Mathematics 32A Lecture 1 Welcome to Mathematics 32A differential calculus in 3D For calculus in more than one variable you need vectors The first part of the course is devoted to vectors Chapter 13 in Rogawaki Multivariable Calculus Then we discuss vector valued functions Chapter 14 and functions of a vector variable Chapter 15 The format of the course will be fairly standard three lectures and one discussion section per week and daily homework assignments from Rogawski s textbook This homework will not be handed in but you can check your answers against those in the back of the book In addition to the homework from the textbook there will be weekly online assignments using Webwork How to use WebWork will be explained in more detail elsewhere There will be two midterms in the course and a final exam on the dates given in the Syllabus that follows There is the inevitable question What happens if I miss an hour exam There are no make ups for missed hour exams but your scores on the other hour exam and the final will be re scaled to partially offset the missed hour exam All exams are closed book i e no notes calculators or cell phones Grading Policy Your grade in the course is determined by the sum of your scores on the final the two hour exams and the WebWork assignments weighted 50 30 and 20 respectively If you get 80 of the possible points you are guaranteed an A or A If you get 50 of the possible points you are guaranteed a C However if necessary I will move the A B line down until 25 of the class gets A or A Likewise if necessary I will move the C C line down until only 15 of the class gets grades below C The median grade in this class is usually B Figuring out this policy and its implications is the first exercise in the course Syllabus and Exercises The exercises listed in the syllabus below are not to be handed in You should certainly do them and as many more of the exercises in Rogawski s text as you have time for It is a good idea to keep the exercises you do in a notebook The problems on the quizzes will be closely related in the eyes of the instructor to the problems listed below The references to Sections refer to the sub chapters of the textbook The quizzes are given in the weeks beginning with Quiz X this week and will usually be based on the homework from the preceding week Syllabus Sept 28 Vectors 13 1 Exercises 5 13 15 21 23 31 35 39 47 55 Oct 1 3D Vectors 13 2 Exercises 3 7 13 27 33 37 41 47 53 61 Oct 3 Dot Product and Angles 13 3 Exercises 11 21 27 33 47 53 65 71 Oct 5 Cross Product 13 4 Exercises 9 11 21 27 33 Oct 8 Planes 13 5 Exercises 5 11 15 17 27 31 33 51 55 59 Oct 10 Vector valued Functions 14 1 Exercises 7 9 17 21 29 31 39 41 Oct 12 Parametric Curves 12 1 Exercises 11 13 19 27 34 43 45 49 53 63 2 Oct 15 Vector valued Functions 14 2 Exercises 19 21 25 31 49 57 63 Oct 17 Arc Length and Speed 14 3 Exercises 3 13 15 17 29 31 Oct 19 Curvature and Motion in 3D 14 4 Exercises 13 23 25 33 14 5 Exercises 17 23 27 29 39 57 Oct 22 Hour Exam I Oct 24 More Variables 15 1 Exercises 7 17 19 23 39 Oct 26 Quadrics 13 6 Exercises 5 15 17 23 33 39 Oct 29 Limits and Continuity 15 2 Exercises 15 17 31 33 37 Oct 31 Partial Derivatives 15 3 Exercises 3 7 11 33 43 49 53 63 Nov 2 Partial Derivatives continued Nov 5 Tangent Planes Linearization and Differentiability 15 4 Exercises 3 9 11 12 Nov 7 15 4 continued Exercises 19 27 31 Nov 9 15 4 continued again Exercises 35 43 45 Nov 12 Veterans Day Holiday Nov 14 Gradient and Directional Derivative 15 5 Exercises 2 3 17 25 59 Nov 16 Chain Rule 15 6 Exercises 3 5 17 19 21 Nov 19 Hour Exam II Nov 21 Chain Rule continued 15 6 Exercises 5 29 31 45 46 Nov 23 Thanksgiving Holiday Nov 26 Optimization 15 7 Exercises 3 5 7 11 19 23 25 31 37 49 Nov 28 Optimization continued Nov 30 Lagrange Multipliers 15 8 Exercises 5 7 11 17 19 25 33 35 45 Dec 3 Lagrange Multipliers continued Dec 5 Review of Course Dec 7 More Review of Course Final Examination Friday December 14 11 30 2 30