COURSE 551
Vector Calculus.
Textbook: Vector Calculus , (second edition), Thomas H.Bar
Instructor: Prof. Dan Burghelea
Office MW752
Tel 614-292-5259
email burghele@math.ohio-state.edu
Office hours: MW 2 PM- 3.25 PM
Grader: Bora Bosna
Office: MW 350
email: bosna@math.ohio-state.edu
Phone: 614-292-7045
About the course:
1.The course is designed to enable students to understand and use the techniques
of vector analysis in 2 and 3-dimensional space. Applications to the geometry of
curves and surfaces will be emphasized
Grading policy: Two midterms, one final
Home work will be assigned, graded and taken in consideration for the final
grade.
Syllabus: Topics from the book.
Chapter 1 Review of vectors (dot product and cross product ), lines and planes
, vector valued functions , derivatives (precisely sections 1.5-to 1.10) This will be
done the first two weeks.
Chapter 4 (sections 4.1, 4.2) Gradient Divergence and curl (next two weeks)
Chapter 5 Arc length, line integrals, surface area, Integral on surfaces. Chapter
6 Conservative vector fields , Green’s Theorem , Divergence Theorem , Stokes
Theorem. (next six weeks)
The material will possibly be complemented by additional discussions of spherical
and cylindrical coordinates from other books (for example Section 3.10 from Vector
analysis Davis/Snyder)
Syllabus in details with the home assignments. (it is not complete and will be
updated every two weeks. The students are supposed to consult it regularly).
While all the problems are highly recommended only those boxed are supposed
to be given for grading
Chapter I
March 30- April 3, Chapter 1 sections 1.5- 1.8
Home assignment
section 1.5
4, 8, 12 , 14 18 19 20 23 25 30.
section 1.6
section 1.7
section 1.8
2, 7, 14, 15 , 21, 26, 28.
7, 16, 22 , 8, 13, 14, 15, 17, 30, 32, 33, 36, 37.
1, 3, 5, 8, 9, 13 , 17, 19, 23, 29, 31.
April 6- April 10, Chapter 1, sections 1.9-1.10
Home assignment
1
2
section 1.8
1, 3, 5, 8, 9, 13, 17, 19, 23, 29, 31, 34
section 1.9
3, 6, 7, 10, 16, 17, 26, 28, 29, 31, 34
section1.10
2, 4, 8, 10, 14, 34, 39 23, 24, 29, 30, 32, 37, 40
April 13- April 17, Chapter 4 section 4.1 and 4.2
Home assignment
section 4.1
6, 14,17, 25, 26, 29, 50, 52, 56, 5, 9, 21, 24, 37, 40, 46, 55
Home assignment
section 4.2
2, 10, 20, 21, 22, 26, 6, 18, 23, 24, 28
April 22 Midterm 1
April 20- April 25, Chapter 5 sections 5.1- 5.3
Home assignment
section 5.1
4, 10, 13, 21, 16, 9, 22
Home assignment
section 5.2
3, 5, 9, 13, 21, 22, 24, 28, 31, 7, 11, 17, 19, 26, 29
Home assignment
Section 5.3
2, 4, 12, 14, 17, 21, 24, 26, 34, 39, 43, 46, 48, 50, 52, 20, 23, 29, 36, 42, 52, 54, 56
April 28- May 1, Chapter 5 sections 5.3- 5.6
Home assignment
Section 5.4
5, 8, 11, 18, 19, 23, 24, 3o, 31, 33, 10, 14, 20, 27
Section 5.5
1, 4, 8, 12, 20, 23, 24, 278, 32, 34, 35, 40, 41, 10, 14, 29, 31, 37, 42
May 4-May 8, sections 5.6- 5.8 , Chapter 6 Section 6.1
Home assignment
Section 5.6
1, 3, 12, 16, 17, 19, 21, 27, 29, 9, 14, 23, 25,
Section 5.7
1, 3, 5, 8, 14, 22, 28, 15, 18, 23, 26
Section 5.8
2, 3, 5, 8, 10, 11, 15, 20, 21. 1, 7, 13, 17, 19
May 11- May 15, Chapter 6, section 6.1, 6.2
Home assignment
Section 6.1
2, 4, 6, 15, 16, 20, 22, 24, 10, 13, 30, 31, 35
Section 6.2
1, 3, 10, 12, 16, 18, 5, 7, 8, 9, 14
May 18- May 22, sections 6.3- 6.4
Home assignment
Section 6.3
, 2, 4, 7, 19, 22, 8, 13, 16, 21
Section 6.4
, 1, 2, 4, 6, 7, 8, 10
May 26 (second midterm)
May 25- May 29 Revue
Home assignment
June 1- June 5. Review
Home assignment
Final Exam Thu June 11 3:30 pm - 5:18 pm