LMA017 Mathematical analysis in several variables

Solutions to 2nd reexam

SolutionsCalculusAugust2024.pdf

Solutions to reexam SolutionsReexamJanuary2024.pdf

Welcome to the course!

Basic info

Course PM.

If by some reason one misses a lecture (e.g. because of of sickness or overlap of schedules ), here is a link to videos of lectures from 2021

https://utb.math.chalmers.se/?Kurskod=LMA017

There are differences and improvements in lectures this year compared with 2021.

I DO NOT recommend to use the videos instead of coming to lectures.

**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.

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 (Thursday 8. 15 and 10.15)	section 3.3: 27, 31, section 3.4: 9, 33, ch.3 review: concept check questions 1, 2, section 4.4: 9, 15, 21, section 12.6: 1, 7, 8, 15*, 17
Week 1	Session 2 (Friday 10.15 and 13.15)	section 14.1: 4, 13, 10, 13, 36, 38, 41, 44* , 53, section 14.2: 8, 10, 24, 23
Week 2	Session 1	section 14.2: 37, 46, 49, 50, 52, section 14.3: 9, 13, 17, 31, 37, 46
Week 2	Session 2	section 14.3: 51, 57, 59, 61, 67, 80, 99, 100, 101, section 14.5:* 3, 11, 13, 27
Week 3	Session 1	section 14.5: 31, 35, section 14.6: 9, 13, 15, 23, 34, 35, 40, 45*
Week 3	Session 2	section 14.7: 15, 19, 23, 33, 35, 45, 47
Week 4	Session 1	section14.8: 5, 11, 13, 27, 29, 35, 39, section 15.1: 29*, 31
Week 4	Session 2	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	section 15.6: 13, 17, 21, 25, 27(a), 57, 58
Week 5	Session 2	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	section 15.6: 43, 45, section 13.1: 8, 14, 35, 51, 57, section 13.2: 3, 27, 35*
Week 6	Session 2	section 16.2: 3, 5, 7, 9, 13, 17, section 13.3: 3, 7, section 16.2:** 21, 23, 41, 43, 49
Week 7	Session 1	section 16.3: 3, 7, 11, 12, 29, 35, 41*
Week 7	Session 1	section16.4: 1, 9, 11, 15, 17, 23, 25* (a), (b)
Week 8	Session 1	section 16.6: 33, 35, 41, 49 , section 16.7: 5, 13, 23, 25, 43*
Week 8	Session 2	section 16.9: 5, 7, 11, section 16.8: 1, 3, 5, 9*, 11, 15a)