Syllabus: M408M
Text: Stewart,
Calculus, Fifth Edition
Responsible
Parties: Kathy Davis, John Gilbert, Gary Hamrick June 19 2003
Prerequisite and degree relevance:
Mathematics 408L or the equivalent
with a grade of at least C.
Only one of the following may be
counted: Mathematics 403L, 408D, 408M (or 308M).
Calculus is offered in two
equivalent sequences: a two-semester sequence, M 408C/408D, which is
recommended only for students who score at least 600 on the mathematics Level I
or IC Test, and a three-semester sequence, M 408K/408L/408M.
For some degrees, the two-semester
sequence M 408K/408L satisfies the calculus requirement . This sequence is also
a valid prerequisite for some upper-division mathematics courses, including
M325K, 427K, 340L, and 362K.
M408C and M408D (or the equivalent sequence M408K, M408L, M408M) are required for mathematics majors, and mathematics majors are required to make grades of C or better in these courses.
Course description:
M408M is one of two first-year calculus courses. It is directed at students in
the natural and social sciences and at engineering students. In comparison with
M408D, it covers fewer chapters of the text. However, some material is covered
in greater depth, and extra time is devoted the development of skills in
algebra and problem solving. This is not a course in the theory of
calculus.
Introduction
to the theory and applications of differential and integral calculus of
functions of several variables. Includes parametric equations, polar
coordinates, vectors, vector calculus, functions of several variables, partial
derivatives, gradients, and multiple integrals.
Syllabus: M408M
Text: Stewart,
Calculus, Fifth Edition
Responsible
Parties: Kathy Davis, John Gilbert, Gary Hamrick June 19 2003
Forty Class Days As:
11 Parametric
Equations and Polar Coordinates (six days)
11.1 Curves
Defined by Parametric Equations
11.2 Calculus with Parametric
Curves
11.3 Polar Coordinates
11.4 Areas and Lengths in Polar
Coordinates
11.5 Conic Sections
11.6 Conic Sections in Polar
Coordinates
13 Vectors and the
Geometry of Space (eight days)
13.1 Three-Dimensional
Coordinate Systems
13.2 Vectors
13.3 The Dot Product
13.4 The Cross Product
13.5 Equations of Lines and
Planes
13.6 Cylinders and Quadric
Surfaces
13.7 Cylindrical and Spherical
Coordinates
14 Vector
Functions (four days)
14.1 Vector Functions and Space
Curves
14.2 Derivatives and Integrals of
Vector Functions
14.3 Arc Length and Curvature
14.4 Motion in Space: Velocity and
Acceleration
15 Partial Derivatives
(ten days)
15.1 Functions of Several
Variables
15.2 Limits
and Continuity
15.3 Partial Derivatives
15.4 Tangent Planes and Linear
Approximations
15.5
The Chain Rule
15.6
Directional Derivatives
and the Gradient Vector
15.7
Maximum and Minimum
Values
15.8 Lagrange
Multipliers
16 Multiple
Integrals (ten days)
16.1 Double Integrals over
Rectangles (review of first three sections)
16.2 Iterated Integrals
16.3 Double Integrals over
General Regions
16.4 Double Integrals in
Polar Coordinates
16.5 Applications of Double
Integrals
16.6 Surface Area
16.7 Triple Integrals
16.8 Triple Integrals in
Cylindrical and Spherical Coordinates
16.9
Change of Variables in
Multiple Integrals