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                                          Math 283 Honors Multivariate Calculus (Fall 2017)

 

                   You can pick up your final exams from me after the break. Email if you

                             you have any questions: pernarow@math.montana.edu

 

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                   title 1   title 2

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        Instructor  
  Mark Pernarowski 
        Textbook  
Calculus: Early Transcendentals, 3rd ed.: J. Rogawski, C. Adams
        Section  
01
        Office Hours   Schedule (Wil 2-236)
        Phone   994-5356
        Classroom  
Wil 1-122  (MTRF 8am)

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Grading: The course % is determined by:

   Midterm 1      M1           100 
   Midterm 2      M2           100
   Final                F            100
   Quizzes           Q           100
  ________________________________
                                        400

         % = (M1+M2+F+HW)/4
 
The final is not comprehensive.
Six quizzes each worth 20 points
will be given. Your best 5 quiz
scores determine Q above.

Exam and quiz dates are indicated
below. Their content will be announced in class.


All exams and quizzes are closed
book and no electronic devices
are permitted.


Syllabus: Material covered in text is from:

Chapter 12: Vector Geometry 
Chapter 13: Vector Valued Functions 
Chapter 14: Differentiation in Several Variables 
Chapter 15: Multiple Integration 
Chapter 16: Line and Surface Integrals 
Chapter 17: Fundamental Theorems of Vector Analysis 

Homework: Suggested homework is listed below.

Although the homework is not graded
it is representative of the kinds of
questions which will be on quizzes
and exams.

Some additional problem sets and/or
handouts will be handed out in class
and/or posted on this site below.

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Schedule Anticipated schedule for lectures showing quizzes (orange), tests (red) and holidays (green).
                   
 Sunday Monday Tuesday Wed Thursday Friday Saturday
27               
28
(12.1/12.2)
29
(12.1/12.2)
30
31
(12.2/12.3)
1
(12.3)
2
3
 
4
Labor Day
5
(12.3/12.4)
6
7
(12.4)
8    (Q1)
(12.4)
9
 
10
 
11
(12.5)
12
(12.5)
13

14
(12.5/12.6)
15
(13.1)
16
 
17
 
18
(13.1)
19
(13.2)
20

21
(13.3)
22  (Q2)
(13.3)
23
 
24
 
25
(13.4)
26
(13.5)
27

28
Review
29
Midterm 1
30
 
1

2
(14.1)
3
(14.2)
4

5
(14.3)
6
(14.3)
7
 
8
 
9
(14.4)
10
(14.5)
11

12
(14.5)
13  (Q3)
(14.6)
14
 
15
 
16
(14.6)
17
(14.7)
18
19
(14.7)
20
(14.7)
21
 
22
 
23
(14.8)
24
(14.8)
25

26
(15.1)
27  (Q4)(15.2) 28
 
29
 
30
(15.2)
31
(15.2)
1

2
Review
3
Midterm 2
4
 
5
 
6
(15.3)
7
(15.3)
8

9
(15.3)/(15.4)
10
Vetran's Day
11
 
12
 
13
(15.4)
14
(15.4)
15
16
(15.4)
17  (Q5)

18
 
19
 
20
(16.1)
21
(16.2)
22
Thanksgiving
23
Thanksgiving
24
Thanksgiving

25
 
26
 
27
(16.2)
28
(16.3)
29
30
(16.4/16.5)
1  (Q6)
(16.4/16.5)
2
3
4
(17.1)
5
(17.2)
6
 
7
(17.3)
8
Last Class
9
10
11
 
12
Final 4-5:50
Wil 1-122
13 14 15
16

 

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Suggested Homework and Syllabus

     
12.1  9,23,33,35,37,39,43,47,61  Vectors in the plane
12.2 5,9,11,19,25,29,31,35,37,43,47,51,52,53  Vectors and lines in R^3
12.3 1,11,13,15,19,21,23,25,35,39,43,,49,55,57,67  Dot Products, angles, orthogonal, projection
12.4 9,11,13,21,28,30,37,41,43,44,45  Cross Product
12.5 3,13,15,17,21-23,25,27,29,39,41,55,57,63,65,69  Planes in 3D
12.6 just read the section  Survey of Quadratic Surfaces
12.7 Will be done in tandem with Volume integrals in Chapte 15  Cylindrical Spherical coordinates
     
13.1  1,2,7,10,12b,12c,17,19,25,33(use "s" for r_2(t)),39  Vector Valued Functions
13.2  3,5,7,9,13,17,20,23,29,31,39,47(integrate),51(integrate twice),57  Calculus of Vector Valued Functions
13.3  1,3,5,9,11,15,25,31  Arclength and Speed
13.4  1,5,7,11,13,37,39,41,43,53 Curvature
13.5  3,5,11,15,33,35,37,41 Motion in Space
     Midterm 1
     
14.1  1,5,7,29,31,33,39a, 39b  Functions of several variables
14.2  7,8,9,13,15,17,18 (polar in chapter 11),29,34  Limits and Continuity
14.3  3,5,7,13,15,17,19,23,25,29,42,43,57,61,67,76  Partial Derivatives
14.4  1,5,11,13,19,21,23,25  Tangent Planes
14.5  5,7,9,11,15,17,19,21,23,25,29,31,37,39,41,44,45,61(hard)  Gradient and Directional Derivatives
14.6  1,3,7,11,13,19,27,29  Chain Rule
14.7  1,3,7,9,11,13,16,19,35,37 (on boundary),47,48  Optimization in Several variables
14.8  1,2,5,7,8,11,17,19,21,23  Lagrange Multipliers
   Chapter 14 Supplementary problems  
      Midterm 2
     
15.1  19,21,31,37  Double Integrals: Rectangles
15.2  3,9,11 (dy dx),17,21,25,27,31,45,49  Double Integrals: General Cartesian
15.3  3,9,11,17,21 (intersect planes),26,35 (dxdydz)  Triple Integrals: Cartesian
15.4  1,3,5,7,9,11,13,15,19,23,25,27,29,31,38,39,42,43,45,47,51,53,55  Integrals: Polar, Cylindrical, Spherical coordinates
15.5  not covering  Integrals: Applications
15.6  not covering  Integrals: Change of Coordinates 2D
     
16.1  13-16, 23,24,27,29,39,41,43  Vector-Fields
16.2  1,3,5,7,9,11,19,21,23,27,28,29,45,53  Line Integrals
16.3  1,57,8,9,12,17,19  Conservative Vector Fields
16.4   4,5,15,17,21,23,25 (Use Eqn 9 on pg 938 for all)  Parametrized Surfaces and Surface Integrals
16.5  2, 5,7,9,11,13 (Nhat=khat)  Flux integrals
   Chapter 15-16 Review questions and examples  
     
17.1  not covering Green's Theorem
17.2  not covering Stokes Theorem
17.3  5,7,9,11,15 Divergence Theorem
     
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 Exam and Quiz Outlines

          Content Description
         Quiz 1     Friday Sep. 8   12.1-12.3 and handout (25 min - no electronic devices)                                                                                                                 
    2 Friday Sep 22    12.4,12.5,13.1,13.2 (25 min - no electronic devices)  
                     3 Friday Oct 13   14.1-14.4 (25 min - no electronic devices) 
    4 Friday Oct 27  
14.5-14.7 (Gradients, Direct. Derivatives, Chain rule, 2nd Deriv. Test
but NO Constrained optimization (14.8)
    5 Friday Nov 17  
15.2-15.4 but no spherical coordinates in 15.4. Quiz will have 3-4 simple-moderate difficulty
questions. There will be one double iterated integral to evaluate. The remainder
will require you to set up double integrlas in cartesian/polar, and triple integrals
in cartesian/cylindrical coordinates. You may be required to reverse the order of 
integration in cartesian double integrals.
    6 Friday Dec 1  
15.4 (Spherical volume integral only), 16.1-16.3 Line integrals: including
scalar and vector line integrals, how to find potential functions when F is
a conservative vector field, Line integral of conservative field and a
simple surface integral from 16.4.
           
  Midterm 1 Friday Sep 29  

 12.1-12.5, 13.2-13.5       Review Sheet

 (50min, No electronic devices or notes/formula sheet) 

 There will be one question on normal and tangential
 accelerations and one question on arclength. 
 There will be no questions involving curvature.
           
           
  Midterm  2 Friday Nov 3  
a) 14.1-14.8 inclusive.    Review Sheet  (mostly corrected)
b) 15-20% of the exam may be on Lagrange multipliers/ constrained optimization for
problems of 2 or 3 variables (and one constraint), i.e f=f(x,y) or f=f(x,y,z), etc.
c) There will be no problems involving maximing f(x,y) on a region like (7) in the Review Sheet above.
           
           
  Final   Tues. Dec 12    Will be in our regular classroom Wil 1-122
     
4:00-5:50pm
Wil 1-122
 
 Will cover all the material cover in Chapters 15-16 (above) and 17.3 (Divergence Theorem)
 A review sheet is  Chapter 15-16 Review questions and examples
 I will give a more thorough description during the Review in class Friday Dec 8.