## Course Syllabus

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.

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 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* 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* 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 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* 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* 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* 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* Session 2 section 16.9: 5*, 7*, 11,  section 16.8: 1*, 3, 5*, 9*, 11, 15a)