LMA017 Mathematical analysis in several variables Autumn 21

Aug 22: Solutions to the 2nd reexam are in the course PM

Jan 3 2022: Files with the reexam and with solutions to the reexam are in the course PM now.

Files with the exam and with solutions to the exam are in the course PM now.

Welcome to the course!

Important information: Since there is no lecture hall big enough to accompany everybody with the current covid-19 restrictions, all lectures will be given remotely via Zoom. The link for the lectures is here

https://chalmers.zoom.us/j/68328094194

with password: 585060

Important: There has been a change of plans with respect to the exercises because of logistics and covid-19 restrictions.

Tuesday and Thursdays exercise sessions that happen right after the lectures (starting 10:15) will happen via zoom. The link for them is

https://chalmers.zoom.us/j/66508856504

Password: 143435

The exercise sessions on Wednesday 10:15 and Thursday 15:15 will be at Lindholmen (not on zoom). Please see TimeEdit for numbers of rooms (they change from week to week).

In TimeEdit the class on Wednesday Sept. 22 has two rooms, but we will use only one - Svea 241.

Basic info

Course PM.

**WEEKLY PLAN FOR LECTURES**
Date	sections	material to cover	Videos
WEEK 1	14.1-2	Functions of several variables. Level curves. Limit values.	LMA017LectureI31082021.mp4 LMA017LectureII31082021.mp4 SlidesW1L1.pdf
	14. 2-3	Continuity. Partial derivatives.	LMA017Lecture02092021.mp4 SlidesW1L2.pdf
	14. 3-4	Higher partial derivatives. Tangent plane.	LMA017PartI03092021.mp4 LMA017PartII03092021.mp4 SlidesW1L3.pdf
WEEK 2	14.5 and a part of section 14.4	Differentiability. Chain Rule.	Lecture07092021.mp4 SlideW2Lecture07092021-1.pdf
	14.5	Chain Rule (continuing). Implicit differentiation.	Lecture09092021.mp4 W2Lecture2Slides09092021.pdf
	14.6	Directional derivatives and the gradient vector.	Lecture10092021.mp4 W2Lecture3Slides10092021.pdf
WEEK 3	14.7	Maximum and minimum values	Lecture14092021.mp4 SlideW3Lecture1.pdf
	14.7, 14.8	Maximum and Minimum Values. Lagrange multipliers	Lecture16092021.mp4 SlidesW3Lecture2.pdf
	14.8	Lagrange multipliers. Review of definite integral of functions of one variable	Lecture17092021.mp4 Slides17092021.pdf
Week 4	15.1 and a part of 15.6	Double integrals over rectangles. Triple integrals over rectangular boxes	Lecture21092021.mp4 Slides21092021.pdf
	15.2	Double integrals over general regions.	Lecture23092021.mp4 SlidesLecturesThursdayW4.pdf
	15.6	Triple integrals over general regions. Computing volumes.	Lecture24092021.mp4 SlidesLectureFridayW4.pdf
Week 5	15.9, 15. 3, 15.7	Change of variables. Polar coordinates. Cylindrical coordinates	Lecture28092021.mp4 Lecture1Week5.pdf
	15.8, parts of 15. 4 and 15.6	Spherical coordinates. Some applications of multiple integrals	Lecture30092021.mp4 Lecture2Week5.pdf
	13.1, 13.2	Curves	Lecture01102021.mp4 Slides01102021.pdf
Week 6	16.2	Line integrals of functions	Lecture10052021.mp4 Slides05102021.pdf
Week 6	16.1, 16.2	Vector fields. Line integrals of vector fields.	Lecture07102021.mp4 Slides07102021.pdf
Week 7	16.3	The fundamental Theorem of line integrals. Conservative vector fields.	Lecture10122021.mp4 SlidesLecture12102021.pdf
	16.4	Green's theorem	Lecture14102021.mp4 slidesThursday2021Oct14.pdf
	16.6, 16.7	Surfaces. Surface integrals of functions.	SlidesFriday2021Oct15.pdf LectureFriday15102021.mp4
Week 8	16.7, 16.9	Surface integrals of vector fields. Divergence Theorem.	SliedesTuesdayLEcturesOct19.pdf Lecture19102021.mp4
	16.8. Review of ch.13 -16	Stokes Theorem. Review of the course	Lecture21102021.mp4 SlidesThursdayOct21Lectures.pdf
		Example Exam	ExampleExam.mp4 SlidesFridayOct22Lectures.pdf

Below you can find recommended exercises for each week. The ones with asterisks will be presented at the exercise sessions. Of course you are recommended to do as many exercises (also not listed below) as you have time for.

WEEKLY EXERCISES
Week		Exercises
Week 1	Session 1 (Tuesday 10.15, Wednesday10.15)	section 3.3: 22, 25, section 3.4: 7, 31, ch.3 review: 1, 2, section 4.4: 12, 20, 21, section 12.6: 1, 3, 4, 11, 12	LMA017ExercisesBothTogether31082021.mp4 SlidesW1L3-1.pdf
Week 1	Session 2 (Thursday 10.15 and 15.15)	section 14.1: 9, 11, 13, 15, 19, 36, 38, 41, 44, 53, 67, section 14.2: 6, 8, 10, 16*	Exercises_multi_var_02_09_2021.mp4 Exercises_02_09_2021.pdf
Week 2	Session 1 (Tuesday 10.15, Wednesday10.15)	section 14.2: 34, 35, 37, 38, 40, 25, section 14.3: 15, 19, 21, 52*	SlidesW2ExercisesTuesday07092021-1.pdf Exercises07092021.mp4
Week 2	Session 2 (Thursday 10.15 and 15.15)	section 14.3: 25, 27, 33, 41, 57, 65, 71, 75, 103, 104, 105*	Exercises_09_09_2021_part_1.mp4 Exercises_09_09_2021_part_2.mp4 Exercises_09_09_2021.pdf
Week 3	Session 1	section 14,5: 1, 7, 9, 22, 27, 31, True-false test after Chapter 14: 1-6, 8, 11	SlidesW3Exercises1.pdf Exercises14092021.mp4
Week 3	Session 2	section14.6: 7, 11, 13, 19, 21, 28, 29, 34, 39	Exercises_16_09_2021.mp4 Exercises_16_09_2021.pdf
Week 4	Session 1	section 14.7: 5, 13, 15, 21, 31, 33, 43, 45	ExercisesTuesday21Sep2021.pdf
Week 4	Session 2	section14.8: 7, 9, 11, 21, 23, 25, 29*	Exercises_23_09_2021.mp4 Exercises_23_09_2021.pdf
Week 5	Session 1	section 15.1: 29, 31, section 15.2: 9, 11, 12, 15, 17, 19, 21, 23, 25, 31, 45, 49, 51, 53, 57, 58* , true-false quiz after chapter 15: 1-5	Exercises28092021.mp4 ExercisesTuesdayWeek5.pdf
	Session 2	section 15.6: 9, 13, 17, 21, 23(a), 53, 54	Exercises_30_09_2021.mp4 Exercises_30_09_2021.pdf
Week 6	Session 1	section 15.9: 23, 25, 28, section 15.3: 1-4, 5, 9, 11, 17, 25, 29, section 15.7:* 9, 17, section 15.8: 7, 9, 15, 21, 25, 27, 41	Exercises10052021.mp4 SlidesExercises05102021.pdf
Week 6	Session 2	section15.6: 39, 41, section 13.1: 7, 12, 27, 43, 49, section 13.2: 3, 25, 33	Exercises_07_10_2021.mp4 Exercises_07_10_2021.pdf
Week 7	Session 1	section 16.2: 3, 5, 7, 9, 13, 15, section 13.3:* 1, 3, section 16.2:* 19, 21, 39, 41, 47	Exercises10122021.mp4 SlideTuesdayoct12exercises.pdf
Week 7	Session 2	section16.3: 3, 5, 7, 11, 13, 15, 23, 29, 31 - 34, 35	Exercises_14_10_2021.mp4 Exercises_14_10_2021.pdf
Week 8	Session 1	section16.4: 1,2, 7, 9, 13, 21, section 16.6:* 33, 35, 40, 41, 45, section 16.7: 5, 7, 11*.	Exercises19102021.mp4 SlidesExerciseTuesdayOct19.pdf
Week 8	Session 2	section 16.7: 21, 23, 29, 43*, section 16.9: 5, 7, 11, 23*	Exercises_21_10_2021.mp4 Exercises_21_10_2021.pdf