MAT 272 Calculus III Spring 2001 MAT 272 2:40 3:30 MWTHF PSA 308 2:40 3:30 TH ECA 221 Professor: J. Rafael Pacheco Office: PSA 823 Office hours: T 8:40 9:30 a.m. and 1:40 2:30 p.m.; Th 9:40 10:30 a.m. or by appointment Web Page: http://math.la.asu.edu/ rpacheco Phone: (480)-965-3750 Prerequisite: MAT 270 271 (Calculus I and II) or equivalent. MAT242 or 342 (linear algebra) is a helpful pre- or co-requisite. Text: Stewart, J., Calculus, fourth edition. There are two versions of the book to choose from: the full version and the multi-variable version. Multi-variable Calculus, fourth edition, contains only the material for the third semester (MAT272). Either version is fine for this course. Note, however, that the chapter numbering between the full edition and the multi-variable edition differs by one, though the content is the same. The chapter numbers in the syllabus refer to the multi-variable version. Optional reference: A. Belmonte and P. Yasskin, Multivariable CalcLabs with Maple. This book describes a Maple package that you may find useful with this course. You are under no obligation to purchase it, however. We will cover the basics of Maple that you will need. Software: This course uses the Maple symbolic algebra package as an instructional tool. Course meetings: Attendance at all class meetings in their entirety is expected. If you cannot attend due to illness or other obligations, I appreciate being notified by email or telephone. Coverage: The course will cover the following topics: Vector geometry (chapter 13) Vector functions (chapter 14) Partial derivatives and applications (chapter 15) Multiple integrals and applications (chapter 16) Vector calculus, emphasizing Stokes, Green s and the divergence theorems (chapter 17) Test: (100 points ). There will be 4 in class exams. Quizzes and Homework: (100 points). No make up Quizzes will be given and late homework will not be accepted. Final Exam: (200 points). All sections of MAT272 will have a common final exam on Saturday, May 5 from 7:40 a.m. 9:30 a.m. The final exam schedule listed in the schedule of classes will be strictly followed. It is the policy of the Department of Mathematics that makeup exams will only be given for the following reasons: 1. Religious conflict (e.g., the student celebrates the Sabbath on Saturday). 2. The student has more than three exams scheduled on the day that includes the mathematics final. 3. There is a time conflict between a student s mathematics final and another final exam. 4. There is a last-minute personal or medical emergency. 1
Make-up exams: Make up exams will not be given. Permission to take an exam at a time other than the schedule one will be granted at the discretion of the instructor. Arrangements must be made before the date of the test. Unexcused absences from exams will result in a grade of zero. Grading and policies: Grades will be based on a combination of homework assignments, in-class exams, and a comprehensive final examination, as follows: 4 midterms (100 points each, total 400 points); homework (100 points); final exam (200 points). Floors for letter grades: A 90%, B 80%, C 70%, D 60%. Exam dates: There will be four midterm examinations, to be administered in class on the following dates. The approximate syllabus is given in the right-hand column. Monday, February 12 Chapters 13 14 Monday, March 12 Chapters 14 15 Monday, April 2 Chapter 16 Monday, April 30 Chapter 17 Comprehensive final exam Saturday, May 5, 7:40 9:30 a.m. Homework: Weekly homework will be given and due one week from the assigned date. Late homework will not be accepted unless prior arrangements are made with the instructor. Portions of computer lab assignments will be due by the end of class each day. Answers to selected homework problems will be available from my home-page or posted outside my office. Estimated workload: Multi-variable calculus is a demanding subject. You will be expected to complete homework assignments diligently and on time in order to keep up with the material. You should expect to spend 8 to 12 hours per week on this course, counting homework, computer labs and lectures. Course content, emphasis and lab use About the course content: You are expected to read the assigned sections of the text before the next class period. Even if you do not understand the details, reading the book ahead of time will make the lectures and computer labs more understandable. The Maple software package: We will use the Maple symbolic algebra package to explore some of the properties of vector calculus. Maple is intended only as a tool to aid understanding, not a means in itself. Previous computer programming experience is helpful but not necessary. We will cover the basics that you will need to know to use the software. The Maple software has been installed on all PC s, Macintosh and Unix computers in every campus computing site, including the Computer Commons, BA 386 and elsewhere. Student editions of Maple are available in the ASU bookstore for approximately $75 and a full edition is available for approximately $125 if you want to buy your own copy. However, you are under no obligation to purchase this software. A pentium-class computer with at least 16MB of memory is recommended. Computer lab availability: The mathematics computer laboratory in ECA 221 and ECA 225 will be open the following hours: Monday Thursday 6:30 10:00 p.m.; Saturday Sunday, 12:00 4:00 p.m. Mathematics Testing Center: Make-up examinations must be taken on your own time in the Mathematics Testing Center, PSA 21. You can take exams at any time during the indicated dates. You will need to bring a computer label and photo identification with you to the Testing Center. Suggestion for study: I encourage you to collaborate with other MAT 272 students, for example by forming a study group of members from class. Working on assigned problems and class attendance are essential to survival. I welcome your questions and your discussions outside of class, and hope that our work together will result in your developing both understanding and enthusiasm when it comes to calculus. 2
Notes: Deviations from the above and changes to the schedule below are at the discretion of the instructor. Topics: Chapter 13: Vectors and the Geometry of Space 13.1: Three-Dimensional Coordinate Systems 13.2: Vectors 13.3: The Dot Product 13.4: The Cross Product 13.5: Equations of Lines and Planes 13.6: Cylinders and Quadric Surfaces 13.7: Cylindrical and Spherical Coordinates Chapter 14: Vector Functions 14.1: Vector Functions and Space Curves 14.2: Derivates and Integrals of Vector Functions 14.3: Arc Length and Curvature 14.4: Motion in Space: Velocity and Acceleration Chapter 15 Partial Derivatives 15.1: Functions of Several Variables 15.2: Limits and Continuity 15.3: Partial Derivatives 15.4: Tangent Planes and Linear Approximations 15.5: The Chain Rule 15.6: Directional Derivatives and the Gradient Vector 15.7: Maximum and Minimum Values 15.8: Lagrange Multipliers Chapter 16 Multiple Integrals 16.1: Double Integrals over Rectangles 16.2: Iterated Integrals 16.3: Double Integrals over General Regions 16.4: Double Integrals in Polar Coordinates 16.5: Applications of Double Integrals 16.6: Surface Area 16.7: Triple Integrals 16.8: Triple Integrals in Cylindrical and Spherical Coordinates 16.9: Change of Variables in Multiple Integrals Chapter 17 Vector Calculus 17.1: Vector Fields 17.2: Line Integrals 17.3: The Fundamental Theorem for Line Integrals 17.4: Green s Theorem 17.5: Curl and Divergence 17.6: Parametric Surfaces and Their Areas 17.7: Surface Integrals and Their Areas 17.8: Stokes Theorem 17.9: The Divergence Theorem 3
MAT 272 Homework Assignments Lecture #1, Introduction to 3D Cartesian Coordinates. 13.1: 2-4,7-9,10af,11,14,15,18,20. (Use results of problem 19 for 20),21,25,29,30,32,33,39 Lecture #2, Vectors 13.2: 1-3,5,7,11,12,13,16,17-21,23,24,26,27,29,31-34 Lecture #3, Dot Product 13.3: 1,3,6-10,16,17,20,24,25,27-29,32,35,40,43,48,51,52,55,56 Lecture #4, Cross Product 13.4: 1,2,5,6,9,12,14,15,20,23,26,29,33. Additional: Show (A cross B) dot C = A dot (B cross C) Lecture #5, Planes 13.5: 20,21,24,28,29,41,42,45,46,53,61-64. Plus, graph using traces and intercepts: 1. 3x + 2y + 6z = 12 2. 4x y + 6z = 18 3. 5x + 2y = 20 4. 2x + 4z = 8 Lecture #6, Lines 13.5: 1,2,3,7,8 (Parametric only on 7,8),11,12,17,30,31,37,38,49,50,54,55 Lecture #7, Review of conics. Lecture #8, Quadric surfaces 13.6: 3,4,7-11,13,15-18,20,21-28,31,32 Lecture #9, Vector functions, derivatives, integrals 14.1: 1,7,9,12,14,17,29 14.2: 3,4,7,9-11,14,15,18,19,24,25,34,35,39,40,44, 47 (Hint, use theorem 3 part 5) Lecture #10, Arc length, velocity, acceleration 14.3: 1,2,4 14.4: 3,5,6,9-12,15,16,21-23 Hint on 22: v 2 = V dotv Lecture #11, Functions of several variables 15.1: 1,6-8,12,13,16,17,23-26,30,35,38,40,41,45, 51-56,57,59,60 Lecture #12, Limits and continuity 15.2: 5,6,7,12,13,17,27,28,30,32 Lecture #13, Partial differentiation 15.3: 3,6,11,13,14,16,19,20,24,27,29,30,33,36,40 41,46,49,50,53,55,56,58,59,62,65,66cf,74,75 Lecture #14, Tangent planes, differentials 15.4: 1,2,4,5,11,14,23-33 (Just find the linearization on 11 and 14) Lecture #15, Chain rule 15.5:1,3,4,6,9-13,18,19,25,28,29,30,36-38,40 Lecture #16, Gradient and applications 15.6: 3,4,7,10,12,13,16,17,19,20 Lecture #17, Gradient and applications cont. 15.6: 21,22,23,26,29,30,37,39,40,42,45,51,52,57 Lecture #18, Optimization, D-test 15.7: 3,7,10,14,15,18,27,31,32,41,42,47,48 Lecture #19, Optimization, Lagrange Multipliers 15.8: 1,3,4,5,9,10,18,19,29,36 Lecture #20, Introduction to double integrals 16.1: 1ad,4,5,6,11-13 Hint on 6: Set up using mid points Lecture #21, Iterated integrals 16.2: 5-7,11,12,14-17,19,26,29,30a,33,34 4
Lecture #22, General regions 16.3: 2,3,5,6-9,11,14,16,19,20,25,27,33,35, 36,38,39,42,50 Lecture #23, Double integrals in polar coordinates 16.4: 1-10,19-23,27,28,32 Lecture #24, Triple integrals 16.7: 5,6,9,10,12,13,16,19,20,27,35,46 Lecture #25, Cylindrical and spherical coordinates 12.7: 7-10,16,17,20,21,25,26,29,31,32,35,36,37,40, 41,43,47,49,50,55,57,58,61 Lecture #26, Integrals in cylindrical and spherical 16.8: 1,3,5,6,8,10,11,13,18,21,22,27,29,33 Lecture #27, Parametric surfaces 16.6: 1-4,11-13,17,19-24,25,26 Try to find nice parameterizations. For 25 and 26, just find the parametric equations. Lecture #28, Parametric surfaces cont. 17.6: 29,30,34,36,37,40,41 17.7: 6,7,10,13,17,18,36 Lecture #29 (Optional), Change of variables 16.9: 1-4,7-13,19-21,23 Lecture #30, Vector fields 17.1: 1,3,5-18,21-24,29-32 Lectures #31,32 (two days), Line integrals 17.2 (Two days): 1-3,6,9,10,14,15,17,18,20-22, 31,32,37,38,41,42 Lecture #33 (Optional), Green s theorem 17.4: 1-4,7-15,17,18 Lectures #34, 35 (two days), Potential, path independence 17.3 (Two Days): 1-7,9-14,19-23 Lecture #36, Divergence and curl 17.5: 1-5,7,8,12-17,19-21,26 Lecture #37, Flux integrals 17.7: 19,20,23,25,27,28,39 Lecture #38, Stokes theorem 17.8: 1-3,5-10,13,19 Lecture #39, Divergence theorem 17.9: 1-4,8,10,11,14-16 References [1] Stewart, J., Multivariable Calculus, Brooks/Cole Publishing Co., Pacific Grove, CA, 1999. [2] Stewart, J., Calculus Fourth Edition, Brooks/Cole Publishing Co., Pacific Grove, CA, 1999. [3] Pacheco, J. R., MAT 272 Lecture Notes. Department of Mathematics, Arizona State University (2000). [4] Pacheco, J. R., Introduction to Maple. Department of Mathematics, Arizona State University (2000). 5