DACC home page About Us Contact Us For Students For Employees Index / Search
Catalog

Table of Contents | Areas of Study | Mathematics | MATH140 syllabus

COURSE NUMBER:
MATH140
COURSE TITLE:
Calculus & Analytic Geometry III
IAI CODE(S):
M1 900 EGR 903 MTH 903
SEMESTER CREDIT HOURS:
3

COURSE DESCRIPTION:
A third course of integrated calculus and analytic geometry; topics include vectors in 2 and 3 dimensions, vector operations, lines and planes in space, quadric surfaces, cylindrical and spherical coordinates, partial derivatives, directional derivatives, gradients, double and triple integrals and their applications. Both the understanding of theoretical concepts and the ability to use manipulative techniques are considered of prime importance.

PREREQUISITES:
Grade of "C" or better in MATH130

COURSE OBJECTIVES / GOALS:
The student should be able to do the following tasks:

  • Find the length of a vector in three-space
  • Find the unit vector in the direction of a given vector
  • Determine whether a set of vectors is linearly independent or linearly dependent
  • Express a vector as a linear combination of a set of linearly independent vectors
  • Find the cosine of the angle between two vectors in three-space
  • Calculate scalar product of two vectors
  • Calculate vector product of two vectors
  • Calculate scaler triple product of three vectors
  • Differentiate vector functions
  • Integrate vector functions
  • Find the tangential and normal components of a vector function
  • Understand the following concepts relating vectors, curves, and surfaces in space

    • Vector equation of a line
    • Parametric equation of a line
    • Symmetric equation of a line
    • Vector equation of a plane
    • Scalar equation of a plane
    • Angle between given planes
    • The arc length function
    • Curvature of space curves
    • Planes and traces
    • Cylinders and rulings
    • Surface of revolution

      
  • Draw the following quadric surfaces and their level curves by using the software in the computer lab:

    • Ellipsoid
    • Elliptic paraboloid
    • Elliptical cone
    • Hyperboloid of one sheet
    • Hyperboloid of two sheets
    • Hyperbolic paraboloid

      
  • Be able to use the following three coordinate systems:

    • Rectangular coordinates
    • Cylindrical coordinates
    • Spherical coordinates

      
  • Understand the following concepts related to partial derivatives:

    • Definition of partial derivatives
    • Notation for partial derivatives
    • Instantaneous rates of change
    • Geometric interpretation of partial derivatives
    • Planes tangent to surfaces
    • Higher-order partial derivatives
    • Limits and continuity of functions of more than one variable
    • Implicit differentiation on functions of several variables
    • Chain rule to obtain partial derivatives
    • The total differential of a function

      
  • Understand the following applications of partial and total derivatives:

    • Finding local extrema
    • Finding global extrema
    • Highest and lowest points of surfaces
    • Applied maximum-minimum problems
    • Increments and differentials
    • The linear approximation theorem
    • Differentiabiltiy of multivariable functions
    • Lagrange multipliers (one constraint)
    • Lagrange multipliers in three dimensions
    • Problems that have two constraints
    • Sufficient conditions for local extrema

      
  • Determine the existence of an exact differential
  • Learn the definition and properties of a double integral
  • Evaluate double integral
  • Apply the double integral concept to the following applications:

    • Density and mass
    • Volume of revolution
    • Surface area of revolution
    • Moments of inertia

      
  • Evaluate double integrals by polar coordinates
  • Learn the definition and properties of a triple integral
  • Evaluate triple integrals
  • Understand and use the following basic concepts of the field theory:

    • The gradient vector field
    • The divergence of a vector field
    • The curl of a vector field
    • Line integral of a function along a curve
    • Line integrals with respect to coordinate variables
    • Line integrals and vector fields
    • Equivalent line integrals
    • The fundamental theorem for line integrals
    • Independence of path
    • Conservative field and potential functions
    • Conservative force and conservation of energy
    • Green's theorem
    • The divergence and flux of a vector field
    • Surface integrals with respect to coordinate elements
    • The flux of a vector field
    • The divergence theorem
    • More general regions and Gauss's law
    • Stokes' Theorem
    • Conservation and irrotational fields


TEXTBOOK / SPECIAL MATERIALS:

  • Edwards & Penney, Calculus with Analytic Geometry, 6th Edition, Prentice-Hall, 1998.

EVALUATION:

  • Four hourly exams are given during the semester.  These examinations determine 50% of the grade.  A comprehensive final exam is given which accounts for 25% of the grade, and homework and/or projects using programmable calculators or computers account for 25% of the grade.
  • Determination of grade based upon all work completed is as follows:

    • A = 90% - 100%
    • B = 80% -   89%
    • C = 70% -   79%
    • D = 60% -   69%
    • F < 60%


BIBLIOGRAPHY:

  • Ellis, Robert and Gulick, Denny; Calculus with Analytic Geometry, Fifth Edition, 1994.
  • Mathematica Software, Wolfram Research, Inc., 100 Trade Center Drive, Champaign, IL  61820-7237
  • Calculus Projects for Mathematica by James Kirkwood, 1994. Wm. C. Brown.

REVISION:
Fall 2001 10/02/2001

RECORD UPDATED:
2002/04/02 07:19:24