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 grad, div 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