MT 283 - Calculus and Analytic Geometry III

• compute the unit tangent and unit normal vectors for a given curve;
• determine the velocity and acceleration vectors of an object when the position vector is specified;
• calculate the sum, difference, dot and cross products of vectors;
• convert coordinates between rectangular, cylindrical and spherical systems;
• compute the partial derivatives for n space and determine related directional derivatives and gradients;
• calculate the maximum and minimum points in n space by use of Lagrange multipliers;
• perform multiple-integration and use this approach to calculate surface area, volume, centroids, and center of mass;
• evaluate line integrals and use this technique to calculate the amount of work performed; and
• identify the Divergence Theorem, Green’s Theorem, and Stokes’ Theorem, and apply this to applications in physics.

Laboratory Objectives: At the end of the course, the student should be able to use the computer algebra system “Maple” for performing various mathematical procedures. These procedures include, but are not limited to the following:

• operations and computations;
  • simplifying and/or evaluating expressions and functions;
  • solving equations;
  • computing limits of functions of one and multiple variables;
  • differentiation: explicit, implicit, partial;
  • integrals;
    definite, indefinite,
    single, multiple, line
    in rectangular, polar, cylindrical, and spherical coordinates
  • maximization and minimization with constraints; using LaGrange multipliers;
  • finding areas, surface areas and volumes in the various coordinate systems: rectangular, polar, cylindrical, and spherical coordinates;
  • finding a tangent plane and a normal line for a surface in case the function has continuous partial derivative in x and y; and
  • finding a tangent and a normal to a space curve.
• two and three dimensional graphics;
  • graphing in rectangular, polar, cylindrical, and spherical coordinates;
  • graphing parametric curves and surfaces in space;
  • plotting two or more functions at once;
  • graphing level curves of functions of two variables; and
  • graphing vector fields in two and three dimensions.
• matrices and vectors;
  • defining matrices and vectors;
  • matrix addition and multiplication; finding determinants and inverses; solving a linear system of equations;
  • dot and cross products; norms;
  • finding the area of a parallelogram and the volume of a parallelepiped;
  • finding the point on a line (or plane) that is closest to a given point not on the line (or the plane);
  • finding the extreme distances between a point and a curve; and
  • finding the intersection of a line and a surface.
• vector calculus;
  • applications on Green’s Theorem, the Divergence Theorem, and Stokes’ Theorem.