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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: 7/2/2018-8/22/2018

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



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:

Unannounced quizzes will be given often. Homework will be assigned and occasionally will be collected to be graded.  The following chart will be used to determine your grade:
  • Quizzes/Homework         20% 
  • Midterm I:                        20%   
  • Midterm II:                       20%   
  • 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.  

Course Policies 

For all the problems and concerns you might have you must talk to me. No makeups will be given other then in case of documented emergencies. Cellular phones or any electronic equipment is NOT allowed during lecture. No calculators of any kind are allowed. 

Further, I do not tolerate any kind of academic dishonesty. Appropriate measures according to Oakland University regulations will be take for any case of cheating or breaking other rules. Attendance is mandatory! With more than three unexcused absences you will not be allowed to enter the final exam and will fail the course.   


Contents:     We will cover chapters 12-16 in Stewart's book  (with some small deviations)
  • 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  Quadratic surfaces 
    • Homework  (due Monday 14)
  • 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