Multivariable Calculus
  • Final
  • Mathematics
  • Multivariable Calculus
  • 4.0
  • Vector valued functions, calculus of functions of more than one variable, partial derivatives, multiple integration, Green’s Theorem, Stokes’ Theorem, divergence theorem.

  • 230
  • One year of Single Variable Calculus (C-ID MATH 210 and MATH 220 OR C-ID MATH 211 and MATH 221 OR C-ID MATH 900S)

  • None

  • None

    1. Vectors and vector operations in two and three dimensions;
    2. Vector and parametric equations of lines and planes; rectangular equation of a plane;
    3. Dot, cross, and triple products and projections;
    4. Differentiability and differentiation including partial derivatives, chain rule, higher-order derivatives, directional derivatives, and the gradient;
    5. Arc length and curvature; tangent, normal, binormal vectors;
    6. Vector-valued functions and their derivatives and integrals; finding velocity and acceleration;
    7. Real-valued functions of several variables, level curves and surfaces;
    8. Limits, continuity, and properties of limits and continuity;
    9. Local and global maxima and minima extrema, saddle points, and Lagrange multipliers;
    10. Vector fields including the gradient vector field and conservative fields;
    11. Double and triple integrals;
    12. Applications of multiple integration such as area, volume, center of mass, or moments of inertia;
    13. Change of variables theorem;
    14. Integrals in polar, cylindrical, and spherical coordinates;
    15. Line and surface integrals including parametrically defined surfaces;
    16. Integrals of real-valued functions over surfaces;
    17. Divergence and curl; and
    18. Green’s, Stokes’, and divergence theorems.

  • Upon successful completion of the course, students will be able to:

    1. Perform vector operations;
    2. Determine equations of lines and planes;
    3. Find the limit of a function at a point;
    4. Evaluate derivatives;
    5. Write the equation of a tangent plane at a point;
    6. Determine differentiability;
    7. Find local extrema and test for saddle points;
    8. Solve constraint problems using Lagrange multipliers;
    9. Compute arc length;
    10. Find the divergence and curl of a vector field;
    11. Evaluate two and three dimensional integrals; and
    12. Apply Green’s, Stokes’, and divergence theorems.

  • Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems.

  • A college level textbook designed for science, technology, engineering and math majors, and supporting the learning objectives of this course.

  • March 31, 2011