Calculus III

    Calculus 3 explores the ideas of functions in multiple variables and graphing in three dimensions.  From here, we investigate vectors, multivariable functions, partial differentiation, multiple integrals, and vector calculus.

Calculus 3 videos include the following topics:

1.   Parametric Equations and Polar Coordinates (Coming Soon)

      We begin this subject exploring parametric and polar equations including the introduction of Parametric Equations, Slope of Tangent Lines and Arc Length of Parametric Equations, the Introduction of the Polar Coordinate System, Graphing Polar Equations, Areas and Arc Lengths in Polar Coordinates, and Revisiting Conic Sections in Polar Coordinates. 

2.   Vectors and 3-Space

       Extending our abilities to three dimensional space, we begin by exploring vectors and continuing our investigation of equations and graphs of figures in three dimensions.  Sections include: Vectors in 2-Space; 3-Space, the Rectangular Coordinate System in Three Dimensions; Vectors in 3-Space; The Dot and Cross Products; Lines in 3-Space; Planes; Cylinders and Spheres; and Quadrric Surfaces and Surfaces of Revolution.

3.   Vector-Valued Functions (Coming Soon)

      Extending graphing in three dimenions and vectors, we introduce vector-valued functions.  Here, we explore how to evaluate and graph vector-valued functions; Applying this notion to Motion on a Curve and understanding Velocity and Acceleration Functions; and continue to Curvature and Compents of Accelerations

4.   Differential Calculus of Functions of Several Variables (Coming Soon)

      Here, we now explore the ideas of multivariable functions; continuity, differentiation, The Directional Derivative; and Extrema of Functions of Two Variables.  Sections include: Functions of Two or More Variables; Limits and Continuity; Partial Differentiation; The Differential and Differentiability; Exact Differentials; The Chair Rule; The Directional Derivative; Tangen Planes and Normal Lines; Extrema for Functions of Two Variables;the Method of Least Squares; and Lagrange Multipliers.

5.   Integral Caclulus of Functions of Several Variables (Coming Soon)

      This Topic explores both Double and Triple Integrals and different coordinate systems and their applications.  Sections include: The Double Integral; Iterated Integrals; Evaluation of Double Integrals; Center of Mass and Moments; Surface Area; The Triple Integral; Triple Integrals in OtherCoordinate Systems; Cylindraical Coordinates; Sphereical Coordinates; and Change of Variables in Multiple Integrals.

6.   Vector Integral Calculus (Coming Soon)

   We conclude this subject with the combination of vectors, multi-variable functions, multiple integrals and applications creating the Vector Integral Calculus.  Sections include: Line Integrals; Line Integrals Independent of the Path; Greens Theorem; Surface Integrals; Divergence and Curl; Stokes Theorem; and the Divergence Theorem.