quadric surfaces they describe; vector functions, velocity and acceleration, arc length, curvature and the moving frame of a curve; functions of several variables, limits along paths, partial derivatives, tangent planes, the chain rule and its Jacobian, directional derivatives and the gradient, and extrema both free and constrained by Lagrange multipliers; double integrals over rectangles and general regions, polar coordinates, triple integrals, cylindrical and spherical coordinates and the change-of-variables formula; and vector calculus — fields, divergence and curl, line integrals, conservative fields and potentials, Green's theorem, surface integrals and flux, and Stokes' and the divergence theorem.

Ages 18+ 32 lessons about 13 hours in all

Cria uma conta para começar Rever as bases

Podes começar já, seja o que for que tenhas feito antes. Não é preciso terminar primeiro nada desta página. Podes fazer uma pausa quando quiseres; o teu progresso é guardado automaticamente.

As lições

Podes abrir qualquer lição agora, por qualquer ordem. O plano recomenda uma; não bloqueia as restantes.

  1. 1 Vectors in space
  2. 2 The dot product
  3. 3 The cross product
  4. 4 The scalar triple product
  5. 5 Lines in space
  6. 6 Planes in space
  7. 7 Cylinders and quadric surfaces
  8. 8 Vector functions and space curves
  9. 9 Velocity and acceleration
  10. 10 Arc length of a space curve
  11. 11 Curvature and the moving frame
  12. 12 Tangential and normal acceleration
  13. 13 Functions of several variables
  14. 14 Limits and continuity in two variables
  15. 15 Partial derivatives
  16. 16 Tangent planes and linear approximation
  17. 17 The chain rule and the Jacobian
  18. 18 Directional derivatives and the gradient
  19. 19 Maxima and minima of two variables
  20. 20 Lagrange multipliers
  21. 21 Double integrals over rectangles
  22. 22 Double integrals over general regions
  23. 23 Double integrals in polar coordinates
  24. 24 Triple integrals
  25. 25 Cylindrical and spherical coordinates
  26. 26 Change of variables in a multiple integral
  27. 27 Vector fields, divergence and curl
  28. 28 Line integrals
  29. 29 Conservative fields and potential functions
  30. 30 Green's theorem
  31. 31 Surface integrals and flux
  32. 32 Stokes and the divergence theorem