MATH 311 Vector Analysis
Syllabus
Instructor:
Instructor Email:
Office:
Office Hours:
Course Location and Time:
Course Length: 3 credit hours
Prerequisite: MATH 264 (Calculus III)
Required Textbook:
Supplementary requirements: Computer and internet access.
Course Description: This course will cover vector algebra, lines, planes, parametric curves, arc length, tangent and normal vectors and curvature of parametric curves, vector identities, gradients and directional derivatives, line, surface and volume integrals, divergence and curl of vector-valued functions, Gauss’s and Stokes’s theorems and geometric interpretations.
MATH 311 meets the following College Wide Goals.
A. Communication:
· Students will solve selected problems in writing and submit them to the instructor.
· Students will discuss problems in class.
B. Critical thought:
· Students will practice distinction between valid and invalid arguments.
· Students will analyze and solve real world problems.
C. Information Competency and Research:
· Students will do online homework (through WebAssign)
· Students will use Blackboard to access lecture notes and supplementary class material.
Student Learning Outcomes: Upon successful completion of this course, the student will be able to:
1. Add and subtract vectors graphically and algebraically.
2. Multiply a vector by a scalar graphically and algebraically.
3. Derive and apply equations of a line and equations of a plane in 3D.
4. Compute and interpret the dot and cross product of two vectors.
5. Use triple scalar products to find the volume of a parallelepiped.
6. Compute velocities, tangents, accelerations and curvatures of a curve parametrized with time.
7. Compute and interpret gradients and directional derivatives of a scalar field.
8. Understand the notion of a vector field.
9. Compute and interpret the divergence and curl of a vector field.
10. Compute the Laplacian of a scalar field.
11. Use cylindrical and spherical coordinates and convert between Cartesian coordinates.
12. Compute line integrals of conservative and non-conservative fields.
13. Compute surface and volume integrals.
14. Understand and apply the Divergence theorem.
15. Understand and apply Stokes’ theorem.
16. Solve application problems e.g. vector equations of electromagnetism and Maxwell’s Equations (time permitting).
Course Requirements: (These are examples and will change depending on the instructor)
1. Attendance, In-Class Participation & Quizzes: Students are expected to attend all class sessions and are responsible for material missed during any absence. Occasionally, short quizzes will be given at the end of class. The objective of the quizzes is to test students' understanding of the material covered in class and to prepare them for exams.
2. Email & Blackboard: Students are expected to check their NNMC email and the course Blackboard page regularly. Lecture notes, as well as some extra material and all the important announcements will be posted on the Blackboard.
3. Homework: Completing the homework is essential to understanding and mastering the course material. Late homework earns no credit unless caused by extenuating circumstances as determined by the instructor. Online homework will be assigned through WebAssign. To activate and access your WebAssign account, go to http://www.webassign.net/ You will need the following class key to enroll into our class section and access the online homework: nnmc xxxx xxxx
For every section we cover, there is a corresponding assignment on WebAssign. Students who register late for the class are responsible to inform the instructor and to complete past assignments as soon as possible.
4. Exams: There will be three in-class exams and a comprehensive final exam. The exams are closed-book, closed-notes. Should there be need for any formulas in order to solve exam problems, they will be provided by the instructor. The exam dates and topics will be announced at least one week in advance. Tentative exam dates are listed in the table below.
5. Evaluation: Grades will be determined according to the weighting scheme:
Three Exams: 45 %
Attendance and Quizzes: 15 %
Homework: 15 %
Final Exam: 25 %
Course Grading Scale: The following grading scale will be used to determine final letter grades:
A+ = 99 –100%
A = 93 –98%
A- = 90 – 92%
B+ = 88 – 89%
B = 83 – 87%
B- = 80 – 82%
C+ = 78 – 79%
C = 70 – 77%
C- = 68 – 69%
D+ = 66 – 67%
D = 63 – 65%
D- = 60 – 62%
F = 0 – 59%
Important note: Grades of C- and below do not count toward graduation and do not meet the criteria for satisfying prerequisites.
Study Assistance:
Northern New Mexico College provides tutors at the Student Success Center and the Math Center. Tutors are available to answer questions and to assist students, but they do not complete students’ homework.
Students with Disabilities:
Northern New Mexico College recognizes its responsibility for creating an institutional climate in which students with disabilities can succeed. In accordance with Section 504 of the Rehabilitation Act and the Americans with Disabilities Act; if you have a documented disability, you may request accommodations to obtain equal access and to promote your learning in this class. Please contact the Verna Trujillo, Coordinator of Accessibility and Resource Center at 505-747-2152 or to inquire about appropriate accommodations. After your eligibility is determined, you will be given a letter, which when presented to instructors, will help us know best how to assist you.
Student Code of Conduct and Academic Dishonesty Policy:
Students in this course and in all college classes are expected to complete their course work in accordance to our College policies. Academic dishonesty on the part of a student including cheating on a test, plagiarism or falsification will be subject to academic sanctions. For more information about academic dishonesty and how such incidents will be handled by your instructor and by the College, please refer to Northern’s student handbook.
Tentative timetable (Actual dates will change depending on the semester and instructor)
Week / Dates / Sections covered / Topics1 / 01/17* / 1.1
1.2
1.3 / Vectors in Two- and Three-Dimensional Space
The Inner Product, Length, and Distance
Matrices, Determinants, and the Cross Product
2 / 01/23 / 2.1
2.2
2.3
2.4 / The Geometry of Real-Valued Functions (review)
Limits and Continuity (review)
Differentiation (review)
Introduction to Paths
3 / 01/30 / 2.6
4.1
4.1 / Gradients and Directional Derivatives
Acceleration and Newton's Second Law
Arc Length
4 / 02/06 / Review
Exam I / Review for Exam I
EXAM I
5 / 02/13 / 4.3
4.4
5.1
5.2 / Vector Fields
Divergence and Curl
Introduction
The Double Integral over a Rectangle (review)
6 / 02/20 / 5.3
5.4
5.5 / The Double Integral over More General Regions
Changing the Order of Integration
The Triple Integral
7 / 02/27 / 1.4
6.2
6.3 / Cylindrical and Spherical Coordinates (review)
The Change of Variables Theorem
Applications of Double and Triple Integrals
8 / 03/06 / Review
Exam II / Review for Exam II
EXAM II
03/13 / Spring Break
9 / 03/20 / 7.1
7.2 / The Path Integral
Line Integrals
10 / 03/27 / 7.3
7.4
7.5 / Parametrized Surfaces
Area of a Surface
Integrals of Scalar Functions over Surfaces
11 / 04/03 / 7.6
7.7 / Surface Integrals of Vector Functions
Applications to Differential Geometry, Physics and Forms of Life
12 / 04/10 / Review
Exam III / Review for Exam III
EXAM III
13 / 04/17 / 8.1
8.2
8.3 / Green's Theorem
Stokes' Theorem
Conservative Fields
14 / 04/24 / 8.4
8.5 / Gauss' Theorem
Applications to Physics, Engineering, and Differential Equations
15 / 05/01 / Review / Review for Final Exam
* 01/16 Martin Luther King Jr. Holiday – College closed