Syllabus

Class Meetings: MTWR 8:00 - 9:10 in E.An 2
INSTRUCTOR: Geoff Hagopian, OFFICE: M12, PHONE: 776-7223.
E-mail: ghagopian@collegeofthedesert.edu
OFFICE HOURS: MTWR: 9:30 – 11:00

COURSE DESCRIPTION: This course extends the concepts of differentiation and integration introduced in the first two semesters of calculus to functions of several variables. Topics include solid Euclidean geometry, vector algebra in 3 dimensions, line and surface integrals, multiple integration in rectangular, cylindrical and spherical coordinates, extreme values, parameterized space curves and surfaces, divergence, directional derivatives, gradients, Gauss', Green's and Stokes' theorems.

Course Objectives: Upon completion of this course, the student will be able to:

a. Analyze graphic, numeric and formulaic representations for functions of several variables.

b. Apply operations on vectors and matrices including dot products, cross products and determinants.

c. Use partial derivatives to compute directional derivatives and gradients.

d. Use the chain rule to compute partial derivatives for composite functions of several variables.

e. Use partial derivatives to compute first order Taylor approximations.

f. Calculate local and global extrema, with and without constraints, including applications.

g. Set up and compute iterated integrals with rectangular, cylindrical and spherical coordinates, including applications.

h. Create and interpret parameterizations of curves and surfaces.

i. Compute line integrals and surface integrals, with applications.

j. Use vector analysis, especially the theorems of Gauss, Green and Stokes to interpret and evaluate divergence, flux, gradients and curl.

TEXTBOOK: Multivariable Calculus: Concepts and Contexts, by James Stewart. Emphasis in this text is on understanding the concepts fundamental to calculus, as well as mastering basic, routine computations. It is critical that you read the text, keep up with the assigned problems and prepare questions about what you're learning for participation in class. We will not be able to cover every problem type or every approach during class, but you will be responsible for everything in the assigned reading and problems from the text.

EXAMS: There will be five chapter tests (one after each chapter) and a cumulative final exam. Please understand that the point of the exams is to provide an opportunity for you to demonstrate your understanding of the concepts covered. The in-class tests are timed: this means you need to really understand the ideas before you start the exam. If you are well prepared, you will have enough time for the exams.

HOMEWORK: You can expect to learn far more calculus at home doing the homework than in the classroom. If you complete (and understand) the homework assignment for each section, you should be well prepared for quizzes and exams. At the beginning of each class, I will answer as many questions over the previous night's homework as time allows. You are expected to have completed the assignment and to have prepared specific questions about these. To get credit for homework assignments you’ll need to use the the online software at ILRN.com.

GRADE: Your grade in this class will be a weighted average of your final exam, chapter test, homework scores.

	Monday	Tuesday	Wednesday	Thursday
8/31 – 9/3	9.1 Three Dimensional Coordinate Systems 2, 3, 4, 5, 6, 9, 10, 12, 13, 16, 18, 19-36	9.2 Vectors 1, 2, 3, 4, 6, 10, 11, 13, 17, 20, 22, 23, 25, 26, 28, 30, 32, 35, 36, 37	9.3 The Dot Product 1, 5, 7, 9, 11, 13, 17, 20, 22, 25, 26, 29, 33 34, 35, 37, 39, 41, 43, 44, 45	9.4 The Cross Product 1-33 odd & Discovery Project 1, 2, 3
9/8 – 9/10	Labor Day Holiday	9.5 Equations of Lines and Planes 1, 3, 8, 12, 13, 15, 17, 19, 23, 27, 29, 33, 40, 43, 45, 47, 49, 51, 53, 56		9.6 Functions and Surfaces 1-33 odd
9/14 – 9/17	9.7 Cylindrical and Spherical Coordinates 1-35 odd	Families of Surfaces 1,2,3	Review	Chapter 9 Test
9/21 – 9/24	10.1 Vector Functions and Space Curves 4, 12, 16, 20, 24, 28, 30, 34, 38, 40 10.2 Derivatives and Integrals of Vector Functions 4, 12, 18, 22, 26, 30, 42, 44	10.3 Arc Length and Curvature 4, 8, 12, 32, 38, 42, 49	10.4 Motion in Space 4, 8, 12, 14, 16, 18, 22, 26, 28, 30, 32, 34, 36	10.5 Parametric Surfaces 2, 4, 6, 10, 18, 22, 24, 28, 30, 32
9/28 – 10/1	Review: Page 727: Kepler's Laws, Page 735, 1-23 all	Review Page 736: 1-8 all	Review	Chapter 10 Test.
10/5 – 10/8	11.1 Functions of Several Variables 1, 4, 6, 7, 9, 12, 13, 20, 22, 26, 30, 36, 42 11.2 Limits and Continuity 3, 4,6, 10, 14, 18, 22, 30, 32, 35, 36	11.3 Partial Derivatives 2, 3, 4, 5, 8, 10, 12, 16, 18, 20, 22, 24, 28, 30, 32, 34, 36, 40, 42, 48, 54, 62, 68, 72, 78, 82	11.4 Tangent Planes and Linear Approximations 1, 4, 6, 8, 13, 16, 17, 22, 23, 27, 31, 34, 37, 38, 42	11.5 The Chain Rule 1, 2, 6, 7, 8, 11, 12, 14, 16, 19, 20, 24, 28 31, 34, 36, 38, 42, 44, 47
10/12 – 10/15	11.6 Directional Derivatives and the Gradient Vector 2, 6, 7, 10, 13, 16, 18, 21, 24, 28,30, 32, 35, 38, 40, 42, 44, 48, 50, 54	11.7 Maximum and Minimum Values 2, 4, 7, 9, 13, 16, 20, 24, 27, 30, 32, 36, 38, 40, 42, 48, 49, 50	Quadratic Approximations and Critical Points Page 812	11.8 Lagrange Multipliers 1, 4, 6, 8, 10, 12, 14, 17, 21, 24, 28, 30, 32, 34, 42, 44
10/19 – 10/22	Review	Chapter 11 Test	12.1 Double Integrals over Rectangle 2, 4, 6, 7, 9, 10, 11, 13, 15, 17, 18	12.2 Iterated Integrals 2, 4, 8, 10, 12, 15, 16, 18, 20, 22, 24, 27, 29, 31, 33, 34
10/26 – 10/29	12.3 Double Integrals over General Regions 1, 3, 5, 8, 10, 12, 14, 15, 18,22, 25, 28, 30, 32, 35, 37, 40, 42, 46, 52, 54	12.4 Double Integrals in Polar Coordinates 1, 3, 5, 8, 10,12, 16, 15, 18, 20, 22, 24, 27, 28, 30, 32, 33	12.5 Applications of Double Integrals 2, 4, 6, 9, 12, 13, 16, 17, 20, 22, 26, 27	12.6 Surface Area 2, 5, 6, 8, 10, 12, 15, 17, 19, 21, 23, 27, 28
11/2 – 11/5	12.7 Triple Integrals 1, 2, 6, 8, 9, 11, 15, 17, 22, 24, 26, 30, 32, 36, 38, 40, 42, 44, 46, 48, 49	12.8 Triple Integrals in Cylindrical and Spherical Coordinates 1, 2,4, 6, 7, 9, 11, 14, 16, 18, 21, 23, 26, 27, 28, 30, 32, 34, 35, 37	12.9 Change of Variables in Multiple Integrals 1, 2, 3, 4, 5, 6, 7, 9, 12, 13, 15, 16, 17, 19, 21, 23, 24	Review
11/9 – 11/12	Review	Chapter 12 Test	Holiday	13.1 Vector Fields 2, 4, 6, 8, 10, 12, 14, 17, 18, 20, 22, 26, 28, 32, 35, 36
11/16 – 11/19	13.3 The Fundamental Theorem for Line Integrals 1, 2, 5, 7, 8, 9, 11, 13, 16, 18, 20, 22, 23, 26, 27, 30, 32, 34	13.2 Line Integrals 1, 4, 6, 8, 10, 12, 14, 15, 17, 19, 22, 24, 26, 27, 29, 31, 34, 36, 38, 40, 42	13.4 Green's Theorem 1, 4, 6, 8, 9, 11, 12, 14, 16, 18, 21, 23, 25, 26, 27, 28, 29	13.5 Curl and Divergence 1, 4, 5, 6, 8, 10, 13, 14, 16, 18, 20, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37
11/23 – 11/26	13.6 Surface Integrals 1, 2, 4, 6, 7, 10, 12, 14, 16, 18, 19, 21, 23, 25, 27, 28	13.6 Surface Integrals 30, 31, 32, 33, 34, 36, 38, 39, 40, 41, 42, 43	13.7 Stokes Theorem 1, 2, 3, 5, 6, 7, 9, 11, 13, 15, 16, 17	Thanksgiving Holiday
11/29 – 12/2	13.7 Stokes Theorem 18, 19, 20	13.8 The Divergence Theorem 24, 25, 26, 27, 28, 29, 30, 31, 32	13.9 Summary	Review
12/7 – 12/10	Review	Chapter 13 Test	Review	Review
12/14 - 12/17	Review (Last Day of Class)			Final Exam