225 Calculus III   Fall 1996

J. Derwent

Text:  Calculus, by Finney and Thomas, Addison-Wesley, 1990, Chapters 11-15.

1.Vectors and analytic geometry in space.  The dot and cross product.
Lines, planes and central quadrics.  Cylindtrical and spherical coordinates.

2.Vector valued functions and motion in space. Derivatives and integrals.
Projectile motion.  Arclength.  The unit tangent, the unit normal, and the
curvature.

3.  Double and triple integrals, change of order of integration, and
calculation. Moments and centers of mass.  Triple integrals in cylindrical
and spherical coordinates.

4.  Vector fields. Various kinds of line integrals. Flux integrals. Green's
theorem.  Surface integrals.  Stokes's Theorem and the Divergence Theorem.

There is written homework for every class, whose aggregate counts the same
as one test.

There were also fourteen Mathematica demonstrations and eleven short
Mathematica assignments.


Syllabus

11 Vectors and Analytic Geometry in Space
(4.5 classes:)
11.1 Vectors in the Plane
11.2 Cartesian (Rectangular) Coordinates and Vectors in Space 
11.3  Dot Products
11.4  Cross Products
11.5  Lines and Planes in Space
11.6  Surfaces in Space
11.7  Cylindrical and Spherical Coordinates

12 Vector-Valued Functions
(5.5 classes:)
12.1 Vector-Valued Functions and Space Curves
12.2 Modeling Projectile Motion
12.3 Arc Length and the Unit Tangent Vector T
12.4 Curvature

(Test 1:one class)

13 Partial Derivatives
(3 classes:)
13.1 Functions of Several Independent Variables
13.2 Limits and Continuity
13.3 Partial Derivatives
13.4 Differentiability, Linearization
(6 classes:)
13.5 The Chain Rule
13.6 Directional Derivatives, Gradient Vectors, and Tangent Planes
13.7 Maxima, Minima, and Saddle Points
13.8 Lagrange Multipliers

14 Multiple Integrals
(5 classes:)
14.1 Double Integrals
14.2 Areas, Moments, and Centers of Mass
14.3 Double Integrals in Polar Form
14.4 Triple Integrals in Rectangular Coordinates

(Test 2: one class)

(3 classes:)
14.5 Masses and Moments in Three Dimensions
14.6 Triple Integrals in Cylindrical and Spherical Coordinates
14.7 Substitutions in Multiple Integrals

15 Integration in Vector Fields
(5 classes)
15.1 Line Integrals
15.2 5 classesVector Fields, Work, Circulation, and Flux
15.3 Path Independence, Potential Functions, and Conservative Fields

(Test 3: one class)

(7 classes:)
15.4 Green's Theorem in the Plane
15.5 Surface Area and Surface Integrals
15.6 Parametrized Surfaces
15.7 Stokes's Theorem
15.8 The Divergence Theorem