AMS 261: Applied Calculus III (Multivariable Calculus)

Fall 2009
Time: Monday, Wednesday & Friday 11:45 am - 12:40 pm
Location: Harriman 137

Recitation 1: Mon 5:20pm--6:15pm in Harriman Hall 112
Recitation 2: Thur. 3:50pm--4:45pm in Physics P118.
Recitation 3: Wed. 5:20pm--6:15pm in Harriman Hall 112


Instructor: Prof. Xiangmin (Jim) Jiao
Email: xjiao@sunysb.edu Phone: 2-4408
Office Hours: Wed. 3:00pm-4:00pm & Fri. 10:30am-11:30am
Office: Math Tower 1-115 		Recitation TA: Mr. Peng Zhang
Email: penzhang@ams.sunysb.edu
Office Hours: Wed. 4:20pm-5:20pm, Thur. 2:50pm-3:50pm
Office: Phys. Bldg. A-134

Recitations Graders

R01 Grader: David H. Chan
Email:  dhchan@ic.sunysb.edu
Office hours: Wed. 9:35am-11:35am
Location: Harriman 010
 R02 Grader: Ying (Sophie) Zhang
Email: zy_sophia_2006@hotmail.com
Office hours: Mon. 3:50pm-5:50pm
Location: Harriman 010
 R03 Grader: Huixia Chen
Email: shadow198707@gmail.com
Office hours: Thur. 1:00pm-3:00pm
Location: Harriman 010


[ Course Description | Course Outline | Class Schedule | Course Policy | University Policy ]
Course Description (back to top)


Vector algebra and analytic geometry in 2- and 3-dimensions; multivariable differential calculus and tangent planes; multivariable integral calculus; optimization and Lagrange multipliers; vector calculus including Green's and Stokes' theorems. May not be taken for credit in addition to MAT 203 or 205.

Prerequisite/Co-requisite: AMS 161 or MAT 127 or 132 or 142 or 171.

Required Textbook

  • Multivariable Calculus, by W. McCallum, Hughes-Hallett, and Gleason et al., Fifth Edition, John Wiley & Sons. ISBN:  978-0-470-13158-9.
Course Outline (back to top)


Outline

  • Vector algebra and analytic geometry in two and three dimensions (2 weeks).
  • Multivariate Differential Calculus- partial derivatives and gradients, tangent planes (2 weeks).
  • Multivariate Integral Calculus:  double and triple integrals, change of variables and Jacobians, polar coordinates, applications to probability (3.5 weeks).
  • Optimization: maxima and minima, Lagrange multipliers (2 weeks).
  • Vector Calculus: vector-valued functions, curves in space, linear integrals, surface integrals, Green's Theorem, Stokes' Theorem (3.5 week).
Class Schedule (back to top)
 
  • Important: All schedules are tentative and are subject to change.

Week Date Topic Slides Reading Notes
1 Mon 08/31 Course overview; Functions of two variables
 slides
 §12.1

Wed 9/2
 Graphs of functions of two variables slides
 §12.2

Fri 9/4 Contour diagrams
 slides §12.3 HW1 out
2 Mon 9/7 No class (Labor Day observed)



Wed 9/9
 Linear functions
 slides §12.4

Fri 9/11 More on linear functions; Functions of three variables slides §12.5
3 Mon 9/14 Limits and continuity; Displacement vectors slides §12.6; §13.1 HW1 due; HW2 out

Wed 9/16
 Vectors in general; The dot product slides §13.2-3

Fri 9/18 More on dot product; The cross product slides §13.3-4
4 Mon 9/21 More on cross product; The partial derivative slides
 §13.4, 14.1 HW2 due; HW3 out

Wed 9/23
 Computing partial derivatives algebraically; Local linearity
 slides §14.1-2

Fri 9/25 The differential; Gradients and directional derivatives slides
 §14.3-4
 sample exam questions
5 Tue 9/29 More on gradients and directional derivatives slides §14.4-5 HW3 due; HW4 out

Wed 9/30
 The chain rule slides §14.6

Fri 10/2 Review for Test 1 slides

6 Mon 10/5 Test 1 (covers up to §14.5)



Wed 10/7
 Second-order partial derivatives slides §14.7

Fri 10/9 Differentiability
 slides §14.8 HW5 out
7 Mon 10/12 Discussions of Test 1; More on differentiability

HW4 due

Wed 10/14
 Local extrema
 slides §15.1

Fri 10/16 Optimization
 slides
 		§15.2 HW6 out
8 Mon 10/19 More on optimization
 slides
 §15.2 HW5 due

Wed 10/21
 Constrained optimization slides §15.3

Fri 10/23 More on constrained optimization slides §15.3 HW7 out
9 Mon 10/26 The definite integral of a function of two variables; Iterated integrals slides §16.1-2 HW6 due

Wed 10/28
 More on iterated integrals slides §16.2

Fri 10/30 Triple integrals; Double integrals in polar coordinates
 slides §16.3-4 HW8 out
10 Mon 11/2 Integrals in cylindrical and spherical coordinates slides §16.5 HW7 due

Wed 11/4
 Parameterized curves slides §17.1

Fri 11/6 Review for Test 2
 slides

11 Mon 11/9 Test 2 (covers material up to §16)    

Wed 11/11
 Motion, velocity, and acceleration; Vector fields
slides §17.2-3

Fri 11/13 Flow of a vector field; Parameterized surfaces slides §17.4-5 HW9 out
12 Mon 11/16 The idea of line integral
§18.1 HW8 due

Wed 11/18
 Computing line integrals over parameterized curves

§18.2

Fri 11/20 Gradient fields of path-independent fields  slides §18.3 HW10 out
13 Mon 11/23 Path-independent fields and Green's theorem 
§18.4 HW9 due

Wed 11/25
 No class (Thanksgiving break)



Fri 11/27 No class (Thanksgiving break)    
14 Mon 11/30 The idea of a flux integral
§19.1

Wed 12/2
 Flux integrals for graphs
§19.2 HW11 out

Fri 12/4 Flux integrals over parameterized surfaces
§19.3 HW10 due
15 Mon 12/7 The divergence of a vector field; The divergence theorem
§20.1-2

Wed 12/9
 The curl of a vector field
§20.3

Fri 12/11 Review for final exam

HW11 due
16 Wed 12/16 Final exam (5:15-7:45pm, Harriman 137)
      

Course Policy (back to top)


Assignments

Homework assignments are due in class typically one week after they are assigned. You are allowed to discuss course materials and homework problems in small groups, but limited to discussion of general ideas only. You must write your solutions completely independently. Under no circumstances may you copy solutions from any source, including but not limited to other students solutions, official solutions distributed in past terms, and solutions from courses taught at other universities. Violation of these rules may result in disciplinary actions.

Homework assignments will be posted on the BlackBoard.

Exams

The exams (including two tests and the final exam) are closed-book, but you are allowed to bring a single-sided, one-page, letter-size cheat sheet, which you must prepare by yourself. (Note: This policy is subject to change during the course of the semester.)

Grading

  • Assignments: 30%
  • Two tests: 40%
  • Final exam: 30%
University Policy (back to top)

Americans with Disabilities Act

If you have a physical, psychological, medical or learning disability that may impact your course work, please contact Disability Support Services, ECC (Educational Communications Center) Building, room128, (631) 632-6748. They will determine with you what accommodations, if any, are necessary and appropriate. All information and documentation is confidential.

Academic Integrity

Each student must pursue his or her academic goals honestly and be personally accountable for all submitted work. Representing another person's work as your own is always wrong. Faculty are required to report any suspected instances of academic dishonesty to the Academic Judiciary. For more comprehensive information on academic integrity, including categories of academic dishonesty, please refer to the academic judiciary website at http://www.stonybrook.edu/uaa/academicjudiciary/

Critical Incident Management

Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of Judicial Affairs any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn.