Multivariable Calculus 01:640:251, Sections 09 and 10, Spring 2010

Instructor: Roderich Tumulka
Phone: 732-445-2390 x 1322
Office: Hill 522
Email: instructor's last name, then @, then math.rutgers.edu

Teaching assistant: Sheena Cho

Grades

Out of 56 people who originally enrolled in sections 09 and 10, 46 took the final exam and reached an average of 63.8%. Distribution of results:
range90-100%80-89%70-79%60-69%50-59% 40-49%0-39%
frequency210313873

Final grades based on the semester average (40% homework quizzes and Maple labs, 15% first midterm exam, 15% second midterm exam, 30% final exam):
gradeAB+BC+CDF
range[87,100][80,87)[72,80)[64,72)[56,64)[47,56)[0,47)
frequency6779584

Textbook

Jon Rogawski: Calculus Early Transcendentals, W.H.Freeman, 2008, ISBN-10: 0-7167-7267-1. It has been augmented with some Rutgers "local matter," which is also available here.

Syllabus

(It is based on the standard syllabus for 251 recommended by the math department and gets continually modified a bit.)
Syllabus for 640:251
LectureTopic(s) and text sectionsHomework problems
112.1 Vectors in the Plane
12.2 Vectors in Three Dimensions		A1,A2
12.1: 5, 9, 11, 15, 21, 40, 47
12.2: 11, 13, 19, 25, 27, 31, 51
212.3 Dot Product and the Angle Between Two Vectors12.3: 1, 13, 21, 29, 31, 52, 57, 63
312.4 The Cross Product12.4: 1, 5, 13, 20, 25, 26, 43, 44
412.5 Planes in Three-Space
13.1 Vector-Valued Functions		12.5: 1, 9, 11, 15, 25, 31, 53
13.1: 5, 13, 15, 18
513.2 Calculus of Vector-Valued Functions
13.3 Arc Length and Speed 		13.2: 4, 14, 30, 31, 33, 41, 49
13.3: 3, 9, 13, 14
613.4 Curvature
13.5 Motion in Three-Space
13.6 Planetary Motion According to Kepler and Newton 		13.4: 1, 7, 17, 21
13.5: 3, 6, 32
13.6: 10, 14
714.1 Functions of Two or More Variables
14.2 Limits and Continuity in Several Variables
14.3 Partial Derivatives 		14.1: 7, 20, 23, 27, 36, 40
14.2: 5, 15, 27, 35
14.3: 3, 19, 21, 39, 47, 50, 53
814.4 Differentiability, Linear Approximation and Tangent Planes 14.4: 3, 4, 7, 15, 27, 33
9 14.5 The Gradient and Directional Derivatives
14.6 The Chain Rule		 14.5: 7, 13, 27, 31, 33, 37, 39, 43
14.6: 1, 5, 7, 17, 20, 23, 27, 30
Maple Lab 0 (instructions)
1014.7 Optimization in Several Variables 14.7: 1, 3, 7, 17, 19, 24, 25, 27, 29
11Exam 1 (Tue 2/23/2010, 10:20-11:40AM)
12cancelled because of snow
1314.7 Optimization in Several Variables 14.7: 1, 3, 7, 17, 19, 24, 25, 27, 29
1414.8 Lagrange Multipliers: Optimizing with a Constraint 14.8: 2, 7, 11, 13, 15
1515.1 Integration in Several Variables 15.1: 10, 15, 23, 25, 33, 37, 44
1615.2 Double Integrals over More General Regions 15.2: 3, 5, 11, 25, 32, 37, 43, 45, 49, 59
17 15.3 Triple Integrals 15.3: 3, 5, 11, 15, 17, 25, 33
18 12.7 Cylindrical and Spherical Coordinates
15.4 Integration in Polar, Cylindrical, and Spherical Coordinates		 12.7: 1, 5, 23
15.4: 1, 5, 9, 19, 23, 27, 31, 37, 39, 42
19
2015.5 Change of Variables 12.7: 31, 41, 43, 48, 53
15.4: 31, 37, 39, 42, 47, 51, 59
15.5: 1, 5, 14, 15, 21, 29, 33, 37
21Exam 2 (Tue 4/6/2010, 10:20-11:40AM)
2216.1 Vector Fields 16.1: 1, 3, 10, 17, 23, 27
23 16.2 Line Integrals 16.2: 3, 9, 13, 21, 27, 35, 39, 40
2416.3 Conservative Vector Fields 16.3: 1, 5, 9, 13, 17, 19, 21
2516.4 Parameterized Surfaces and Surface Integrals
16.5 Surface Integrals of Vector Fields		 16.4: 1, 5, 8, 11, 19, 21, 37
16.5: 1, 6, 9, 12, 15, 17, 23
2617.1 Green's Theorem 17.1: 1, 3, 6, 9, 12, 23, 27
2717.2 Stokes' Theorem 17.2: 1, 5, 9, 11, 19, 23
2817.3 Divergence Theorem 17.3: 1, 5, 7, 11, 14, 15, 18

Final exam: Wednesday May 12, 8:00-11:00am, in the usual room SEC-202

Participants who cannot attend a lecture or recitation class, or cannot hand in their homework in time are expected to contact me by email.
Maintained by R. Tumulka and last modified 14 May 2010