24136 Calculus (4)

Course Description

Topics include: Multi-variable functions, partial derivatives(function of two or more variables, limits and continuity, partial derivatives, chain rule, non independent variables, gradients, directional derivatives and tangent plans, higher order derivatives, partial deferential equations from physics, linear approximation and increment estimation, maxima, minima, and saddle points, Lagrange multipliers, least square), multiple integrals, area physical applications changing to polar coordinates, triple integrals in rectangular coordinates, physical applications in three dimensions, integrals in cylindrical and spherical coordinates, surface area) integration in vector fields(Green’s theorem, surface area and surface integrals, parameterized surfaces, stoker’s theorem, divergence theorem and a unity theory).

Learning Objective

  • Upon completion of this course, the student should be able to:
  • 1. Define functions of several variables and their limits
  • 2. Calculate the partial derivatives of functions of several variables
  • 3. Apply the chain rule for functions of several variables
  • 4. Calculate the gradients and directional derivatives of functions of several variables 5. Solve problems involving tangent planes and normal lines 6. Determine the extrema of functions of several variables 7. Use the Lagrange multiplier method to find extrema of functions with constraints 8. Define double integrals over rectangles 9. Compute iterated integrals 10. Define and compute double integrals over general regions 11. Compute double integrals in polar coordinates 12. Find moments and centers of mass using double integrals 13. Compute triple integrals in Cartesian coordinates, cylindrical coordinates and spherical coordinates 14. Define vector fields 15. Use Green’s theorem to evaluate line integrals along simple closed curves 16. Compute surface integrals 17. Apply Stokes’ theorem to compute line integrals along the boundary of a surface



Books for this Course

  • Culculus with Analytic Geometry(Alternative Edition), Earl W.Swokowski

Times Offered

  • September
  • January

Course Prerequisite