LMA017 Mathematical analysis in several variables Autumn 22

Solutions2ndReexamAugust2023.pdf

SolutionsReexamJanuary2023.pdf

Welcome to the course!

Basic info

Course PM.

Here is a link to webpages of all previously taught courses LMA017 where in particular you can find videos of lectures from the previous year(s). It might be helpful if by some reason you cannot attend

lectures.

https://www.chalmers.se/sv/institutioner/math/utbildning/grundutbildning-chalmers/hogskoleingejor-och-sjofart/maskiningenjor/Sidor/lma017.aspx

**WEEKLY PLAN FOR LECTURES**
(subject to change)
Date	sections	material to cover
WEEK 1	14.1-2	Functions of several variables. Level curves. Limit values.
	14. 2-3	Continuity. Partial derivatives.
	14. 3-4	Higher partial derivatives. Tangent plane (shortly). Differentiability.
WEEK 2	14.5	Chain Rule. Implicit differentiation.
	14.6	Directional derivatives and the gradient vector.
	14.7	Maximum and minimum values. 2nd derivative test
WEEK 3	14.7	Absolute max and min values
	14.8, beginning of 15.1	Lagrange multipliers. Review of definite integral of functions of one variable. Double integrals over rectangles.
	15.1 and a part of 15.6	Double integrals over rectangles. Triple integrals over rectangular boxes
WEEK 4	15. 2	Double integrals over general regions.
	15.6	Triple integrals over general regions. Computing volumes
	15.9, 15. 3	Change of variables. Polar coordinates.
WEEK 5	15.7, 15.8, parts of 15. 4 and 15.6	Cylindrical coordinates. Spherical coordinates. Some applications of multiple integrals
	13.1, 13.2	Curves
	16.2	Line integrals of functions
WEEK 6	16.1, 16.2	Vector fields. Line integrals of vector fields.
	16.3	The Fundamental Theorem of line integrals. Conservative vector fields.
	16.3
WEEK 7	16.4	Green's theorem
	16.6, 16.7	Surfaces. Surface integrals of functions.
	16.7 and, if time permits, 16.9	Surface integrals of vector fields and, if time permits, Divergence Theorem.
WEEK 8	16.8 and, in the case we did not cover it at previous lecture, 16.9	Stokes Theorem and, in the case we did not cover it at previous lecture, Divergence Theorem.
	Review of ch.13 -16	Review of the course
		Example Exam

Below you can find recommended exercises for each week. The ones with asterisks will be presented at the exercise sessions. Since the exercises in Edition 8 and Edition 9 of the book slightly differ, I write the sets of exercises separately for Edition 8 and Edition 9. The ones with asterisks are identical for both editions, they just have different numbering.

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)	Edition 8: section 3.3: 21, 25, section 3.4: 9, 31, ch.3 review: 1, 2, section 4.4: 9, 15, 21, section 12.6: 1, 7, 8, 13, 15 (Edition 9: section 3.3: 27, 31, section 3.4: 9, 33, ch.3 review: 1, 2, section 4.4: 9, 15, 21, section 12.6: 1, 7, 8, 15, 17)
Week 1	Session 2 (Thursday 10.15 and 15.15)	Edition 8: section 14.1: 10, 13, 15, 19, 36, 38, 41, 44, 53, section 14.2: 6, 8, 14, 18* (Edition 9: section 14.1: 4, 13, 10, 13, 36, 38, 41, 44* , 53, section 14.2: 8, 10, 24, 23)
Week 2	Session 1 (Tuesday 10.15, Wednesday10.15)	Edition 8: section 14.2: 25, 34, 37, 38, 40, section 14.3: 15, 19, 25, 24, 41, 52 (Edition 9: section 14.2: 37, 46, 49, 50, 52, section 14.3: 9, 13, 16, 30, 37, 46)
Week 2	Session 2 (Thursday 10.15 and 15.15)	Edition 8: section 14.3: 56, 63, 65, 66, 71, 75, 103, 104, 105, section 14.5:* 1, 7, 9, 23 (Edition 9: section 14.3: 50, 57, 59, 60, 67, 80, 99, 100, 101, section 14.5:* 3, 11, 13, 27 )
Week 3	Session 1 (Tuesday 10.15, Wednesday10.15)	Edition 8: section 14.5: 27, 31, section 14.6: 7, 11, 13, 19, 28, 29, 34, 39* (Edition 9: section 14.5: 31, 35, section 14.6: 9, 13, 15, 23, 34, 35, 40, 45*)
Week 3	Session 2 (Thursday 10.15 and 15.15)	Edition 8: section 14.7: 13, 15, 21, 31, 33, 43, 45 (Edition 9: section 14.7: 15, 19, 23, 33, 35, 45, 47)
Week 4	Session 1 (Tuesday 10.15, Wednesday10.15)	Edition 8: section14.8: 5, 9, 11, 21, 23, 25, 29, section 15.1: 29, 31 (Edition 9: section14.8: 5, 11, 13, 27, 29, 35, 39, section 15.1:* 29*, 31)
Week 4	Session 2 (Thursday 10.15 and 15.15)	Edition 8: section 15.2: 9, 11, 12, 15, 17, 19, 21, 23, 45, 51, 53, 58, true-false quiz after chapter 15:* 1-5 (Edition 9: section 15.2: 13, 15, 16, 19, 23, 25, 27, 31, 55, 61, 63, 68, true-false quiz after chapter 15:* 1-5)
Week 5	Session 1 (Tuesday 10.15, Wednesday10.15)	Edition 8: section 15.6: 9, 13, 17, 21, 23(a), 53, 54 (Edition 9: section 15.6: 13, 17, 21, 25, 27(a), 57, 58)
Week 5	Session 2 (Thursday 10.15 and 15.15)	Edition 8: 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, 21, 25, 27, 41 (Edition 9: section 15.9:* 25, 27, 31, section 15.3: 1-6, 7, 11, 13, 22, 35, 39, section 15.7:* 9, 19, section 15.8: 7, 9, 23, 27, 29*, 43 )
Week 6	Session 1 (Tuesday 10.15, Wednesday10.15)	Edition 8: section15.6: 39, 41, section 13.1: 8, 12, 27, 43, 49, section 13.2: 3, 25, 33* (Edition 9: section 15.6: 43, 45, section 13.1: 8, 14, 35, 51, 57, section 13.2: 3, 27, 35* )
Week 6	Session 2 (Thursday 10.15 and 15.15)	Edition 8: section 16.2: 3, 5, 7, 9, 13, 15, section 13.3:* 3, 5, section 16.2:* 19, 21, 39, 41, 47 (Edition 9: section 16.2: 3, 5, 7, 9, 13, 17, section 13.3: 5, 7, section 16.2:** 21, 23, 41, 43, 49
Week 7	Session 1 (Tuesday 10.15, Wednesday10.15)	Edition 8: section16.3: 3, 7, 11, 13, 23, 29, 35* (Edition 9: section 16.3: 3, 7, 11, 19, 29, 35, 41*)
Week 7	Session 2 (Thursday 10.15 and 15.15)	Edition 8: section16.4: 1, 2, 7, 9, 13, 19, 21* (a), (b) (Edition 9: section16.4: 1, 2, 9, 11, 17, 23, 25* (a), (b) )
Week 8	Session 1 (Tuesday 10.15, Wednesday10.15)	Edition 8: section 16.6: 33, 35, 41, 49 , section 16.7: 5, 13, 23, 25, 43* (Edition 9: section 16.6: 33, 35, 41, 49 , section 16.7: 5, 13, 23, 25, 43* )
Week 8	Session 2 (Thursday 10.15 and 15.15)	Edition 8: section 16.9: 5, 7, 11, section 16.8: 1, 3, 5, 9, 11a) (Edition 9: section 16.9:* 5, 7, 11, section 16.8: 1, 3, 5, 9*, 15a) ).