VECTOR CALCULUS / MA 602

VECTOR CALCULUS / MA 602

SPRING SEMESTER 2008

INSTRUCTOR: MAZHAR JAMIL

Office: Room # 101(class in 313) Phone: (318)-357-3174 ext. 129 e-mail: Mjamil@lsmsa.edu

TEXT: Calculus and Analytic Geometry, 8th Edition by Thomas & Finney.

COURSE Advanced Calculus is a one-semester course design to acquaint students with the theory, techniques, and

DESCRIPTION: applications of several variables and vector calculus. The course, together with the prerequisite of multivariable calculus, should prepare students Advanced Physics and beyond the Advanced Placement Calculus BC exam.

COURSE In order to demonstrate that a student is in the process of achieving the major course objectives, the student must

REQUIREMENT: be able to work problems on major tests and quizzes similar to those problems regularly assigned as homework.

5% of your grades are taken from homework assignments, homework is an integral part of the course and provides

the student can learn mathematical concepts. It is doubtful that the student will be able to pass the course means by which the without working the homework assignments.

ATTENDANCE: Students are expected to be present and on time to every class. Attendance, including tardiness, will be recorded

and turned in daily. Three tardiness will accumulate to one unexcused absent. Students should note that absence

from excused or unexcused, does not give students the right to postpone quizzes or tests that follow and from the

class, submission of homework. It is the student's responsibility to look into the schedule or find out from the

classmates what was done in class and also about the homework. Unexcused absences and tardiness will

negatively affect the final grade.

RULES FOR 1. If any student has legitimate reason for being unable to take a test that student must notify Mr. Jamil at TEST TAKING: least 2 days before the exam unless excused by the school.

2. If a student fails to take an exam or quiz on the scheduled test date without previously notifying Mr. Jamil, 10% points will be taken off of that student's test grade, and NO bonus points will be available for that student.

GRADING: There will be five tests and a final. Pop quizzes and assignments will be administered throughout the course.

PROCEDURE: One test and a quiz will be dropped before the final grade is given. Any testing may be cumulative. The final exam will be comprehensive. The break-up is as follows:

Tests 60%

Pop quizzes 10%

Assignments 5%

Class participation 5%

Final 20%

OFFICE HOURS: M 8:00 – 10:00 & 11:00 – 12:00 T 9:30 – 11:45 & 2:15 – 4:00 (by appointment only)

W 9:3 0 – 10:00 & 11:00 – 12:00 R 10:00 – 11:00 & 2:15 – 4:00 (by appointment only) F 9:30 – 10:00, 11:00 – 12:00

GUIDED STUDY: Mondays / Room #242 4:00 - 5:30

Syllabus for Vector Calculus / MA 602 / Spring Semester 2008

DATE WEEK READING ASSIGNMENT (Page number)

1/ 14 / 2008 1 Distribution and discussion about the course.

Review of Chapter 10: Vector and Analytic Geometry in Space

10.1-10.2 Vector in Plane ( 699 ), Cartesian Coordinates and Vectors in Space ( 708 )

10.3-10.4 Dot Products ( 718 ), Cross Products ( 725 )

10.5-10.6 Lines and Plane and Space ( 731 ), Products of Three Vectors or More ( 741 )

10.7-10.8 Surfaces in Space ( 746 ), Cylindrical and Spherical Coordinates ( 758 )

1 / 21 / 08 2 Chapter 11: Vector Valued Functions and Motion in Space

11.1 Vector Valued Functions and Space Curve ( 767 )

11.2 Modeling Projectile Motion ( 779 )

11.3 Directed Distance and the Unit Tangent Vector T ( 786 )

1 / 28 / 08 3 11.4 Curvature, Torsion, and the Frenet Frame ( 791 )

11.5 Planetary Motion and Satellites ( 802 )

1 / 30 / 08 TEST # 1

2 / 4 / 2008 4 Mardi Gras Holidays

2 / 11 / 08 5 Chapter 12: Function of Two or More Variables and Their Derivatives

12.1 Function of Two More Independent Variables ( 815 )

12.2 Limits and Continuity ( 825)

12.3 Partial Derivatives ( 833)

12.4 Differentiability, Linearization, and Differentials ( 842 )

2 / 18 / 08 6 12.5 The Chain Rule ( 854 )

12.6 Partial Derivatives with Constrained Variables ( 862 )

2 / 22 / 08 TEST # 2

2 / 25 / 08 7 12.7 Directional Derivatives, Gradient Vectors, and Tangent Planes ( 869 )

12.8 Maxima, Minima, and Saddle Points ( 881 )

12.9 Lagrange Multipliers ( 891 )

3 / 3 / 08 8 12.10 Taylor’s Formula, Second Derivatives, and Error Estimates ( 902 )

Chapter 13: Multiple Integrals

13.1 Double Integrals ( 915 )

3 / 10 / 08 9 13.2 Areas, Moments, and Center of Mass ( 928 )

13.3 Double Integrals in Polar Forms ( 937 )

13.4 Triple Integrals in Rectangular Coordinates: Volume & Average Values ( 943 )

3 / 17 / 08 10 SPRING BREAKS

3 / 24 / 08 11 13.5 Masses and Moments in Three Dimensions ( 950 )

3 / 26 / 08 TEST # 3

3 / 31 / 08 12 13.6 Triple Integrals in Cylindrical and Spherical Coordinates ( 955 )

13.7 Substitutions in Multiple Integrals ( 962)

4 / 7 / 08 13 Chapter 14: Integration in Vector Fields

14.1 Line Integrals ( 973)

14.2 Vector Fields, Works, Circulation and Flux ( 979 )

14.3 Green’s Theorem in the Plane ( 988 )

4 / 11 / 2008 TEST # 4

4 / 14 / 08 14 14.4 Surface Area and Surface Integrals ( 1001 )

14.5 Divergence Theorem ( 1013 )

14.6 Stokes’s Theorem (1023 )

14.7 Path Independence, Potential Functions, & Conservative Fields ( 1030 ) (Optional)

4 / 21 / 08 15 Chapter 15: Differential Equations

15.1 Separable First Order Function ( 1045 )

15,2 Exact Differential Equations ( 1052)

4 / 28 / 08 16 15.3 Linear First Order Equations ( 1055 )

4 / 30 / 2008 TEST # 5

5 / 5 / 08 17 15.4 Linear Homogeneous Second order Equations ( 1061 )

15.5 Second Order Equations; Reduction of Order ( 1066 )

5 / 12 / 08 18 15.7 Power Series and Numerical Methods(1084) (Optional)

5 / 15 / 2008 FINALS