# SYLLABUS

## Vector Analysis (Math 550, Section 1) Fall 2001, USC

Lecture
M W F 10:10-11:20 LC 401
Instructor
Check the course web site periodically to obtain revised versions of this syllabus, homework assignments, and copies of old tests.

Course Description
We study calculus of vector valued functions. Main topics include parametrized curves and surfaces, change of variables formula and Jacobians, line and path integrals, surface integrals, theorems of Green, Gauss, Stokes, and various applications to problems in Physics, Engineering, and Geometry.

Prerequisites
Math 241--familiarity with basics of vector algebra (dot products and cross products), partial derivatives, gradients, and multiple integrals.

Textbook
Vector Calculus, by Jerrold E. Marsden and Anthony J. Tromba, fourth edition.

Homework and Quizzes
There will be homework assignments due every Wednesday. Late homeworks will not be accepted.

 Dates Lectures Aug 24 F 1.1 Intro. to vector geometry 272931 MWF 1.21.2,1.31.3 Dot products, lengthPractice Quiz 1Cross products Sep 357 MWF ..2.4, 4.1 Labor Day-no classesPractice Quiz 2Intro to space curves 101214 MWF 4.1.. ParametrizationsReview Exam 1 171921 MWF 4.14.24.3 Velocity and accelerationArc-length, Practice Quiz 3Vector fields 242628 MWF 4.3.4.3 Vector FieldsPractice Quiz 4Vector Fields Oct 135 MWF 4.44.45.1 Curl and Divergence Curl and DivergenceIntro. to Volumes, Cavalieri's principle 81012 MWF 5.25.3. Double integrals over rectanglesDouble integrals over general domains Exam 2 151719 MWF .5.61.4 Fall Break-no classesTriple IntegralsSpherical and Cylindrical Coordinates
 Oct 222426 MWF 6.1,6.26.36.3 Change of Variables in IntegralsApplicationsApplications 2931 MW 7.17.2 Path IntegralsLine Integrals Nov 2 F 7.2,7.3 Line Integrals, Parametrized Surfaces 579 MWF 7.37.4. Parametrized SurfacesArea of SurfacesExam 3 121416 MWF 7.57.68.1 Integral of scalars on surfacesInegral of vectors on surfacesGreen's Theorem 192123 MWF 8.2.. Stokes TheoremThanksgiving-no classesThanksgiving-no classes 262830 MWF 8.38.48.4 Conservative FieldsGauss' TheoremGauss' Theorem Dec 357 MWF 8.58.5. ApplicationsApplicationsReview 14 F . Final Exam
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Assignments
 Homework # Due Date Problems 1 Aug 29 1.1) 6, 8, 11, 13, 16, 17, 23, 24, 26. 2 Sep 5 1.2) 2, 14, 17, 19, 22; Practice Quiz 1. 1.3) 4, 6, 16. 3 Sep 12 1.3) 17, 20, 24, 31; First 4 problems in Practice Quiz 2. 4 Sep 19 2.4) 2, 10, 14, 16, 18; 4.1) 6, 14, 18, 20, 21. 5 Sep 26 4.2) 1, 10, 11, 12, 13; All problems in Practice Quiz 3. 6 Oct 3 4.3) 2, 4, 8, 11, 15, 17; All problems in Practice Quiz 4. 7 Oct 10 4.4) 10, 13, 26, 30; p. 290) 7, 8. 8 Oct 17 5.1) 3, 4, 5, 6; 5.2) 1c, 2c, 5, 6; 5.3) 1c, 2a, 3, 8, 11, 12. 9 Oct 24 5.6) 4, 5, 10, 19; 1.4) 1b, 4, 9. 10 Oct 31 6.2) 1, 3a, 9, 13, 21, 29; 6.3) 2, 4, 9, 10; 6.4) 12; p.394) 21. 11 Nov 7 7.1) 2c, 3b, 9, 11, 12; 7.2) 1b, 2a, 3, 4, 10, 14, 17. 12 Nov 14 7.3) 2, 5, 11, 12; 7.4) 3, 4, 6, 7, 11, 14, 16. 13 Nov 19 7.5) 2, 4, 9, 10, 11; 14 Nov 28 7.6) 2, 3, 4, 15, 16; 8.1) 2, 3a, 4, 12, 13, 20. 15 Dec 5 8.2) 2, 3, 7, 8, 17, 19; 8.3) 1, 4, 5, 6, 7, 12.

Tests and Exams
There will be 3 midterms on Fridays Sep 14, Oct 12, and Nov 9. The Final Exam is on Friday, December 14 , 9-12 am.