Math& 254

Several Variable Calculus

LEARNING OUTCOMES

 

Upon successful completion of Math& 254, the student should be able to:

 

  1. Visualize, plot and interpret points, lines, vectors, curves, and surfaces in 2-D and 3-D.

 

  1. Translate among rectangular, cylindrical and spherical coordinate systems and state some advantages and disadvantages of each system.

 

  1. Perform basic vector operations and apply these operations.

 

  1. Write equations for and solve problems involving lines and planes and their intersections.

 

  1. Interpret the fundamental ideas of rates of change and accumulation for curves in higher dimensions:

i.         tangent vectors,

ii.      arc length,

iii.    curvature,

iv.    simple line integrals.

 

  1. Interpret the fundamental ideas of rates of change and accumulation for surfaces in higher dimensions:

i.         partial derivatives,

ii.      directional derivatives,

iii.    tangent planes,

iv.    gradient vectors,

v.       max/min applications,

vi.    volumes & surface areas.

 

  1. Use CAS and the listed tools to solve multi-step problems and applications.