# 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

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

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.

 Date sections material to cover Videos WEEK 1 14.1-2 Functions of several variables. Level curves. Limit values. LMA017LectureI31082021.mp4 LMA017LectureII31082021.mp4 14. 2-3 Continuity. Partial derivatives. LMA017Lecture02092021.mp4 14. 3-4 Higher partial derivatives.   Tangent plane. WEEK 2 14.5 and a part of section 14.4 Differentiability. Chain Rule. 14.5 Chain Rule (continuing). Implicit differentiation. 14.6 Directional derivatives and the gradient vector. WEEK 3 14.7 Maximum and minimum values 14.7, 14.8 Maximum and Minimum Values. Lagrange multipliers 14.8 Lagrange multipliers. Review of definite integral of functions of one variable Week 4 15.1 and a part of 15.6 Double integrals over rectangles. Triple integrals over rectangular boxes Slides21092021.pdf 15.2 Double  integrals over general regions. 15.6 Triple integrals over general regions. Computing volumes. Week 5 15.9, 15. 3, 15.7 Change of variables. Polar coordinates. Cylindrical coordinates 15.8, parts of 15. 4 and 15.6 Spherical coordinates. Some applications of multiple integrals 13.1, 13.2 Curves Week 6 16.2 Line integrals of functions 16.1, 16.2 Vector fields. Line integrals of vector fields. Week 7 16.3 The fundamental Theorem of line integrals. Conservative vector fields. 16.4 Green's theorem 16.6, 16.7 Surfaces. Surface integrals of functions. Week 8 16.7, 16.9 Surface integrals of vector fields. Divergence Theorem. 16.8. Review of ch.13 -16 Stokes Theorem. 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 (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 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* 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* 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