Welcome to the Mathematics Department at UCSB


Vector Calculus

Math 5B - Spring 2006



Update:
You can download the review sheet for the Final Exam here.

You can download the solutions for the First Midterm here.

You can download the solutions for the Second Midterm here.


Instructor: Paolo Cascini

Teaching Assistants: Garrett W Johnson

Lectures: MWF 12:00 - 12:50pm - NH 1006
Please check GOLD for the time and location of your discussion section. Note that attendance at a discussion section is mandatory.

Course Description: Math 5B is the first quarter of a two quarter sequence in vector calculus. A thorough knowledge of single variable calculus is assumed. See the Math 5B Course Description for more details.
The Class Schedule will be continuosly updated during the quarter.

Office Hours: Mon. 3:00pm - 4:00pm , Wed. 2:00pm - 4:00pm and by appointment.

Textbook: Wilfred Kaplan - Advanced Calculus - Fifth Edition. Addison-Wesley Higher Mathematics.

Please read the list of Frequently Asked Questions, before joining the Waiting List.



Grading: Quizzes 20%, Midterms 30%, Final Exam 50%.

Books, notes, calculators, scratch paper or collaboration will NOT be permitted on any of the exams or quizzes.

Midterms: There will be two midterms given in class on Friday Apr. 28 and Friday May 26. Only the highest score within the two midterms will be counted for the final grade. There will be NO make-up exam for any of the midterms.

Quizzes: There will be three quizzes given during discussion section. Only the two highest scores will be counted for the final grade. There will be NO make-up date for any of the quizzes.

Homeworks: There are homework assignments for each day's lecture. The assignments are posted on the website. You are not required to turn in the homework.

Final Exam: The final exam will be held on Tuesday, June 13 from 12:00 to 3:00 pm. The exam will cover all the material of the entire course. An incomplete may be assigned only for documented medical reasons.






Class Schedule



    Date         Topics         Readings         Homeworks    
M 4/03 Review of Linear Algebra     Ch. 1.1-5 Ch. 1.5 - Ex. 2,5,6,7
W 4/03 Cancelled    
F 4/07 Matrices Ch. 1.6-12 Ch. 1.8 - Ex. 1,2
Ch. 1.9 - Ex. 1,2
Ch. 1.11 - Ex. 1,2,3,4
M 4/10 Functions of Several Variables Ch. 2.1-3  
W 4/12 Limits, Continuity Ch. 2.4 Ch. 2.4 - Ex. 2,4,6
F 4/14 Partial Derivatives Ch. 2.5,6 Ch. 2.6 - Ex.1,4
M 4/17 Jacobian and Chain Rule Ch. 2.7,9 Ch. 2.7 - Ex. 1,3
Ch. 2.9 - Ex. 1
W 4/19 Implicit Functions Ch. 2.10 Ch. 2.11 - Ex 1
F 4/21 Implicit Functions Ch. 2.10  
M 4/24 Geometrical Applications Ch. 2.13 Ch. 2.13 - Ex. 1,2
W 4/26 Geometrical Applications Ch. 2.13 Ch. 2.13 - Ex. 10,11,12
F 4/28 First Midterm    
M 5/01 Partial Derivatives of Higher Order   Ch. 2.15 Ch. 2.18 - Ex. 1,2
W 5/03 Cancelled    
F 5/05 Cancelled    
M 5/08 Local Maxima and Minima Ch. 2.19 Ch. 2.21 - Ex. 1,4
W 5/10 Lagrange Multipliers Ch. 2.20 Ch. 2.21 - Ex. 6 (a,b,c) , 8 (a,b)
F 5/12 Definite Integral Ch. 4.1 Ch. 4.1 - Ex. 1,2,3
M 5/15 Double Integral Ch. 4.3 Ch. 4.5 - Ex. 2
W 5/17 Change of Variables in Integrals Ch. 4.6 Ch. 4.6 - Ex. 1,4
F 5/19 Triple Integrals Ch. 4.4 Ch. 4.5 - Ex. 4
M 5/22 Arc Length Ch. 4.7 Ch. 4.7 - Ex. 1
W 5/24 Surface Area Ch. 4.7 Ch. 4.7 - Ex. 2 (a)
R 5/25 Review    
F 5/26 Second Midterm    
M 5/29 Memorial Day    
W 5/31 Line Integrals in the Plane Ch. 5.1-2 Ch. 5.3 - Ex. 1,2,3
F 6/02 Line Integrals as Integrals of Vectors Ch. 5.3-4 Ch. 5.3 - Ex. 4
M 6/05 Green's Theorem Ch. 5.5 Ch. 5.5 - Ex. 1,5
W 6/07 Independence of Path Ch. 5.6  
F 6/09 Review    







Department of Mathematics, South Hall. Room 6607 University of California Santa Barbara, CA 93016, phone (805) 893-2171, fax (805) 893-2385, 
email www.ucsb.edu, office hours m-f 8-12, 1-4