MA 213 Course Syllabus Fall 2013
Sections 9/10/11/12
MWF 0100 –
0150
CP 320
1 Instructors
Richard
Carey
Office:
POT 965
E-Mail
richard.carey@uky.edu
Phone:
(859) 257-3745
Office
Hours: MW 2:15-3:30 & by appt.
Jiaqi
Liu, section 9/ TR 8:00-8:50 in FPAT 265; section 10/ TR 9:30-10:20 in CB 238
Fernando Camacho, section 11 /11:00-11:50 in CB 212; section 12/ TR 12:30-1:20 in CB 201
2 Text
The
text for the course is Calculus Early
Transcendentals, Second Edition, John Rogawski, ISBN -10:1-4292-0838-4 . We
will cover Chapters 12-16 except for surface integrals and part of Chapter
17.This is calculus in several variables including vector geometry, motion
along a curve, higher dimensional derivatives, calculus for surfaces, multiple
integrals, line integrals and vector
field theory.
3 Grading
69% D, 0-59% E) on the basis of 425 points
earned as follows:
2 in-class exams 100 points each
1 final exam 125
points
The final exam is on Wednesday December 18, 2013 in CP 320 at 1:00 pm.
4 Course
Goals
The course is an introduction to multivariable calculus. We
shall extend the ideas you saw in basic calculus to higher dimensions. So you
shall learn to calculate with functions of more than one variable. Some
of this material will be a review of material you learned in Calculus I and
Calculus II. The goal of this type of exercise is to develop reading ability in
mathematics.
Starting with the coordinatization of three dimensional space via Cartesian coordinates, the algebraization of geometry continues with the introduction of vectors - directed line segments. Geometric operations on line segments may be interpreted as algebraic operations on vectors in both the plane and three dimensional spaces. Not only does this include addition and multiplication by scalar quantities, it also provides two different types of multiplication - the dot and cross product. These products are geometrically defined and we spend some time applying vector algebra to the geometry of three dimensions. Applications of this are to the geometry of the motion. If time permits one shows that the geometry of curves in space is characterized by the Frenet- Serret formulas. For surfaces there is the extension to functions of several variables. Here the analogs of many of the formulae from the calculus of one variable are more complicated. In particular when considering higher derivatives we find that there are phenomena that do not occur in the calculus of functions of a single variable. One of the consequences of this is the existence of critical points of saddle type which make the application of several variable calculus to optimization problems far more involved than in the single variable case. Applications include the method of Lagrange multipliers for constrained problems. The integral calculus also generalizes to functions of several variables. . Applications include moments of inertia as well as the calculation of masses, centers of mass and several integral identities that come from the application of the change of variables formula for integrals of functions of several variables. This involves the use of the Jacobian and connections with linear algebra are developed in a self contained fashion for integrals in both two and three dimensions. The geometry of the regions of integration is a far more crucial ingredient in these calculations.
As with the vector algebra, there are several possible derivatives for a vector field - the curl and the divergence which correspond to the cross and dot products, respectively. For scalar functions the corresponding derivative is the gradient. There are surprising relations between these - the curl of a gradient is always zero as is the divergence of a curl. These can also be expressed as identities involving integrals of vector fields over one, two and three dimensional regions, respectively. The mathematical expression of these identities are Stokes, Gauss' and the fundamental theorem for line integrals. Physical applications of these appear as identities involving total charge, angular momentum in electromagnetism and mechanics and conservative vector fields in all areas of physics and mechanics respectively.
Starting with the coordinatization of three dimensional space via Cartesian coordinates, the algebraization of geometry continues with the introduction of vectors - directed line segments. Geometric operations on line segments may be interpreted as algebraic operations on vectors in both the plane and three dimensional spaces. Not only does this include addition and multiplication by scalar quantities, it also provides two different types of multiplication - the dot and cross product. These products are geometrically defined and we spend some time applying vector algebra to the geometry of three dimensions. Applications of this are to the geometry of the motion. If time permits one shows that the geometry of curves in space is characterized by the Frenet- Serret formulas. For surfaces there is the extension to functions of several variables. Here the analogs of many of the formulae from the calculus of one variable are more complicated. In particular when considering higher derivatives we find that there are phenomena that do not occur in the calculus of functions of a single variable. One of the consequences of this is the existence of critical points of saddle type which make the application of several variable calculus to optimization problems far more involved than in the single variable case. Applications include the method of Lagrange multipliers for constrained problems. The integral calculus also generalizes to functions of several variables. . Applications include moments of inertia as well as the calculation of masses, centers of mass and several integral identities that come from the application of the change of variables formula for integrals of functions of several variables. This involves the use of the Jacobian and connections with linear algebra are developed in a self contained fashion for integrals in both two and three dimensions. The geometry of the regions of integration is a far more crucial ingredient in these calculations.
As with the vector algebra, there are several possible derivatives for a vector field - the curl and the divergence which correspond to the cross and dot products, respectively. For scalar functions the corresponding derivative is the gradient. There are surprising relations between these - the curl of a gradient is always zero as is the divergence of a curl. These can also be expressed as identities involving integrals of vector fields over one, two and three dimensional regions, respectively. The mathematical expression of these identities are Stokes, Gauss' and the fundamental theorem for line integrals. Physical applications of these appear as identities involving total charge, angular momentum in electromagnetism and mechanics and conservative vector fields in all areas of physics and mechanics respectively.
5 Additional
Course Policies
- Course policy of academic accommodations due to disability: If you have a documented disability that requires academic accommodations, please see me as soon as possible during scheduled office hours. In order to receive accommodations in this course, you must provide me with a Letter of Accommodation from the Disability Resource Center (Room 2, Alumni Gym, 257-2754, email address jkarnes@email.uky.edu) for coordination of campus disability services available to students with disabilities.
- Course policy for attendance: See the supplementary recitation syllabus.
- Make-up opportunities: The instructor shall give the student an opportunity to make up the work and/or the exam missed during an excused absence... implies the student shall not be penalized for the excused absence.
- Verification of Absences: Students missing work due to an excused absence bear the responsibility of informing the instructor about their excused absence within one week following the period of the excused absence (except where prior notification is required) and of making up the missed work.
- Course policy for submission of assignments: Students shall return all assignments on the due date. No late assignments shall be accepted without an excused absence.
- Course policy on academic integrity: All assignments, projects, and exercises completed by students for this class should be the product of the personal efforts of the individual(s) whose name(s) appear on the corresponding assignment. Misrepresenting others work as ones own in the form of cheating or plagiarism is unethical and will lead to those penalties outlined in the University Senate Rules (6.3.1 & 6.3.2) at the following website: http://www.uky.edu/USC/New/rules_regulations/index.htm. The Ombud site also has information on plagiarism found at http://www.uky.edu/Ombud.
- Course policy on classroom civility and decorum: The university, college and department has a commitment to respect the dignity of all and to value differences among members of our academic community. There exists the role of discussion and debate in academic discovery and the right of all to respectfully disagree from time to time. Students clearly have the right to take reasoned exception and to voice opinions contrary to those offered by the instructor and/or other students (S.R. 6.1.2). Equally, a faculty member has the right - and the responsibility - to ensure that all academic discourse occurs in a context characterized by respect and civility. Obviously, the accepted level of civility would not include attacks of a personal nature or statements denigrating another on the basis of race, sex, religion, sexual orientation, age, national/regional origin or other such irrelevant factors.
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