Till KTH:s startsida Till KTH:s startsida

Plan for the course

Plan for the lectures with recommended exercises

Week 1 Recommended exercises
  10.1 Analytic geometry in three dimensions F1 11, 25, 27, 29, 31, 33, 35, 37, 39
  10.6 Cylindrical and spherical coordinates 3, 5, 9, 13
  11.1 Vector values functions in on variable F2 17, 21, 33
  11.2 Applications of vector differentiation 3
  11.3 Curves and parametrizations 5, 7, 11, 13, 15
  12.1 Functions in sevaral variables F3 5, 9, 13,15, 17, 23, 27, 33
  12.2 Limits and continuity 5, 7, 9, 11, 15
Week 2
  12.3 Partial derivatives F4 5, 7, 13, 23
  12.4 Higher order partial derivatives 5, 7, 11, 15, 17
  12.5 The chain rule F5 7, 11, 17, 21
  12.6 Linear approximation, differentiability and differentials 3, 5, 17, 19
  12.7 Gradients and directional derivatives F6 3, 5, 13, 17, 25
Week 3
  12.8 Implicit functions F7 13, 17
  12.9 Taylor's formula, Taylor series and approximations F8 1, 3, 5, 7, 11
  13.1 Extreme values 5, 7, 9, 19, 23, 25
  13.2 Extrem values of functions with constraints F9 3, 5, 9, 15
  13.3 Lagrange's multiplicators 3, 9, 11, 15
  13.4 Lagrange's multiplicators in Rn 1, 3
Week 4
  14.1 Double integrals F10 15, 19, 21
  14.2 Iterated integration Cartesian coordinates 3, 5, 15, 23
  14.3 Generalized integrals and the mean value theorem F11 1, 3, 13, 27
  14.4 Double integrals in polar coordinates 5, 9, 15, 19, 21
  14.5 Triple integrals F12 5, 7, 9
  14.6 Change of variables in triple integrals 3, 7, 11
  14.7 Applications of multiple integrals 5, 9, 13, 21,27
Week 5
  15.1 Vector fields and scalar fields F13 3, 5, 17,
  15.2 Conservative fields 3, 5, 7, 21
  15.3 Line integrals F14 7, 11
  15.4 Line integrals of vector fields 1, 5, 7, 15
  15.5 Surfaces and surface integrals F15 1, 7, 13
  15.6 Oriented integrals and flux integrals 5, 9, 13, 15
Week 6
  16.1 Gradient, divergence and curl F16 3, 7, 11
  16.2 Some identiteties involving graddiv and curl 9, 15, 17
  16.3 Green's Theorem in the plane F17 3, 5, 9
  16.4 The Divergence Theorem in three-space 5, 11, 15
  16.5 Stoke's Theorem in three-space F18 1, 3, 5