Lecture plan

Each week, there will be live lectures on tuesdays and fridays. There will also be two (shorter) virtual lectures. The plan is subject to change. The literature sections may cover more than is discussed in the lecture.

Week	Number	Themes	Literature section	Video link	Notes
I	1	Functions $LaTeX: \mathbb{R}^n\to\mathbb{R}^m$	13.1, 14.1, 16.1	link	notes
	virtual	Visualization	14.1, 16.1	link	notes
	virtual	Definition of continuity	14.2	link	notes
	2	Limits and continuity	14.2	link	notes
II	3	Partial and multi-dimensional derivatives	14.3,14.4,14.6, Section 1 of Multidimensional_derivative	link	notes
	virtual	More about multidimensional derivatives	Section 1 of Multidimensional_derivative	link	notes
	virtual	The second derivative and Hessians	14.3	link	notes
	4	The general chain rule and the 'Schrankensatz'	14.5, Section 2 and 3 of Multidimensional_derivative	link	notes
III	5	Optimization on open sets	14.7	link	notes
	virtual	The second order derivative criterion	14.7	link	notes
	virtual	Lagrange multipliers	14.8	link	notes
	6	Optimization with constraints	14.8	link	notes
IV	7	Multiple integrals and the theorem of Fubini	15.1, 15.2	link	notes
	virtual	Integrals and probability	15.4	link	notes
	virtual	General variable substitution	15.9	link	notes
	8	Polar coordinates	15.3	link	notes
V	9	Spherical and cylindrical coordinates	15.7.15.8	link	notes
	10	Line integrals and potentials	13.2, 13.3, 16.2, 16.3	link	notes
	virtual	Calculations of the spherical and cylindrical Jacobians	16.2,16.3	link	notes
	virtual	Simply connected domains and potentials	16.3	link	notes
	11	More on potentials: The curl criterion	16.3	link	notes
VI	12	Scalar surface integrals	16.6,16.7	link	notes
	virtual	Definition of surface integrals	16.6,16.7	link	notes
VII	13	Flow integrals	16.7	link	notes
	virtual	A proof sketch of the Stokes and Gauß theorems	16.8, 16.9	link	notes
	14	The Stokes (and Green) Theorems	16.8, 16.4,16.5	link	notes
VIII	15	The Gauß (divergence) theorem	16.9	link	notes
	16	The exercise exam	-	link	notes
	17	Q and A	-

Recommended exercises

The demonstrations will be uploaded as videos to youtube. The plan is subject to change.

The exercises chosen so that they pair with the themes in the lectures in the same week. That means, you may want to solve some of them the week after.

Week	Demonstrations	Self study	Video links	Notes
I	14.1: 38,45 14.2: 28, 37	13.1: 7-14,21-26,27. 14.1: 8,32,36,46-47,61-66. 16.1: 1-5,11-14,15-18,33 14.2: 5-6,9-14, 38, 44 Review chapter 13 True/False: 1,2,3. Review chapter 14: True/False 5,8	14.1.38: link 14.1.45: link 14.2.28: link 14.2.37: link	14.1.38: notes 14.1.45: notes 14.2.28: slides pdf 14.2.37: slides pdf
II	14.3: 27,33, 14.4;21, 14.5:35	14.3: 5,15-20,37, 53-58,83, 14.4: 17-18, 46 14.5:7,36,39 14.6: 19, 21-22, 30, 45, 69 All exercises in Multidimensional_derivative.pdf (some are hard) Review chapter 14: True/False 1,4,6,9.	14.3.27/33: link 14.4.21: link 14.5.35; link	14.3.27/33; pdf slides 14.4.21: notes 14.5.35; pdf slides
III	14.7:22,33 14.8:23	14.7: 3,5-9, 21,41,49,52, 14.8:3,5,7,15,27,29,50 Review chapter 14: True/False: 7,12.	14.7.22: link 14.7.33: link 14.8.23: link	14.7.22: notes slides 14.7.33: notes 14.8.23: notes slides
IV	15.2:45, 15.3: 19, 15.4:15, 15.6:13	15.1: 15-17,39. 15.2:7-8,19,23-24,46-48, 15.3: 7-11, 35,36, 39 15.4:11-12, 20 15.6:9-13, 39 Revision chapter 15 True/False: 1,2,5,6	15.2.45: link 15.3.19: link 15.4.15: link 15.6.13: link	15.2.45: notes 15.3.19: notes slides 15.4.15: notes slides 15.6.13: notes
V	15.7:21 15.8:26 16.2:3,19 16.3: 13	15.7:23-25, 29, 15.8:19,24,30,35, 47 16.2: 17, 20,22, 36, 45, 47. 16.3:3-6,21,28. Revision chapter 15 True/False: 9. Chapter 16 True/False: 4,5	15.7.21: link 15.8.26: link 16.2.3: link 16.2.19: link 16.3.13: link	15.7.21: see description in video 15.8.26: notes 16.2.3: notes 16.2.19: notes 16.3.13: see description in video
VI	16.6:20,22. 16.7: 39	16.6:19,21-23, 39,43-46. 16.7:12	16.6.20,22: link 16.7.39: link	16.6.20,22: see description in video 16.7.39: notes
VII	16.7: 22 16.8: 13	16.7: 21, 23, 24 ,27, 47. 16.8: 1, 2, 5,14, 16, 20, 16.4: 11-12 Revision chapter 16 True/False 11,12	16.7.22: link 16.8.13: link	16.7.22: notes 16.8.13: see description in video
VIII	16.9:2	16.9: 3, 7,13,24 Revision chapter 16 True/False: 7	16.9.2: link	16.9.2: notes
Exam prep	-	Revise old exercises. Also take a look at problem_solving_exercises.pdf and the practice exam

There is no need to do all exercises, but learning by doing is the way to go! You may thus want to do even more about certain concepts you feel unsure about. Remember that the group exercises will also give you an opportunity to learn. It is also a good idea to save some exercises for exam revision. There is some use in pushing yourself, but absolutely no use in pushing yourself too hard.

The red self study exercises are probably a bit more theoretical and/or hard. (This does not mean that the others are 'easy')

The concept check sections is excellent for exam revision.