# SYLLABUS

## Vector Analysis (Math 550, Section 1) Spring 2002, USC

Lecture
M W F 12:20-1:10 LC 401A
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
A grade of C or better in Math 241--familiarity with basics of vector algebra (dot products and cross products), partial derivatives, gradients, and multiple integrals.

Textbook
Vector Calculus, by Susan Colley, second edition.

Homeworks
There will be homework assignments due every Wednesday. Late homeworks will not be accepted.

Lecture and Reading Schedule
 Dates Lectures Jan 141618 MWF 1.11.21.3 Intro to vectorsIntro to vectorsDot products 212325 MWF .1.41.4 MLK dayCross ProductsCross Products 2830 MW 1.51.5 Equations for planesDistance problems Feb 1 F 1.5 Distance problems 468 MWF 3.13.13.1 Parametrized curvesParametrized curvesKepler's and Newton's Laws 111315 MWF 3.33.4. Vector fieldsDivergence and Curl Midterm 1 182022 MWF 3.23.25.1 Arc Length Arc LengthCavalieri's Principle 2527 MW 5.25.2 Double integralsDouble integrals Mar 1 F 5.3 Changing the order of int. 468 MWF 5.45.45.5 Triple IntegralsTriple IntegralsChange of Variables
 Mar 111315 MWF ... Spring BreakSpring BreakSpring Break 182022 MWF 5.65.66.1 Applications of integralsApplications of integralsScalar and Vector Line integrals 252729 MWF 6.1.. Scalar and Vector Line integralsReview Midterm 2 Apr 135 MWF .6.26.2 EasterGreen's theoremGreen's theorem 81012 MWF 6.36.37.1 Conservative vector fieldsConserative vector fieldsParametrized surfaces 151719 MWF 7.17.27.2 Parametrized surfacesSurface integralsSurface integrals 222426 MWF 7.37.37.3 Stokes's and Gauss's TheoremsStokes's and Gauss's TheoremsStokes's and Gauss's Theorems 29 M 7.4 Maxwell's equations May 1 W . Review 7 Tu . Final Exam (Comprehensive)

Assignments
 # Due Date Problems 1 Jan 23 1.2) 6--10, 13--18, 24, 25, 28, 1.3) 4, 6, 8, 9, 10, 11, 12, 14, 15, 16, 24, 25, 26. 2 Jan 30 1.3) 21; 1.4) 3, 6, 7, 9, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 31; 1.8) 18a, 19a, 20. 3 Feb 6 1.5) 1, 2, 3, 4, 5, 6, 7, 20, 21, 22, 23, 24, 25, 27, 28, 29; 1.8) 12, 15. 4 Feb 13 3.1) 3, 7, 8, 15, 16, 17, 20, 21, 22, 25, 26, 27, 28. 5 Feb 20 3.3) 1, 2, 3, 23; 3.4) 2, 3, 8, 14, 15, 16, 18, 23. 6 Feb 27 3.2) 1, 2, 3, 7, 8, 9, 10, 12; 5.1) 1, 2, 3, 4, 7, 10, 11. 7 Mar 6 5.2) 1, 2, 3, 4, 5, 12, 13, 15, 20, 21, 23, 26; 5.3) 1, 2, 5, 6, 8, 9, 11, 12, 14. 8 Mar 20 5.4) 1, 2, 5, 6, 8, 11, 14, 15; 5.5) 9, 13, 14, 15, 16, 21, 23, 24, 25, 28; 5.7) 19. 9 Mar 27 5.6) 3, 9, 14, 18; 5.7) 11, 12, 16a. 10 Apr 3 6.1) 1, 2, 6, 7, 11, 12, 16, 20, 21. 11 Apr 10 6.2) 1, 2, 5, 8, 10, 12, 13, 16, 17. 12 Apr 17 6.3) 1, 2, 3, 4, 7, 8, 14, 15, 19; 6.4) 1, 4, 22. 13 Apr 24 7.1) 1, 8, 10, 16, 18, 20; 7.2) 1, 7, 8, 9, 12, 13, 17, 18; 7.5) 4, 7. 14 May 1 7.3) 1, 2, 6, 7, 10, 11, 12, 15, 18, 20, 23.

Tests and Exams
There will be 2 midterms on Fridays Feb 15 and Mar 29. The Final Exam is on Tuesday, May 7 , 2-5 pm.