MAT 211 Calculus III, Section 81, CN 45112 Fall 2021

Class meets MWF 1:00 PM - 2:25 PM, in SAC 3136

Instructor: Serban Raianu, office: NSM E-108, office phone: (310) 243-3139, cell phone (657) 204-5612

office hours: (via zoom, the zoom meeting information will be announced on Blackboard)

Monday, Wednesday: 8:20 AM – 9:50 AM, Friday: 11:30 AM – 12:30 PM, or by appointment.

Course Description: MAT 211, Calculus III, covers from the textbooks:

Multivariable calculus: analytic geometry, scalar and vector products, partial differentiation, multiple integration, change of coordinates, gradient, optimization, line integrals, Green's theorem, elements of vector calculus.

Text: CLP-3 Multivariable Calculus and CLP-4 Vector Calculus, by Joel Feldman, Andrew Rechnitzer, Elyse Yeager, available online at http://www.math.ubc.ca/~CLP/

Objectives: After completing MAT 211 the student should be able to:

• Gain an intuitive understanding of functions of several variables via level curves and surfaces, and related concepts of limit, continuity and differentiability.
• Perform partial differentiation and multiple integration of functions of several variables.
• Change from Cartesian co-ordinates to polar, cylindrical or spherical co-ordinates and vice versa, perform differential (partial or ordinary) and integration (multiple or single) in curvilinear co-ordinate systems and effect transformation via the Jacobian.
• Utilize vectors to deal with spatial curves and surfaces, and calculus of several variables
• Understand and use the concepts of vector calculus: gradient, curl, divergence, line and surface integrals, Green's, Stokes' and the divergence theorem.

Prerequisites: MAT 193 or equivalent with a grade of "C" or better.

Grades: Grades will be based on two zoom video meetings 15-minutes examinations (50% total), a comprehensive final examination (20%), and quizzes, homework, video and other assignments (30%) for the remainder.

An oral examination will consist in giving a definition or a statement for a notion or result studied in class, and explaining two homework problems from the homework assignments. A list of the possible definitions and statements is posted on Blackboard. A definition or a statement will be chosen by selecting a random number from 1 to the number of definitions and statements on the list. The homework problems will be selected by choosing randomly the lecture number, then a problem number from 1 to the total number of problems in the assignment corresponding to that lecture. For example, the definition/statement number 5 will refer to the fifth item on the list of possible definitions or statements on the list. The homework problem (1,13) will refer to problem 9 in Section 1.3 in CLP-1: this is the 13th problem in the homework assignment for Lecture 1.1. Each of the two oral exams will be graded on a 100 scale, then the sum of the scores is divided by 4 and denoted by E.

Homework will be due every week, the day before quiz days, and each homework is worth 10 points. Each week one of the problems from the homework due for that week will be selected and graded on a scale from 0 to 4. The remaining 6 points will be awarded for completeness of the homework assignment. Submitting solutions copied from the back of the book is not forbidden but strongly discouraged, since copying solutions will not prepare you for answering questions during the oral examinations. The average of all homework scores is denoted by H. Homework will be submitted as a pdf with your paper work on Gradescope. There is no need to match the pages with the problems when submitting the homework, see

Gradescope can be accessed from the link in Content in your Blackboard course, and you can practice submitting your work on Gradescope using the assignment called Submission practice, which will remain open throughout the semester. You might be asked to explain your work on a submitted problem. Failure to provide an explanation might result in a score of zero for the entire homework assignment.

15 minutes quizzes will be given in principle every week, and will be graded on a scale from 1 to 10. The average of the quizzes scores is denoted by Q. Each quiz will consist of one problem, similar but not necessarily identical to one of the homework problems assigned for that week.

There are also 10 points awarded for explaining one homework problem on video. This portion of the grade is denoted by V. Videos will be due the day before quiz days and will have to be uploaded on Flipgrid

The homework problems from which to choose one problem to explain on video will be announced in class.

The final exam, which will consist of fifteen problems similar to problems assigned as homework throughout the semester, will be graded out of a maximum possible 200, then the score is divided by 10 and denoted by F.

To determine your final grade, compute E+H+Q+V+F. The maximum is 100, and the grade will be given by the rule:

A: 93‑100; A‑: 90‑92; B+: 87‑89; B: 83‑86; B‑: 80‑82

C+: 77‑79; C: 73‑76; C‑: 70‑72; D+: 67‑69; D: 60‑66; F: Less than 60. You will be able to follow your progress in the class in Blackboard under Grade Center throughout the semester.

Accommodations for Students with Disabilities: California State University, Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Student disAbility Resource Center (SdRC) and to talk with me about how I can best help you. All disclosures of disabilities will be kept strictly confidential. Please note: no accommodation may be made until you register with the SdRC in WH D-180. For information call (310) 243-3660 or to use telecommunications Device for the Deaf, call (310) 243-2028.

Academic Integrity: The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)

Technology: Symbolic calculators, such as TI-89, TI-92 or TI-nspire CAS are not acceptable for this course.

Tentative schedule and homework assignments

M 8/23:           Lecture 1.1: From CLP-3: 1.1 Points: 1,2,3; 1.2.1 Vectors, add, multiply by scalar: 1,2,16

(6 problems)

W 8/25:           Lecture 1.2: 1.2.2 Dot product: 3,6,7,21,22,23 (6 problems)

F 8/27:            Lecture 1.3: 1.2.5 Cross product: 8,9,10,26,27,28,29 (7 problems)

M 8/30:           Lecture 1.4: 1.3 Lines in 2d: 5,6,7; 1.4 Planes in 3d: 4,5,6,7,8; 1.5 Lines in 3d: 3,4,5,6,7

(13 problems)

W 9/1:             Lecture 1.5: 1.6 Curves and their tangent vectors: 10,11,12,13,14,15,16,17 (8 problems)

F 9/3:              Lecture 1.6: 1.7,1.8,1.9 Surfaces: 7,8,9,10,11 (5 problems)

M 9/6:             Labor Day

W 9/8:             Lecture 1.7: 2.1 Limits: 6,7,8,9,10,11 (6 problems)

F 9/10:            Lecture 1.8: 2.2 Partial derivatives: 3,4,5,6; 2.3 Higher order derivatives: 3,4,5 (7 problems)

M 9/13:           Lecture 1.9: 2.4 Chain rule: 1,4,5,6,7,8,9 (7 problems)

W 9/15:           Lecture 1.10: 2.5 Tangent planes and normal lines: 5,6,7,8,9,10,11,12,13 (9 problems)

F 9/17:            Lecture 1.11: 2.6 Linear approximation and error: 3,4,5,6,7 (5 problems)

M 9/20:           Lecture 1.12: 2.7 Directional derivatives and the gradient: 1,2,3,4,5,6,7  (7 problems)

W 9/22:           Lecture 1.13: 2.9 Maximum and minimum values: 4,5,6,15,16,17 (6 problems)

F 9/24:            Lecture 1.14: 2.10 Lagrange multipliers: 3,4,5,6,7,8 (6 problems)

M 9/27:           Lecture 1.15:  3.1 Double integrals: 1,2,3,4,5,6,7 (7 problems)

W 9/29:           Lecture 1.16: 3.2 Double integrals in polar coordinates: 1,2,3,4,5,6,7,8,9,10 (10 problems)

F 10/1:            Lecture 1.17: 3.3 Applications of double integrals: 2,3,4,5,6 (5  problems)

M 10/4:           Lecture 1.18: 3.4 Surface area: 4,5,6,7,8,9,10 (7 problems)

W 10/6:           Lecture 1.19: 3.5 Triple Integrals: 1,2,3,5,6 (5 problems)

F 10/8:            Review

M 10/11:         Oral Exam Week 1

W 10/13:         Oral Exam Week 1

F 10/15:          Oral Exam Week 1

M 10/18:         Lecture 2.1: 3.6 Triple integrals in cylindrical coordinates: 1,2,3,4,5,6,7,8 (8 problems)

W 10/20:         Lecture 2.2: 3.7 Triple integrals in spherical coordinates: 1,2,3,4,5,6,7,8,9,10 (10 problems)

F 10/22:          Lecture 2.3: From CLP-4: 1.1 Curves, derivatives, velocity, etc.: 1,2,3,4,14,15,16,17

(8 problems)

M 10/25:         Lecture 2.4:  1.2 Reparametrization: 1,2,3,4,5 (5 problems)

W 10/27:         Lecture 2.5: 1.6 Integrating along a curve: 1,2,4,5,6,7,8 (7 problems)

F 10/29:          Lecture 2.6: 2.1 Vector fields, definitions and first examples: 1,2,3,4,5,6,7,8 (8 problems)

M 11/1:           Lecture 2.7: 2.3 Conservative vector fields: 1,2,3,4,5,6,7,8 (8 problems)

W 11/3:           Lecture 2.8: 2.4 Line integrals: 3,4,5,6,8,9,10,11,12 (9 problems)

F 11/5:            Lecture 2.9: 3.1 Parametrized surfaces: 1,2,3,4,5,6 (6 problems)

M 11/8:           Lecture 2.10: 3.2 Tangent planes: 6,7,8,9,10,11,12 (7 problems)

W 11/10:         Lecture 2.11: 3.3 Surface integrals: 4,5,6,7,8,9,10 (7 problems)

F 11/12:          Lecture 2.12: 3.4 Interpretation of flux integrals: (from 3.3) 24,25,28,29,30,35,36 (7 problems)

M 11/15:         Lecture 2.13: 4.1 Gradient, divergence and curl: 1,2,3,4,5 (5 problems)

W 11/17:         Lecture 2.14:  4.2 The divergence theorem: 1,2,3,4,5 (5 problems)

F 11/19:          Lecture 2.15: 4.3 Green’s theorem: 1,2,3,4,5,6,7,8 (8 problems)

M 11/22:         Lecture 2.16: 4.4 Stokes’ theorem: 1,2,3,4,5,6,7 (7 problems)

W 11/24:         Review

F 11/26:          Thanksgiving Day Break

M 11/29:         Oral Exam Week 2

W 12/1:           Oral Exam Week 2

F 12/3:            Oral Exam Week 2

Final examination: Monday, December 6, 1:00 PM - 3:00 PM.

Important Dates: