Course Syllabus

 

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 

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 

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

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

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 

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 

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 

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 

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