LMA017 Mathematical analysis in several variables Autumn 25

Welcome to the course!

 

Basic info

Course PM.

 

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.
16.4

Green's theorem
WEEK 7


 16.6, 16.7

Surfaces. Surface integrals of functions.
16.7

Surface integrals of vector fields.
16.9

Divergence Theorem.
WEEK 8


 16.8 

Stokes 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 (Monday and Thursday)

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)

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 2

 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)