Math 251:M1, M-Th, 10:30am -12:25pm, ARC-108 (BUS), Summer  2026

                                                     Syllabus and General Information

 


Lecture Date Topic(s) and text sections Suggested Practice Problems
1 6/22 12.1 3D coordinate systems
12.2 Vectors in 2D and 3D		 12.1/ #3,9,15,16,21,23,39,59
12.2/ #9,19,23,25,31,41,47
2 6/23 12.3 Dot Product and the Angle Between Two Vectors
12.4 The Cross Product		 12.3/ #3,13,18,19,22
12.4/ #7,15,21,23,27,33,35,45
3 6/24 12.5 Planes in Three-Space
12.6 Cylinders and Quadric Surfaces		 12.5/ #6,6,9,23,27,31,37,41, 47, 57
12.6/ #1-12, 13, 15, 21, 25
4 6/25 13.1 Curves in Space and Their Tangents
13.2 Calculus of Vector-Valued Functions
 13.1/ #1,15,19,23, 31
13.2/ #3,5,8,11,15,19
5 6/29 13.3 Arc Length and Speed
Quiz 1
 13.3/ #5,9,13,15
6 6/30 14.1 Functions of Two or More Variables
14.2 Limits and Continuity in Several Variables 		 14.1/ #6,6,9,15-18,27,31,41,58,59
14.2/ #11,15,20-22,31,47,48,53,59
7 7/01 14.3 Partial Derivatives 
14.3/ #9,14-18,27,3046,67
8 7/02 14.4 The Chain Rule
14.4/ #7,28,29,33,39,44
9 7/06 14.5 The Gradient and Directional Derivatives
Quiz 2		 14.5/ #3-6,9,10,21,28,29,31
10 7/07  14.6 Tangent Planes and Differentials
 14.6/ #5,9,13,19,21,31
11 7/08  14.7 Optimization in Several Variables 14.7/ #13,19,29,33,35,43,45,62
12 7/09 14.8 Lagrange Multipliers Review for Exam 1 14.8/ #1,5,9,13,17,21,29
13 7/13 Exam 1  (80 min) on material covered in Lectures 1- 6
 15.1/ #7,11,13,18,23,27,29,36
14 7/14 15.1 Double Integrals 15.1/ #7,11,13,18,23,27,29,36
15 7/15 15.2 Double Integrals over  General Regions 15.2/ #1-8,12,15,18,23,29,35,38,43,53
16 7/16 15.3 Area by Double Integration
15.4  Integration in Polar Coordinates  Quiz 3
 15.3/ #6-8,16,18,21
17 7/20 15.4 Integration in Polar Coordinates 
 15.4/ #1-6,9,11,16,23,25,28,35
18 7/21   15.5 Triple Integrals in Rectangular Coordinates
 15.5/ #3,6,17,21,27,28,37,45
19 7/22 15.7 Triple Integrals in Cylindrical and Spherical Coordinates 15.7/ #3-7,13-17,25,31,38,47,59,65
20 7/23 15.8 Change of Variables in Multiple Integrals
Review for Exam 2		 15.8/ #1,3,6,7,9
21 7/27 Exam 2  (80 min) on material covered in Lectures 7 - 17
start 16.1		  
22 7/28 16.1 Line Integrals of Scalar Functions
16.2 Vector Fields & Line Integrals: Work, Circulation, Flux
 16.1/ #1-9,14,15,25,26,29,35,36
16.2/ #3,7,11,14,15,18,25,27,29,30,35,39,40,57,59
23 7/29 16.3 Conservative Vector Fields, Path Independence 16.3/ #3,5,9,11,19,22,25,29,31
24 7/30 16.4 Green's Theorem in the Plane 

16.4/ #2,5,9,13,16,17,21,29,31,37
25 8/03 16.5 Surface and Area 
 16.5/ #1,7,11,13,15,27,41,43
26 8/04  16.6 Surface Integrals
 16.6/#3,5,6,17,23,26,28,43
27 8/05 16.7 Stokes' Theorem.  Quiz 4
 16.7/ #5,7,11,19,23,28
28 8/06 16.8 The Divergence Theorem 16.8/ #9,11,13,15,27,28
29 8/10 Catch-up and Review for the Final  Exam  
30 8/11 Review for the Final  Exam  
31 8/12 Final exam : TBA