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                                          Math 283 Honors Multivariate Calculus (Fall 2018)

                            Final Exam: Tuesday, Dec 11, 4:00-5:50pm in Wil 1-138 (our classroom)

 

Grades will be entered either late Thursday afternoon or Friday morning.

Email me at pernarow@math.montana.edu to request final exam scores and course % and grade.

You may pick up the exams from me when you return in January

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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 1-138  (MTRF 11am)

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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
26              
27
(12.1/12.2)
28
(12.1/12.2)
29
30
(12.2/12.3)
31
(12.3)
1
2
 
3
Labor Day
4
(12.3/12.4)
5
6
(12.4)
7    (Q1)
(12.4)
8
 
9
 
10
(12.5)
11
(12.5)
12

13
(12.5/12.6)
14
(13.1)
15
 
16
 
17
(13.1)
18
(13.2)
19

20
(13.3)
21  (Q2)
(13.3)
22
 
23
 
24
(13.4)
25
(13.5)
26

27
Review
28
Midterm 1
29
 
30

1
(14.1)
2
(14.2)
3

4
(14.3)
5
(14.3)
6
 
7
 
8
(14.4)
9
(14.5)
10

11
(14.5)
12  (Q3)
(14.6)
13
 
14
 
15
(14.6)
16
(14.7)
17
18
(14.7)
19
(14.7)
20
 
21
 
22
(14.8)
23
(14.8)
24

25
(15.1)
26  (Q4)(15.2) 27
 
28
 
29
(15.2)
30
(15.2)
31

1
Review
2
Midterm 2
3
 
4
 
5
(15.3)
6
Election Day
7

8
(15.3)/(15.4)
9
(15.4)
10
 
11
 
12
Vetran's Day
13
(15.4)
14
15
(15.4)
16  (Q5)
(15.4)
17
 
18
 
19
(16.1)
20
(16.2)
21
Thanksgiving
22
Thanksgiving
23
Thanksgiving

24
 
25
 
26
(16.2)
27
(16.3)
28
29
(16.4/16.5)
30  (Q6)
(16.4/16.5)
1
2
3
(17.1)
4
(17.2)
5
 
6
(17.3)
7
Last Class
8
9
10
 
11
Final 4-5:50
12 13 14
15

 

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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
  Chapter 12-13 Supplementary problems  
     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. (extra material)
16.5  2, 5,7,9,11,13 (Nhat=khat)  Flux integrals (extra material)
   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
     
Supplemental Notes 12a   here - most of 12.1-12.4 in text
     

 

 Exam and Quiz Outlines

          Content Description
  Quiz Sep. 7  

Quiz is on 12.1-12.3 (text and in class) and you must know how to compute a cross pruduct. (25 min - no electronic devices). 

 
Quiz
2
Sep 21
  

12.4-12.5 Cross product applications and all manor of geometry problems: lines, planes intersections, orthogonal vectors and planes, angles between and distance between. Also for 13.2 must know tangent lines/vectors. No graphing of curves.(25 min - no electronic devices)

 
 
3
Oct 12 
 
14.2-14.4 Limits, Partial derivatives, Tangent planes and Linear approximations, Gradients and Directional derivatives. For limits concentrate on a) if you're told a limit exists can you compute it b) if you're told it does not, show that it does not. Partial derivatives might be 1-2 very simple calculations. Section 14.5 has the most material. Know how to compute gradients, their geometric properties, rates of change, chain rule, tangent planes. Lastly, know the implicit differentiation questions done in class.
    4 Oct 26  

14.5-14.8 Gradients, Directional Derivatives, The chain rule for F(t)=f(x(t),y(t)) and F(s,t)=f(x(s,t),y(s,t)) only, critical points and the second derivative test, Lagrange multipliers. There will be no question on maximizing a function f(x,y) on a closed bounded region. Also, for Lagrange multipliers, you will only be asked to optimize a function of two variables: max of f(x,y) subject to g(x,y) and not: max of f(x,y,z) .....

    5 Nov 16  
15.1-15.4 (but not spherical coordinates in 15.4). Specifically double integrals in cartesian coordinates, interchanging limits of integration, double integrals in polar coordinates, triple integrals in cartesian (15.3) and cylindrical (15.4) coordinates. 
    6 Nov 30  
15.4 (Spherical coordinates only), Knowing div(F), curl(F) and grad(V) in 16.1, 16.2 eqn 4 and 16.2 eqn 8, and conservative vector fields and line integral properties in 16.3, especially Theorem 1 and how to find potential functions.
           
  Midterm 1 Sep 28  

12.1-12.5, 13.2-13.5       Review Sheet

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

  • recommended HW questions (above) and the Review Sheet especially are accurate representations of the kind of Midterm questions 
  • 50 minutes. No electronic devices, notes/formula sheet
  • There will be no question on curvature
  • There will be a question on tangential and normal acceleration
  • There will be a question on arclength
           
           
  Midterm  2 Nov 2  
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   Dec 11    4:00-5:50pm Location: Wil 1-138 (our classroom)
         
 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
 
  • You have 1hr 50min but I'm trying to write a 75min exam.
  • There will be 10 questions
  • you'll be required to evaluate about half the integrals. The rest you will only be required to "set up" the integrals

There will be:

  • one double integral
  • one reversing the order of integration on a double integral
  • a triple integral in cartesian, cylindrical and spherical coordinates
  • two line integrals (one conservative, one not)
  • a surface integral
  • a flux integral
  • a Divergence Theorem question