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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  
NAH 337  (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
or emailed to you.

Handouts: Review sheets and supplementary materials will either be handed out in class or emailed to you. They will NOT be posted. Below such materials are indicated by a bold (S)

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Schedule Anticipated schedule for lectures showing quizzes (orange), tests (red) and holidays (green).
                   
 Sunday Monday Tuesday Wed Thursday Friday Saturday
25              
26
(12.1/12.2)
27
(12.1/12.2)
28
29
(12.2/12.3)
30
(12.3)
31
1
 
2
Labor Day
3
(12.3/12.4)
4
5
(12.4)
6    (Q1)
(12.4)
7
 
8
 
9
(12.5)
10
(12.5)
11

12
(12.5/12.6)
13
(13.1)
14
 
15
 
16
(13.1)
17
(13.2)
18

19
(13.3)
20  (Q2)
(13.3)
21
 
22
 
23
(13.4)
24
(13.5)
25

26
Review
27
Midterm 1
28
 
29

30
(14.1)
1
(14.2)
2

3
(14.3)
4
(14.3)
5
 
6
 
7
(14.4)
8
(14.5)
9

10
(14.5)
11  (Q3)
(14.6)
12
 
13
 
14
(14.6)
15
(14.7)
16
17
(14.7)
18
(14.7)
19
 
20
 
21
(14.8)
22
(14.8)
23

24
(15.1)
25  (Q4)(15.2) 26
 
27
 
28
(15.2)
29
(15.2)
30

31
Review
1
Midterm 2
2
 
3
 
4
(15.3)
5
(15.4)
6

7
(15.4)
8
(15.4)
9
 
10
 
11
Vetran's Day
12
(15.4)
13
14
(16.1)
15     (Q5)
(16.2)
16
 
17
 
18
(16.2)
19
(16.3)
20

21
(16.4/16.5)
22  
(16.4/16.5)
23
 
24
 
25
(17.1)
26     (Q6)
(17.1/17.2)
27
Thanksgiving
28
Thanksgiving
29
Thanksgiving
30
1
2
(17.2)
3
(17.3)
4
 
5
(17.3)
6
Last Class
7
8
9
 
10
11
12
Final 4-5:50
13
14

 

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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
  (S) 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
   (S) 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)
   (S) Chapter 15-16 Review questions and examples  
     
17.1 TBA Green's Theorem
17.2 TBA Stokes Theorem
17.3  5,7,9,11,15 Divergence Theorem
     

 

 Exam and Quiz Outlines

                Content Description
  Quiz Sep. 6  

Quiz is on 12.1-12.3 (text and in class) (25 min - no electronic devices). 

 
Quiz
2
Sep 20
  

Quiz on 12.4, 12.5, 13.2 (not 12.6,13.1). Know how to compute a cross product and its properties. Most of the exam will be on 12.5 material including equations of planes, distance from points to lines and planes, etc. 13.2 is basically differentiating and integrating vector valued functions.

 
 Quiz
3
Oct 11 
 
Quiz will be on 14.2-14.5. You'll need to know how to show a limit does not exist, evaluate it when it does, compute partial derivatives (explicit and implicit), compute tangent planes, vectors normal to z=f(x,y), and all of 16.5 on gradients with applications: normals to level sets, directional derivatives, gradients, ....
   Quiz 4 4 Oct 25  

Quiz will be on 14.6 (Chain Rule), 14.7 (critical points, Second derivative test...), and 14.8 (Lagrange multipliers). There won't be any questions like 14.7 #29-45 in the HW (max/min on bounded regions).

   Quiz 5 5 Nov 15  
Will only cover material in 15.2-15.4 but with no spherical coordinate problem.
There will be one question from each of the following catergories:
a) 15.2 Double Cartesian integral (x,y-slices and/or interchange integration order)
b) 15.3 Triple cartesian integral
c) 15.4 Double polar integral
d) 15.4 Triple cylindrical integral
Three of the four problems will be of the "set up but do not evaluate" type.
I might ask you to evaluate one of the double integrals.
   Quiz 6 6 Nov 26  
Tuesday, Nov 26 in class:
Will only cover material from 15.4, 16.2,16.4,16.5
There will be one question from each of the following catergories:
a) 15.4 Triple spherical coordinate integral
b) 16.2 Vector Line integral
c)  16.4 Surface/Surface area integral of a graph z=f(x,y)
d)  16.5 A Flux integral through a surface defined by z=f(x,y)

There will be no questions from 16.1, 16.3 (Vector potentials).

We are not doing parametrized surfaces on this quiz...only surface integrals on graphs z=f(x,y). In the text this means eqn 8-9 on pg 938 of 16.4.

           
  Midterm 1 Sep 27  

Textbook Sections: 12.1-12.5 and 13.2-13.5

 (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 
  • dot and cross product properties and identities
  • equations of lines and planes (big topic)
  • velocity, speed, acceleration, arclength, arclength parametrization
  • computing arclength
  • unit tangent, normal and binormal
  • computing curvature (Thm 1, Sec 13.4)
  • tangent and normal components of acceleration (Thm 1, Sec 13.5)
           
           
  Midterm  2 Nov 1  
Textbook 14.1-14.8 inclusive.    
    
  • Review Sheet is indicative of test questions.
  • 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. Possibly a simple word problem.
  • 20% of the exam will be a find and classify critical point problem.
  • 20-30% will be on Directional derivatives, geometry of gradients, and/or chain rule
  • 10% on limits
  • balance will be just simple calculations.
  • There will be NO problems involving maximing f(x,y) on a region like (7) in the Review Sheet emailed to you.
           
           
  Final   Dec 12    4:00-5:50pm Location: NAH 337 (our classroom)
         
TENTATIVE DESCRIPTION
Will cover material from 15.1-15.4, 16.1-16.5 and 17.3 (Divergence Theorem)
 
  • You have 1hr 50min but I'm trying to write a 75min exam.
  • There will be 9-10 questions. Some should be easy.
  • you'll be required to evaluate about half the integrals. The rest you will only be required to "set up" the integrals

Specific Topics:

  • double integrals in cartesian coordinates
  • reversing the order of integration on a double integral
  • double integrals in polar coordinates
  • triple integral in cartesian coordinates
  • triple integral in cylindrical coordinates
  • triple integrals in spherical coordinates
  • scalar line integrals
  • Vector line integrals
  • line integrals of conservative vector fields
  • surface integrals (graphs z=f(x,y) only)
  • flux integrals (graphs z=f(x,y) only)
  • Divergence Theorem

Notable exclusions:

  • parametrized surfaces and surface integrals
  • Stokes Theorem
  • Greens Theorem
 

LEARNING

OUTCOME

     

 later