Ventura College Course Name: Multivariable Calculus
Ventura College CRN: 70128
Format: Lecture Based with Computer Component
Meeting Times: Tuesday and Thursday from 10-12:15pm in Sci-107
Last Day to Add Class: 8/25/2017
Last Day to Drop with Refund: 8/25/2017
Last Day to Drop without “W”: 8/27/2017
Last Day to Drop with “W”: 11/17/2017
MyMathLab Instructor Course ID:
Course Description: This course includes: vectors in two and three dimensions; planes, lines and surfaces in space; vector-valued functions and motion in space; partial differentiation; multiple integrals including change of variables; vector fields, including gradient, divergence, and curl; line and surface integrals; and Green’s Theorem, Stokes’ Theorem and the Divergence Theorem.
Student Learning Outcomes: Students will use appropriate techniques to evaluate vector quantities, and graph and analyze multi-variable functions; evaluate derivatives of multi-variable functions and solve application problems; and evaluate integrals of multi-variable functions and solve application problems.
Course Objectives: Upon successful completion of this course, the student will be able to demonstrate the following measurable skills and abilities:
- Perform vector operations in two and three dimensions including dot, cross, triple products and projections.
- Determine vector and parametric equations of lines.
- Determine vector and rectangular equations of planes.
- Find limits and determine continuity of multivariable and vector-valued functions using properties of limits and continuity.
- Determine differentiability and perform differentiation including partial derivatives, chain rule, higher-order derivatives, directional derivatives, and the gradient.
- Find derivatives and integrals of vector-valued functions including velocity and acceleration for motion in space.
- Compute arc length and curvature.
- Find tangent, normal and binormal vectors of vector-valued functions.
- Find level curves and surfaces of real-valued functions of several variables.
- Find and determine local and global maxima, minima, and saddle points.
- Solve constraint problems using Lagrange multipliers.
- Evaluate double and triple integrals using Fubini’s Theorem.
- Perform applications of multiple integration such as area, volume, center of mass, or moments of inertia.
- Evaluate integrals in polar, cylindrical, and spherical coordinates.
- Perform change of variables in multiple integrals using Jacobian.
- Find gradient vector field, determine conservative vector field, and compute curl and divergence of a vector field.
- Evaluate line and surface integrals including parametrically defined surfaces.
- Apply Green’s, Stokes’, and divergence theorems.
Pre-requisite(s): Math V21B or equivalent with grade of C or better
Materials: Calculus Early Transcendentals 2nd Edition by Briggs/Cochran/Gillett and/or a MyMathLab Access Code for online access to the text, scientific calculator, pencil, graph paper, ruler, Test Crib Sheet, Mathematica ($45 optional)
Pre-reading: It is helpful to pre-read topics and/or watch lecture videos before class. This stimulates the learning process and will help the student learn more effectively. In addition, I may not lecture on every topic. I will announce in class which topics you are expected to learn on your own.
MyMathLab: We will be using an on-line educational system called MyMathLab. To access it, navigate to pearsonmylab.com. The program is entirely on-line and can be accessed from nearly any computer with Internet access. There is free temporary 14 day access. You may be dropped from the class if you are not registered into MyMathLab by the 2nd day of class. Everyone should sign up with free temporary access to get going as soon as possible and then pay later. To get registered into MyMathLab, follow the instructions here. You will need the MyMathLab Instructor course ID found above in red. As you register you will come to a page that looks like this. Click where it says “Get temporary access without payment for 14 days.” If you run into technical difficulty, please see the support website here. There is live 24/7 chat, email and phone support.
Mathematica: Mathematica is a computational software program used in scientific, engineering, mathematical and computational fields based on symbolic mathematics. You can think of it as a glorified computer algebra system you find in more advanced calculators… but it includes a lot more functionality. I will be using Mathematica to illustrate concepts with interactive animations coded in Mathematica. I will also present lectures using Mathematica. If you would like to view animations on your own computer you need to download the free Mathematica CDF player here. Feel free to bring your laptops to class so you can interact with the animations on your own.
Lectures: Handouts containing class notes will be made available in my dropbox the night before each class. The notes will contain most of the material we cover in class the next day. I encourage you to annotate these notes with your own notes to aid in your understanding of material. You should print out our notes for class every day and be prepared to work through the examples with me.
Attendance: An attendance sheet will be passed around when class starts. It is important that you are not late to class. If you are late it is your responsibility to ask me for the roll sheet so you can change your attendance from absent to tardy. If a student misses the first day of class, they may be dropped as per college policy. If at any point during the semester, a students absences exceeds 1/9 of the total class contact hours (4 class days), they may be dropped. Upon missing any day of class for any reason, it is the students responsibility to find out what material and or announcements they missed by asking fellow students. Every student should have a contact list of fellow students specifically for this reason.
Homework: Students are expected to complete the homework at the same pace as the lectures. Homework sets will be due at the beginning of class every class day. Every homework assignment will be graded. Late work will not be accepted. I will be checking for organization, completeness, neatness, and correct notation. They must be done in pencil or they will not be accepted.
Tests: There will be 4 tests. Some homework questions will be included verbatim on tests. On test days, all bags will be placed at the front of the classroom with all cell phones inside and turned off. Bathroom breaks are not permitted barring emergency, so please use the bathroom beforehand. You will be allowed to use a study card that I supply on tests. Single purpose scientific (non graphing) calculators are allowed on tests. No graphing calculators. CELL PHONE CALCULATORS ARE NOT ALLOWED.
Quizzes: We will have a number of pop quizzes on material from the previous lecture. For this reason it is extremely important you attend class and be prepared every day and if you miss class, find out what you missed by contacting your fellow students.
Classroom Conduct: Be cognizant of your peers. If you have a question for me during a test, please do not interrupt others by stating your question out loud. Quietly come up to my desk and ask me your question. Please use a quiet voice as not to interrupt the thought process of others while taking their tests. Please use the restroom before lecture or during break. If you need to leave the classroom during lecture, please choose a time when the lecture comes to a break in topic. Also, if you have a question during lecture please raise your hand so that I can call on you at the right time and not in the middle of a sentence. Sleeping is not permitted and you will be asked to leave. It is important that you follow these rules or your In-Class Grade may be zeroed out for that day.
Math Help: I am available for help during my office hours. In addition, the college offers free math tutoring on campus. Please click here for more information. You can also try out a forum like http://math.stackexchange.com.
Homework – 10%
Quizzes – 10%
Tests – 80%