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MTH 254: Calculus III



MTH 254
           Multivariable Calculus (4 credits)
Instructor          Dr. Shaska


Room:              164 MSC (Mathematics and Science Center) 
Time:               12:00-13:35
                        MTWR: 5/9/2016-6/29/2016

Office hours:     TR:  11:00-12:00
Final Exam:     TBA, 12:00-3:00

Description:  A study of vectors, polar coordinates, three-dimensional geometry, differential calculus of functions of several variables, multiple integrals, line and surface integrals, and vector fields including Green's theorem, Stoke's theorem, and Divergence theorem.

Prerequisite: MTH 155 or equivalent. 

Textbook:     Calculus with Early Transcendentals by Stewart, 8-th edition.

Grading:
  • Homework                       10% 
  • Midterm I:                        25%   
  • Midterm II:                       25%   
  • Final                                40%                              
  •                                  ___________
          Total                                T

Grades will be computed using the Oakland University guidelines: 94% --> 4.0, 50% ---> 1.0.  Using a linear model we have   Grade = (T-35)/15, where T is the total score for the semester.  

Contents:     We will cover chapters 12-16 in Stewart's book  
  • Chapter 12: Vectors and geometry of space
    • 12.1  Three dimensional coordinate system
    • 12.2  Vectors
    • 12.3  The dot product
    • 12.4  The cross product
    • 12.5  Equations of lines and planes
    • 12.6  Cylinders and quadric surfaces
  • Chapter 13: Vector functions
    • 13.1  Vector functions and space curves
    • 13.2  Derivatives and integrals of vector functions
    • 13.3  Arc length and curvature 
    • 13.4  Motion in space: velocity and acceleration
  • Chapter 14: Functions of several variables, partial derivatives
    • 14.1  Functions of several variables
    • 14.2  Limits and continuity
    • 14.3  Partial derivatives
    • 14.4  Tangent planes and linear approximation
    • 14.5  The chain rule 
    • 14.6  Directional derivatives and the gradient
    • 14.7  Maximum and minimum values 
    • 14.8  Lagrange multipliers
    • 14.9  Taylor series for functions of several variables*      (not in the book)
  • Chapter 15: Multiple integrals 
    • 15.1   Double integrals over rectangles
    • 15.2   Iterated integrals
    • 15.3   Double integrals over general regions
    • 15.4   Double integrals in polar coordinates
    • 15.5   Applications of double integrals
    • 15.6   Surface area
    • 15.7   Triple integrals
    • 15.8   Triple integrals in cylinder coordinates
    • 15.9   Triple integrals in spherical coordinates
    • 15.10 Change of variables in multiple integrals
  • Chapter 16: Vector Calculus
    • 16.1   Vector fields
    • 16.2   Line integrals
    • 16.3   The fundamental theorem of line integrals
    • 16.4   Green's theorem
    • 16.5   Curl and divergence
    • 16.6   Parametric surfaces and their areas
    • 16.7   Surface integrals
    • 16.8   Stoke's theorem 
    • 16.9   The divergence theorem
Homework:

12.1:  11-18, 22, 30-34, 37-38, 41-43, 
12.2: 27-52
12.3: 23-24, 45-64
12.4: 33-53
12.5: 23-82
12.6:  29-36, 41-50

13.1:  7-20, 28-32, 41-46
13.2:  9-28, 33-40
13.3:  1-9, 11-25
13.4:  19-28

14.1:  14-30, 
14.2:  9-22
14.3:  15-72
14.4:  4-32
14.5:  1-20
14.6:  11-17, 27-30, 41-46
14.7:  5-20, 31-38, 41-48
14.8:  3-14, 21-23

15.1: 15-26,  27-34, 37-43 
15.2:  7-10, 17-22
15.3: 7-14, 19-27
15.4:  3-10
15.5: 1-12
15.6:  3-8, 9-18
15.7:  3-13, 17-28
15.8: 5-18
15.9: 1-20

16.1:  11-25
16.2:  1-26, 43-51
16.3:  10-24, 
16.4:  1-31
16.5:  1-18