Math 251:12-14, TTh, 2pm-3:20pm, TIL-116,  Fall 2023

                                 Syllabus and General Information    

• 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: Scott James,  Email: sjj70@scarletmail.rutgers.edu
• Departmental web page for Math 251
• 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	9/05	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	9/07	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	9/12	12.5 Lines and Planes in Space	12.5/ #6,6,9,23,27,31,37,41, 47, 57
  4	9/14	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	9/19	13.2 Integrals of Vector-Valued Functions, Projectile Motion	13.2/ #3,5,8,11,15,19
  6	9/21	13.3 Arc Length in Space	13.3/ #5,9,13,15
  7	9/26	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	9/28	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	10/03	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	10/05	Catch up & Review
  	10/09	Exam 1, 9:20pm - 10:40pm
  11	10/10	14.7 Extreme Values and Saddle Points	14.7/ #13,19,29,33,35,43,45,62
  12	10/12	14.8 Lagrange Multipliers	14.8/ #1,5,9,13,17,21,29
  13	10/17	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	10/19	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	10/24	15.5 Triple Integrals in Rectangular Coordinates	15.5/ #3,6,17,21,27,28,37,45
  16	10/26	15.7 Triple Integrals in Cylindrical and Spherical Coordinates	15.7/ #3-7,13-17,25,31,38,47,59,65
  17	10/31	15.8 Substitution in Multiple Integrals	15.8/ #1,3,6,7,9
  18	11/02	16.1 Line Integrals of Scalar Functions	16.1/ #1-9,14,15,25,26,29,35,36
  19	11/07	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	11/09	Catch up & Review
  	11/13	Exam 2, 9:20pm - 10:40pm
  21	11/14	16.3 Path Independence, Conservative Fields, Potentials	16.3/ #3,5,9,11,19,22,25,29,31
  22	11/16	16.4 Green's Theorem in the Plane	16.4/ #2,5,9,13,16,17,21,29,31,37
  23	11/21	Catch up & Review
  24	11/28	16.5 Surfaces and Area	16.5/ #1,7,11,13,15,27,41,43
  25	11/30	16.6 Surface Integrals	16.6/#3,5,6,17,23,26,28,43
  26	12/05	16.7 Stokes' Theorem	16.7/ #5,7,11,19,23,28
  27	12/07	16.8 The Divergence Theorem & A Unified Theory	16.8/ #9,11,13,15,27,28
  28	12/12	Review for the Final Exam