Math 302, Spring 2004
Math 302  Vector Calculus
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 Spring 2004
Class Meetings
MTW-F, 11:00 – 11:50 AM, in Lovejoy 413
Instructor
Otto Bretscher, Olin 342
E-mail: obretsch@colby.edu
Office Phone: 872-3688
Home Phone: 872-6281
Tentative Office Hours: MTW, 1 PM – 3 PM, and by appointment.
Web Page
www.colby.edu/~obretsch
Grading
Course grades will be based upon two exams (20% each), the final exam (30%),
homework (15%), and quizzes (15%). Active class participation will earn you a few extra
points.
Homework
Homework will be due on Wednesday, starting February 11, to be submitted in class or in
office hours (by 3 PM). The grader, Kimberly Prescott (kbpresco), will announce
policies regarding late homework and other relevant matters.
Tests and Quizzes
There will be a number of short in-class quizzes testing your command of basic
techniques and concepts. The hour exams will be given in class as well. There will be at
least a week’s notice for the hour exams, but no advance notice for the quizzes. You will
be allowed one hand-written reference sheet (“cheat sheet”) for all quizzes and exams.
There will be no make-ups for missed quizzes.
Class Attendance
Students are expected to attend all of their classes and are responsible for any work
missed. Failure to attend can lead to a warning, grading penalties, and dismissal from the
course with a failing grade. Students are excused in the case of a critical emergency
(verified by the Dean of Students Office) or illness (verified by the College Health
Center). Excuses may be granted for athletic or organizational trips if I’m notified well in
advance.
Text
Susan J. Colley: Vector Calculus, 2/E, Prentice Hall, 2002.
Calculators
Feel free to use a scientific calculator to help you with tedious computations in the
homework. However, calculators will not be allowed in quizzes and exams.
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Syllabus
We will closely follow the text, Vector Calculus, by Susan Colley.
Chapters 1, 2, 4, and parts of 5 of the text present material that you have seen in Math
122 (or 161/162), maybe with slightly different notations. Use these parts of the text for
review and as a reference.
In Math 302, we will work through Chapters 3, 5, 6, and 7 of the text.. If time allows, we
will take a look at Chapter 8.
Chapter 3: Vector-Valued Functions
3.1
3.2
3.3
3.4
Parametrized Curves and Kepler's Laws
Arclength and Differential Geometry
Vector Fields: An Introduction
Gradient, Divergence, Curl and the Del Operator
Chapter 5 : Multiple Integration
5.1
5.2
5.3
5.4
5.5
5.6
Introduction: Areas and Volumes (a brief review)
Double Integrals (a brief review)
Changing the Order of Integration (a brief review)
Triple Integrals
Change of Variables
Applications of Integration
Chapter 6 : Line Integrals
6.1 Scalar and Vector Line Integrals
6.2 Green's Theorem
6.3 Conservative Vector Fields
Chapter 7 : Surface Integrals and Vector Analysis
7.1
7.2
7.3
7.4
Parametrized Surfaces
Surface Integrals
Stokes' and Gauss's Theorem
Further Vector Analysis: Maxwell's Equations
Chapter 8 : Vector Analysis in Higher Dimensions
8.1 Introduction to Differential Forms
8.2 Manifolds and Integrals of k-forms
8.3 The Generalized Stokes' Theorem
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This material is review from Multivariable Calculus (Math 122 or equivalent). We will
go over it very briefly.
Chapter 3 : Vector Functions of One Variable
3.1 :Vector Differentiation, 3.2: Geometric Interpretation of R¢,
3.3: Higher-Order Derivatives, and 3.4: Curves, Length and Arc Length
Chapter 4: The del operator Ñ
Sections 4.1 through 4.4 are essentially review of Math 122 material, and we will discuss
those only briefly.
4.5 : Divergence and Curl of a Vector Field, 4.6 : Physical Interpretation of Divergence,
4.7 : Physical Interpretation of the Curl, 4.8 : The Laplacian Operator Ñ 2 ,
4.9 : Vector Identities
Chapter 5 : Line, Surface, and Volume Integrals
5.1 : Introduction, 5.2 : Line Integrals and Vector Functions, 5.3 : Work,
5.4 : Line Integrals Independent of Path, 5.5 : Conservative Vector Fields,
5.6 : Surface Integrals, 5.7 : Orientation of a Surface, 5.8 : Volume Integration,
5.9 : Triple Integrals in Cylindrical Coordinates,
5.10 : Triple Integrals in Spherical Coordinates
Chapter 6 : Integral Theorems
6.1 : Green’s Theorem, 6.2 : Regions with Holes, 6.3 : Integrals over Vector Fields,
6.4 : Stokes’ Theorem, 6.5 : Green’s Theorem in 3-D, 6.6 : The Divergence Theorem
Chapter 7 : Applications
We will discuss parts of this chapter as time allows.
Possible applications in Physics are:
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Electromagnetic Theory: Maxwell’s Equations
Fluid Dynamics: Euler’s Equation and Bernoulli’s Equation
Heat Conduction
Ocean Waves
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