Course Objectives:

1.         Grasp and implement polar coordinates for finding tangent lines, areas of regions and lengths of arcs.
2.         Develop basic skills and making steady progress in vector theory, explain how to implement dot product and cross product of vectors for solving real world problems.
3.         Be able to differentiate functions in two variables and find directional derivatives, gradients and divergences.
4.         Calculate double, triple integrals, line integrals and surface integrals.
5.         Attain some conceptual understanding of Gauss Theorem and Stokes’ Theorem.
6.         Increase the quality and quantity of mathematical communication and use integral calculus to solve applied problems
 
 

Topical Outline:

1.         Convert the Polar equation into Cartesian form.
2.         Calculate the area of a region in polar coordinates.
3.         Compute dot, cross and triple product for vectors in 3-space.
4.         Find the parametric equations of the line in 3-space.
5.         Construct the equation of the plane in 3-space.
6.         Write the equation of a curve in parametric form.
7.         Analyze quadric surfaces.
8.         Express the equation of the surface in cylindrical coordinates.
9.         Evaluate the arc length of the vector-valued function.
10.       Find the curvature of the vector-valued function.
11.       Determine the acceleration of a particle moving along a given curve.
12.       Compute partial derivatives for a given function.
13.       Estimate the total differential and approximation of the change in F (x, y) as (x, y) varies from P to Q.
 14.      Evaluate the gradient of a function.
15.       Construct the equation of the tangent plane to the surface at a given point.
16.       Evaluate the double integral.
17.       Determine the triple integral.
18.       Find the Jacobian.
19.       Compute the divergence of the vector field.
20.       Calculate the line integral.
21.       Evaluate the potential function for a conservative vector field.
22.       Determine the flux integral.
23.       Apply the Green’s theorem for line integrals.
24.       Demonstrate the divergence theorem and flux integral.