Spring 2005. Syllabus for Calculus III (MAC 2313; Section 034).
Instructor/office/contact info/office hours:
Instructor: Dr. Ognjen Milatovic Office: Building 14, Room 2733
Phone: 620-1745 E-mail:
Office hours: Tuesday 8:50 a.m.-9:50 a.m.;
Tuesday 3:15 p.m.-4:15 p.m.;
Thursday 8:50 a.m.-9:50 a.m.;
Thursday 3:15 p.m.-4:15 p.m.;
Or by appointment
Instructor’s Web Page:
Prerequisite: MAC 2312–Calculus II.
Text: Larson, Hostetler, Edwards, Calculus. Early Transcendental Functions, 3rd Edition
Calculator: A graphing calculator, such as TI-82 or higher (TI-83 is recommended). Graphing calculators TI-89 and TI-92 will not be allowed on tests, quizzes and the final exam.
Course Objectives:To have students understand the concepts of vectors, vector functions, and functions of more than one variable, and their derivatives and integrals, and to enable students to display that understanding through a variety of applications. Specific, measurable manifestations of your understanding that will be tested during the semester include your ability to
• algebraically and graphically manipulate vectors, find their components, and determine length and direction
• calculate dot products, projections, and angles between vectors
• solve physics problems, involving velocity, acceleration, force, and work, by using vectors
• differentiate and integrate vector functions
• differentiate the position vector function to obtain the tangent, velocity, and acceleration vectors
• integrate the acceleration and velocity vector functions to obtain the position vector function
• calculate the position, velocity, and acceleration vector functions of a projectile
• calculate polar coordinates given Cartesian coordinates, and vice-versa, and draw graphs of polar equations
• calculate the cross product of two vectors in 3-dimensional space to find normal vectors to planes
• apply the cross product to calculate areas of triangles and parallelograms, and to find the torque vector
• produce equations of lines and planes in 3-dimensional space
• sketch cylinders and quadric surfaces, and recognize their equations
• differentiate dot products and cross products of vector functions
• identify the domain of a function of several variables, and produce a rough sketch of the graph
• sketch the level curves of a function of several variables
• match functions of several variables with their level curves and graphs
• calculate partial derivatives of functions of several variables
• calculate partial derivatives via the multivariable chain rule
• calculate the gradient vector of a function of several variables at a point
• calculate the directional derivatives of a function of several variables, and determine the directions of most and least rapid increase of the function, and the directions in which the function remains constant
• produce equations of the tangent plane to the graph of a function of several variables at a point
• approximate changes in the function by using the tangent plane, the local linearization, and the differential
• determine the critical points of a function of several variables, and determine whether they correspond to local maxima, local minima, saddle points, or none of these
• sketch the graph and level curves of a function of several variables near local maxima, local minima, and saddle points
• determine absolute extreme values on closed, bounded regions
• approximate double integrals by using partitions
• calculate indefinite and definite double integrals
• reverse the order of integration to calculate double integrals
• use double integrals to calculate the volume beneath surfaces
• calculate double integrals in polar coordinates
• calculate triple integrals in rectangular coordinates
• calculate the average value of a function of several variables
• calculate triple integrals in spherical and cylindrical coordinates
By the end of the semester, you will
- extend what you learned in Calculus I and II to functions of several variables
- learn some important mathematical tools widely used by scientists and engineers
- strengthen your skills in numerical and symbolic computation, mathematical reasoning, and mathematical modeling
- gain skills in learning and communicating mathematics
It is essential that you attend classes regularly. The easiest way for you to learn the material, and to know what material has been covered, is to come to class each day. You are responsible for finding out what material has been covered or what announcements have been made on days that you miss class.
Excused Absences or Late Work:
In order to turn in assignments late or to take make-up quizzes/tests, you must bring written proof of some emergency situation; notes from doctors or nurses, documents verifying court appearances, receipts from having a car towed are all examples of valid documentation. Notes from family members are not acceptable. If a situation is of a personal nature, discuss the matter with your academic advisor; an e-mail message from your advisor saying that he/she believes that you should be allowed to make up work is acceptable.
Reading, Homework, Quizzes and Class Participation:
It is strongly recommended that you read the assigned section from the textbook ahead of time. Thus, when you then see the corresponding section covered in class, you will be able to follow along much more easily (as opposed to seeing the material for the very first time in class).
Homework will be assigned with each section. Some homework exercises may be collected and graded. If I choose to collect a particular homework assignment, I will inform you, in advance, when the assignment will be collected and what exercises will be graded. For grading purposes, such homework assignment will be counted as a quiz.
It is essential that you do homework exercises regularly: working these exercises will help you get a solid grasp of fundamental concepts and techniques of calculus and will increase your confidence as you proceed to learn new ideas. Furthermore, questions on quizzes and tests will be very similar to assigned homework exercises and the examples discussed during class. To help you work and understand homework exercises, we will go over a limited number of homework exercises at the beginning of each class.
While doing homework, do not just write down answers. Think about the problems posed, your strategies, the meaning of your computations, and the answers you get. It is often in this reflection that the greatest learning takes place. The main point is not to come up with specific answers to the specific problems you are working on, but to develop an understanding of what you are doing so that you can apply your reasoning to a wide range of similar situations.
To ensure that you are keeping up with the homework, there will be several short (10-20 minute) quizzes during the semester (roughly, one quiz every week).
Every class member will be expected to participate in class discussions. Your participation in class can be, for example, your contribution to course discussions and your contribution to answering in-class or homework questions. Please remember that your questions are a valuable part of our discussion of course topics.
The final exam is cumulative and will count as 25% of your course grade. Quizzes, graded homework exercises and class participation will together count as 25% of your course grade. I will drop your worst quiz grade. Two in-class midterm tests will together count as the remaining 50% of your course grade (each midterm test will count 25% of your course grade). Course grades will be assigned as follows:
[90 - 100 %: A-, A], [80 – 89%: B-, B, B+],
[70 – 79%: C, C+], [60 – 69%: D], [59% and below: F].
Cheating is an insult to honest students – it will not be tolerated.
Chapter 9 (Sections 9.1 – 9.4)
Chapter 10 (Sections 10.1 – 10.7),
Chapter 11 (Sections 11.1 – 11.5),
Chapter 12 (Sections 12.1 – 12.9),
Chapter 13 (Sections 13.1 – 13.3 and 13.6 – 13.8)
Chapter 14 (Selected sections, time permitting)
Some sections may be omitted.
March 21—26 Spring Break (no classes)
March 28 (Monday) Deadline to Withdraw
April 28 (Thursday) Final Exam (9:00 a.m. – 10:50 a.m.)