In Math 2720 we learn how to develop the principles and methods in calculus into the vector spaces. This will enable us to deal with multivariable and vector valued functions. Contents include vectors and their operations, vector valued functions, partial derivatives, total derivatives, line integrations, double integrations, surface integrations, triple integrations, Green's theorem and their applications. These roughly corresponds to Chapters 1-4 and part of Chapter 5 and 6 of the text. Students are responsible for all material in the text and all material presented in class. This includes any material not in the text and all material in the text that was not presented in class.
Prerequisites:
A passing grade (C or better) in Math 1230 or Math 1710.
Objectives:
1. Understanding how vectors and their operations related to real world
models, in particular, to goemetrical and physical models.
2. Mastering
vector operations.
3. Understanding the concepts of limites and derivatives
of vector valued functions, interpreting it geometrically, physically and using
it in optimization and linear approximation.
4. Understanding the concepts
of partial and total derivatives and relating them to applications in physics
and geometry.
5. Understanding double and triple integration and their
relationship with partial and total differentiation and applying them.
6.
Strenthening the proper use of mathematical notation.
7. Developing
sufficient computational skills in vectors and their differential and integral
operations for subsequent calculus courses and for applications in other
areas.
8. Strenthening abilities to tackle multi-step problems and to explain
the process.
9. Strenthening the ability of using modern computer algebra
systems (Maple) in assisting the analysis of problems in calculus and the
visualization of their solutions.
10. Strenthening skills in mathematical
reasoning.
11. Developing a broad perspective of how various topics in
calculus fit together.
Academic Integrity: Students are responsible for making themselve aware of and understanding the policies and procedures in the Undergraduate (pp. 274-276) [Graduate (pp.25-27)] Catalog that pertain to Academic Honesty. These policies include cheating, fabrication, falsification and forgery, multiple submission, plagiarism, complicity and computer misuse. If there is reason to believe you have been involved in academic dishonesty, you will be referred to the Office of Student Conduct. You will be given the opportunity to review the charge(s). If you believe you are not responsible, you will have the opportunity for a hearing. You should consult with me if you are uncertain about an issue of academic honesty prior to the submission of an assignment or test.
Calculator and Maple:
A graphing calculator is required for this class. A TI-89 or TI-92 PLUS is recommended. We will use many of the extra capabilities of these calculators. You can find help and examples prepared by Professor Pence here.We will also use the software package Maple. Some maple worksheets can be found here.
Homework:
A list of problems to work can be find here. Although none of the homework will be collected, you are responsible for all of the problems. If you have any questions about problems, please ask them in class or in office hours.
Quizzes:
A total of 5 quizzes will be given. No make up quiz will be given. However, I will drop your worst quiz.
Final:
The final exam will be April 23, Wednesday from 12:30--2:30pm.
Grading:
The final is 28% and the quizzes count for 72%.
This gives a total of 100%.
Grading scale is approximately as
follows:
A (85-100%) BA(78-84.99%) B (71-77.99%) CB(63-70.99%)
C(56-62.99%) DC(50-55.99%) D(43-49.99%) E(0-42.99%)