Math 250A, Calculus III

Course Outline

Spring 2017

Section: Math 250A-13, #19193Time: MW 1730-1920Room: MH-464Textbook: Stewart, James, Essential Calculus, EarlyTranscendentals, 2e (Custom 2013), ISBN: 978-1-285-10734-9

Instructor Information:name: Randy Scottoffice: MH-65

office phone: 657-278-7639 (Do NOT call; email!)email: rscott@fullerton.edu

office hours: M 1930-2100

Prerequisite: Math 150B with a grade of C or better.

Required Materials & Equipment: At each class meeting you should have (i) pencil (ii) paper (iii) calculator(graphing preferred). You will need to have the textbook in either paper or electronic form, but it is up toyou if you wish to carry it to class.

Evaluation:

Exams: We will have two midterm examinations: Wednesday, March 1, 2017 and Wednesday, April19, 2017. Makeup exams are given for only the most dire, objectively documented, situations.Final Exam: A comprehensive final exam will be given on Monday, May 15, 2017, during 1700-1850.Attendance at the final exam is mandatory; there will be no makeup final exams given.Quizzes: Based on the homework; given about once per week. There are NO make up quizzes forany reason. I will drop your lowest quiz score at the end of the semester.Homework: We will NOT be using WebAssign for homework in this class. You will be completingyour homework assignments with pencil on paper. Very retro. Assignments are to be completedbefore the next class meeting. Homework assignments will be collected on a random basis, with aone class-period notice. NO late homework collected for any reason.Attendance: Timely, consistent attendance is required and constitutes a small part of your coursegrade. You paid (or your parents’ paid, or, in the case of financial aid, the taxpayers’ paid) a lot ofmoney to take this course. Come to class everyday. Really. Everyday.Extra Credit: No extra credit will be given. Ever. Don’t embarrass yourself by asking. There areplenty of opportunities during the semester to earn your grade.

Grade Computation and Standards:

Your grade is computed using aweighted average of the mean ofthe percent scores for the assign-ments in each of the followingcategories:

Exams 50%Quizzes 15%

Homework 10%Attendance 5%Final Exam 20%

Your letter grade is assigned using the fol-lowing scheme. Let p = your total percent-age and l = your letter grade.

If p ≥ 99%, then l = A+If 99% > p ≥ 92%, then l = AIf 92% > p ≥ 90%, then l = A-If 90% > p ≥ 88%, then l = B+If 88% > p ≥ 82%, then l = BIf 82% > p ≥ 80%, then l = B-If 80% > p ≥ 78%, then l = C+If 78% > p ≥ 70%, then l = CIf 70% > p ≥ 60%, then l = D

If 60% > p, then l = F

Classroom Management: You paid a lot of money to take this class, and I expect you to behave assuch:

• Attend class each and every day.• Our class begins at 1730 and ends at 1920. I expect you to be on time and to stay for the entire class.• Please do NOT have your cell phone out for any reason during class. Turn your phone OFF before

1730. (If you have an emergency that requires you to be in contact with the outside world, pleasenotify me before class begins.)

• Please attend to any biological needs BEFORE 1730.

Math 250A, Calculus III Course Outline 2

• Please sit at the front of the classroom. I promise to maintain appropriate dental hygiene.

All of these expectations are intended to make you more successful in the class.

General Education Requirements: Math 250A does not meet any specific general education requirements.(You would have already met the mathematics requirement in a prerequisite course.) However, Math 250Awill satisfy the following general education learning goals:

1. To understand and appreciate the varied ways in which mathematics is used in problem-solving.2. To understand and appreciate the varied applications of mathematics to real world problems.3. To perform appropriate numerical calculations, with knowledge of the underlying mathematics, and

draw conclusions from the results.4. To demonstrate knowledge of fundamental mathematical concepts, symbols, and principles.5. To solve problems which require mathematical analysis and quantitative reasoning.6. To summarize and present mathematical information with graphs and other forms which enhance

comprehension.7. To utilize inductive and deductive mathematical reasoning skills in finding solutions, and be able to

explain how these skills were used.8. To explain the overall process and the particular steps by which a mathematical problem is solved.9. To demonstrate a sense of mastery and confidence in the ability to solve problems which require

mathematical concepts and quantitative reasoning.

Course Objectives & Learning Goals:

1. To understand and graph parametric curves and vector-valued functions in two and three-space, tounderstand and use the concepts of limits and continuity for vector-valued functions, and to be ableto find and interpret their derivatives. To understand the geometry of three-dimensional real space, oflines, planes, spheres and vectors.

2. To understand the concepts of, and to be able to calculate, the unit tangent, unit normal and unitbinormal vectors, as well as arc length and curvature for planar and space curves.

3. To grasp the concepts of the velocity and acceleration of a particle moving according to a giventrajectory described by a differentiable curve, to be able to integrate vector-valued functions, and toapply this knowledge to solve a variety of application problems.

4. To understand the concept of a function f(x,y) of two variables, to be able to determine the domainand range of f(x,y), and to successfully sketch wire frame diagrams of these functions in three-space.

5. To grasp the concepts of contour lines and level surfaces and to be able to sketch their graphs.6. To study and grasp the concepts of limits and continuity for f(x,y), and to be capable of calculating

a limit (if it exists) or showing that a limit does not exist.7. To understand the concept of a partial derivative and to be able to calculate and interpret partial

derivatives of multivariate functions.8. To know the equation of the tangent plane to the graph of a function f(x,y), and to know how to use

the function’s local linearization and differential to solve problems.9. To successfully apply the Chain Rule to take derivitives of multivariate composite functions.

10. To understand, calculate, and interpret directional derivatives and gradient vectors.11. To be able to categorize critical points for a function f(x,y) using the Second Derivative Test, to

effectively use the method of Lagrange Multipliers to find global extrema for functions of two andthree variables subject to a constraint, and to use this knowledge to solve application problems.

12. To understand the concept of a double Riemann Sum, to understand the theory of the double integraland its geometric interpretation, and to be able to calculate double integrals over rectangular regionsusing iterated integrals.

13. To be able to describe general regions in two-space with sets of inequalities, and to use these to set-up,evaluate and interpret double integrals as iterated integrals over general regions.

14. To successfully convert and evaluate double integrals in polar coordinates and to be able to tell whento use this method to evaluate double integrals.

15. To understand and evaluate triple integrals in rectangular, cylindrical, and spherical coordinate sys-tems, and to be able to calculate double and triple integrals using a change of variables.

Math 250A, Calculus III Course Outline 3

16. To grasp the concept of vector fields in two and three-space, and to understand the meaning of (andto be able to calculate) line integrals of a function of two or three variables along a curve with respectto arclength, and with respect to its input variables.

17. To be able to evaluate line integrals of vector fields along curves and to interpret the result, whereapplicable, as work.

18. To understand the Fundamental Theorem for Line Integrals, path independence, and the theoremsconcerning conservative vector fields.

19. To study curl and divergence of vector fields, oriented surfaces and flux, surface integrals of both scalarand vector fields, and to understand and effectively use Greens Theorem, Stokes Theorem, and theDivergence Theorem.

These goals are achieved through the course work, including homework, classroom activities, quizzes, ex-ams, and projects, which require the students to demonstrate understanding of the mathematical conceptspresented in the course and to apply these concepts to the solutions of real-world applications.

Academic Integrity: Cheating obtaining or attempting to obtain credit for work by the use of any dishonest,deceptive, fraudulent, or unauthorized means. Helping someone commit an act of academic dishonesty. (UPS300.021). Examples include, but are not limited to:

1. Unacceptable examination behavior communicating with fellow students, copying material from an-other students exam or allowing another student to copy from an exam, possessing or using unautho-rized materials, or any behavior that defeats the intent of an exam.

2. Plagiarism taking the work of another and offering it as ones own without giving credit to that source,whether that material is paraphrased or copied in verbatim or near-verbatim form.

3. Unauthorized collaboration on a project, homework or other assignment where an instructor expresslyforbids such collaboration.

4. Documentary falsification including forgery, altering of campus documents or records, tampering withgrading procedures, fabricating lab assignments, or altering medical excuses.

Students who violate university standards of academic integrity are subject to disciplinary sanctions, in-cluding failure in the course and suspension from the university. Since dishonesty in any form harms theindividual, other students and the university, policies on academic integrity are strictly enforced. I ex-pect that you will familiarize yourself with the academic integrity guidelines found in the current studenthandbook.

Emergency Information: In the event of an emergency such as earthquake or fire:

• Take all your personal belongings and leave the classroom (or lab). Use the stairways located at theeast, west, or center of the building.

• Do not use the elevator. They may not be working once the alarm sounds.• Go to the lawn area towards Nutwood Avenue. Stay with class members for further instruction.• For additional information on exits, fire alarms and telephones, Building Evacuation Maps are

located near each elevator.

Anyone who may have difficulty evacuating the building, please see the instructor.

Student Disabilities: On the CSUF campus, the Office of Disabled Student Services (DSS) has been delegatedthe authority to certify disabilities and to prescribe specific accommodations for students with documenteddisabilities. DSS provides support services for students with mobility limitations, leaning disabilities, hear-ing or visual impairments, and other disabilities. Counselors are available to help students plan a CSUFexperience to meet their individual needs. If you require accommodations in this course for documentedspecial needs, contact the Disabled Student Services office, UH 101, (714) 278-3117.

Math 250A, Calculus III Course Outline 4

CSU, Fullerton, Spring 2017, Mr. ScottMath 250A, Intermediate CalculusText: Stewart, James Essential Calculus: Early Transcendentals, 2e (Custom 2013)ISBN: 978-1-285-10734-9

* adjacent to the problem number indicates that 21st Century technology is required.

Ch. 10 Vectors and the Geometry of SpaceSection Assignment10.1 Three-Dimensional Coordinate Systems 1, 2, 3, 4, 5, 6, 7a, 10, 11, 13, 15, 17b, 18, 21-29 odd10.2 Vectors 2, 3, 5, 9, 11, 13, 15, 17, 18, 21, 22, 23, 24, 25, 26,

29, 3310.3 The Dot Product 1, 3, 4, 6, 7, 9, 10, 11, 13, 15, 17, 19, 23, 29, 31, 32,

33, 37, 38, 39, 40, 4510.4 The Cross Product 1-7 odd, 9, 10, 11, 13, 15, 19, 27, 29, 32, 33, 35, 39,

40, 43, 5310.5 Equations of Lines and Planes 1, 2-5, 7, 9, 11, 15, 16, 17, 21, 22, 23, 25, 27, 29, 33,

41, 49, 5110.6 Cylinders and Quadratic Surfaces 1, 2, 3-8 (sketch in R3), 9, 11, 15, 17, 18, 19, 23, 25,

3010.7 Vector Functions and Space Curves 1, 3, 4, 5, 7, 9, 13, 15, 16, 23, 26*, 31*, 32*, 33, 37,

39-43 odd, 45, 49, 53, 59-63 odd, 67, 6810.8 Arc Length and Curvature 1, 3, 6*, 7, 9, 10, 11, 12, 13, 15, 17, 21, 24, 29, 39,

40, 41, 4310.9 Motion in Space: Velocity and Acceleration 1-5 odd, 7, 9, 11, 13, 14, 15, 29, 31, 33

Ch. 11 Partial DerivativesSection Assignment11.1 Functions of Several Variables 1, 3, 5, 7, 10, 11, 12, 15, 17, 18, 21, 25, 29, 31, 37*,

39*, 41-4611.2 Limits and Continuity 3-15 odd, 21, 22, 23, 29-3111.3 Partial Derivatives 1, 2, 3, 7, 9, 12, 13, 16, 17, 19, 20, 23, 29, 39-42, 45,

47, 49, 55, 57, 58, 62ac, 63, 69, 78ab11.4 Tangent Planes and Linear Approximations 1, 3, 5, 11, 13, 17, 20, 21, 23, 25, 29, 30, 3311.5 The Chain Rule 1, 3, 6, 7, 15, 17, 20, 21, 23, 25, 27, 29, 31, 34, 3511.6 Directional Derivatives and the Gradient Vector 1, 3, 6, 7, 9, 11, 15-18, 20, 23, 25, 31, 35, 3911.7 Maximum and Minimum Values 2, 3-13 odd, 17, 23, 25, 27, 39, 44, 4611.8 Lagrange Multipliers 3, 5, 6, 7, 13, 15, 17, 19, 21, 25

Ch. 12 Multiple IntegralsSection Assignment12.1 Double Integrals over Rectangles 1, 5, 7-9, 11-19 odd, 21-25 odd, 27, 28, 29, 33, 39, 4012.2 Double Integrals over General Regions 1-5 odd, 8, 9, 13, 14, 17, 19, 23, 27, 29, 33, 34, 37-41

odd, 43-47 odd12.3 Double Integrals in Polar Coordinates 1-4, 5, 6, 7-12, 13-19 odd, 21, 23, 25, 2612.4 Applications of Double Integrals 1, 2, 3, 7, 9, 13, 14, 1712.5 Triple Integrals 3-6, 7, 9, 11, 15, 16, 17, 19, 21*, 25, 26, 27, 31, 32,

33, 34, 39, 43*, 4912.6 Triple Integrals in Cylindrical Coordinates 1, 3, 5, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 19, 23, 25,

27, 29, 3012.7 Triple Integrals in Spherical Coordinates 1, 3, 5, 6, 7, 8, 9, 10, 11, 12, 14, 15, 16, 17, 18, 19,

20, 21, 23, 27, 30, 33, 35*, 37, 39Continued on next page

Math 250A, Calculus III Course Outline 5

12.8 Change of Variables in Multiple Integrals 1, 3, 5, 15, 17, 19, 23, 25

Ch. 13 Vector CalculusSection Assignment13.1 Vector Fields 1, 3, 5, 19*, 21, 23, 24, 3113.2 Line Integrals 1, 3, 5, 9, 13, 15, 17, 18, 19, 21, 22, 23*, 29*, 31, 39,

4313.3 The Fundamental Theorem for Line Integrals 3, 6, 7, 9, 11, 13, 14, 16, 17, 21, 22, 23*13.4 Green’s Theorem 1, 3, 7, 8, 11, 13, 14, 1713.5 Curl and Divergence 3-7 odd, 8, 9, 10, 11-15 odd, 1713.6 Parametric Surfaces and Their Areas 1-4, 5-9 odd, 11-14, 17, 19, 20, 21, 33, 35, 4313.7 Surface Integrals 5, 7, 9, 13, 17, 19, 21, 25, 27, 29, 41, 4213.8 Stokes’ Theorem 3, 5, 8, 11, 12, 1313.9 The Divergence Theorem 1-4, 7, 9, 13

Useful Websites:

http://www.wolframalpha.com/ Computes derivatives and integrals (and so much more!)

http://web.monroecc.edu/calcNSF/ Excellent Java-based Grapher.

http://mathinsight.org/ Source of many enlightening explanations.