Math 251

Lecturer : Dr. Vladimir Shtelen

Office Hours: Hill Center, Room 203, Tuesdays & Fridays 10-11am

e-mail address: shtelen@math.rutgers.edu

web site: http://www.math.rutgers.edu/~shtelen

TA: Songhao Zhu, email: sz446@rutgers.edu

Textbook: Thomas' CALCULUS Early Transcendentals, 2023, 15th ed. by Joel Hass, Christopher Heil, and Maurice Weir. Pearson Education. ISBN: 978-0137559756

Grading (500 points): Midterm exams - 100 each, Final exam -150, Quizzes - 100, Homework (MyLab) - 40, Geogebra -5, Conceptual Problems -5

Lecture	Date	Topic(s) and text sections	Suggested Homework
1	9/06	12.1 Three Dimensional Coordinate Systems 12.2 Vectors	12.1/ #3,9,15,16,21,23,39,59 12.2/ #9,19,23,25,31,41,47
2	9/11	12.3 The Dot Product 12.4 The Cross Product	12.3/ #3,13,18,19,22 12.4/ #7,15,21,23,27,33,35,45
3	9/13	12.5 Lines and Planes in Space	12.5/ #6,6,9,23,27,31,37,41, 47, 57
4	9/18	12.6 Cylinders and Quadric Surfaces 13.1 Curves in Space and Their Tangents	12.6/ #1-12, 13, 15, 21, 25 13.1/ #1,15,19,23, 31
5	9/20	13.2 Integrals of Vector-Valued Functions, Projectile Motion	13.2/ #3,5,8,11,15,19
6	9/25	13.3 Arc Length in Space	13.3/ #5,9,13,15
7	9/27	14.1 Functions of Several Variables 14.2 Limits and Continuity in Higher Dimensions	14.1/ #6,6,9,15-18,27,31,41,58,59 14.2/ #11,15,20-22,31,47,48,53,59
8	10/02	14.3 Partial Derivatives 14.4 The Chain Rule	14.3/ #9,14-18,27,3046,67 14.4/ #7,28,29,33,39,44
9	10/04	14.5 Directional Derivatives and Gradient Vectors 14.6 Tangent Planes and Differentials	14.5/ #3-6,9,10,21,28,29,31 14.6/ #5,9,13,19,21,31
10	10/09	Catch up & Review
	10/09	Exam 1, 9:20pm - 10:40pm
11	10/11	14.7 Extreme Values and Saddle Points	14.7/ #13,19,29,33,35,43,45,62
12	10/16	14.8 Lagrange Multipliers	14.8/ #1,5,9,13,17,21,29
13	10/18	15.1 Double and Iterated Integrals Over Rectangles 15.2 Double Integrals over General Regions	15.1/ #7,11,13,18,23,27,29,36 15.2/ #1-8,12,15,18,23,29,35,38,43,53
14	10/23	15.3 Area by Double Integration 15.4 Double Integrals in Polar Form	15.3/ #6-8,16,18,21 15.4/ #1-6,9,11,16,23,25,28,35
15	10/25	15.5 Triple Integrals in Rectangular Coordinates	15.5/ #3,6,17,21,27,28,37,45
16	10/30	15.7 Triple Integrals in Cylindrical and Spherical Coordinates	15.7/ #3-7,13-17,25,31,38,47,59,65
17	11/01	15.8 Substitution in Multiple Integrals	15.8/ #1,3,6,7,9
18	11/06	16.1 Line Integrals of Scalar Functions	16.1/ #1-9,14,15,25,26,29,35,36
19	11/08	16.2 Vector Fields & Line Integrals: Work, Circulation, Flux	16.2/ #3,7,11,14,15,18,25,27,29,30,35,39,40,57,59
20	11/13	Catch up & Review
	11/13	Exam 2, 9:20pm - 10:40pm
21	11/15	16.3 Path Independence, Conservative Fields, Potentials	16.3/ #3,5,9,11,19,22,25,29,31
22	11/20	16.4 Green's Theorem in the Plane	16.4/ #2,5,9,13,16,17,21,29,31,37
23	11/27	Catch up & Review
24	11/29	16.5 Surfaces and Area	16.5/ #1,7,11,13,15,27,41,43
25	12/04	16.6 Surface Integrals	16.6/#3,5,6,17,23,26,28,43
26	12/06	16.7 Stokes' Theorem	16.7/ #5,7,11,19,23,28
27	12/11	16.8 The Divergence Theorem & A Unified Theory	16.8/ #9,11,13,15,27,28
28	12/13	Review for the Final Exam