SM221X Multivariable Calculus with Infinite Series Syllabus. Spring Semester
2013-2014. Text: Stewart, Calculus: Early Transcendentals, 7th Edition. 1.
SM221X Multivariable Calculus with Infinite Series Syllabus Spring Semester 2013-2014 Text: Stewart, Calculus: Early Transcendentals, 7th Edition 1. Objectives: A. Set up and evaluate double integrals over general plane regions. B. Set up and evaluate triple integrals over general space regions. C. Apply coordinate systems appropriate to the symmetries of the problem at hand. D. Evaluate path integrals for vector fields in two and three dimensions. E. Evaluate flux integrals for vector fields in three dimensions. F. Apply the theorems of vector calculus. G. Distinguish convergent and divergent infinite sequences and series. H. Apply convergence tests to infinite sequences and series. I. Calculate power series expansions of single-variable functions and use them to analyze the given function. J. Find intervals of convergence for infinite power series. K. Review and consolidate skills from one-variable calculus. 2. Please visit http://www.usna.edu/MathDept/academics/index.php for current information about this course and others, including this syllabus, practice exams, etc. 3. If you would like help in the course, you should contact your instructor for extra instruction. Also try the Math Lab in CH130. It is staffed all six periods every class day with instructors who should be able to answer your questions. The Midshipman Group Study Program (MGSP) will be available evenings from Sunday through Thursday. Upper-class midshipmen will help you work on Calculus III in groups. More information will be available early in the semester; also see http://intranet.usna.edu/AcCenter/MGSP.htm 4. Mathematica, DPGraph, and other software programs are available for graphing in three dimensions. All students in this course are expected to have a calculator like the Voyage 200 which can graph and do symbolic calculations. There will be assignments and questions on the final exam for which such a calculator will be essential. At the same time, performing simpler computations by hand is extremely important. There will be questions on the final exam for which using calculators is not allowed. More details on the final exam will be available later in the semester. 5. Your instructor may modify the schedule and list of problems listed. # 1 2 3 4 5 6 7 8 9 10 11 12 13
Section 10.3 15.4 15.5 15.7 15.7 15.7 15.8 15.8 15.9 15.9
16.1
Topics Polar Coordinates Polar Double Integrals Applications Triple Integrals Triple Integrals Triple Integrals Cylindrical Coordinates Cylindrical Coordinates Spherical Coordinates Spherical Coordinates Review Exam on Chapter 15 Vector Fields
Homework p662 1-12,15-18,21,23,25 p1002 1-6,7-13 odd, 29,31,35 p1012 3-13 odd p1025 5-13 odd p1025: 15-21 odd p1025: 12-18 even p1031: 3-10,17,19 p1031: 21-29 odd p1037: 3-10, 15,16,19,20,21 p1037: 23-29 odd,39,42
p1061: 7-14,21,23,29-32
14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48
16.2 16.2 16.3 16.3 16.4 16.4 16.5
16.6 16.6 16.7 16.7 16.8 16.8 16.9 16.9
11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.7 11.8 11.9 11.10 11.10
Line Integrals Line Integrals Fundamental Theorem Fundamental Theorem Green’s Theorem Green’s Theorem Curl & Divergence Review Exam Parametric Surfaces Parametric Surfaces Flux Integrals Flux Integrals Stokes’ Theorem Stokes’ Theorem Divergence Theorem Divergence Theorem Review Exam on Chapter 16 Sequences Series Integral test Comparison test Alternating series Ratio and root tests Strategy More strategy Power series Power series representations Taylor and Maclaurin series Taylor and Maclaurin series Review Exam on Chapter 11 Review Review
p1072: 5,7,13,15 p1072: 17,18,19,21,39,45 p1082: 1,2,3-11 odd p1082: 13-19 odd, 21,22,23,25,26 p1089: 5-9 odd p1089 11,13,17,19,22 p1097 1-7 odd,9-13,15
p1108 p1108 p1121 p1121 p1127 p1127 p1133 p1133
13-18,19-25 odd 39-47 odd 21-25 odd 27-31 odd 1,3,5,6 7,9,11,16 5,7,9 11-17 odd
p700: p711: p720: p726: p731: p737: p740: p740: p745: p751: p765: P765:
3-11 odd, 23-35 odd 5,7,15,16,17-25 odd,31,33,67 1-7 odd, 11, 15, 17, 21 1,2,3-19 odd 1-11 odd 1-13 odd 1-11 odd 13-21 odd 3-15 odd 1,2,3-13 odd 5-19 odd, 29-37 odd 6-20 even, 47-53 odd
Course coordinator: Prof. W. D. Withers
[email protected]
