11.3 Dot Product II

Apply dot product to find angles in a triangle.  Introduce the projection vector. Demonstrate the use of website.

11.3 Dot Product I

Define dot product apply to find the angle between two vectors. Demonstrate the use of website.

11.2 Vectors II

11.2 Vectors I

Introduce vectors. Show how to find components, lengths, unit vectors, vector sums, and scalar multiples. Demonstrate vectors graphically.

14.6 Triple Integrals IV

Show how to find the centroid/center of mass of a solid by setting up the order of integration and limits and evaluate the triple integrals. Use a website to check the answers.

14.6 Triple Integrals III

Show how to set up the order of integration and limits to for the volume of a solid and evaluate the triple integral. Use a graphing utility to show different views of the solid in 3D and 2D and a website to check the answers.

14.6 Triple Integrals II

Show how to set up the order of integration and limits to find the volume of a solid.  Use a graphing utility to show different views, both 3D and 2D, of the solid.

14.6 Triple Integrals I

Show how to evaluate the triple integrals.

14.5 Moments and Center of Mass I

Show how to find the centroid and center of mass using double integrals.

14.5 Momemts and Center of Mass I

Show how to determine the absolute maximum and absolute minimum of f with a given domain, bounded region. Use the website to check answers.

13.9 Extreme Values III

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Show how to sketch the region of integration, change the order of integration, and evaluate the double integral. Use websites for graphs and check answers.

14.2 Double Integrals Over Gen R I

Introduce the definition of partial derivatives of functions of two variables. Use a website to demonstrate the partial derivatives. Show how to find the first order partial derivatives using the definition and rules of differentiation.

13.4 Partial Derivatives I

Lagrange Multipliers

Apply Lagrange Multiplier to determine the maximum and minimum of f subject to a constraint. Use a website to demonstrate the geometric and graphical interpretation and a website to check the answers.

13.10 Lagrange Multipliers II

13.4 Partial Derivatives IV

13.4 Partial Derivatives III

13.2 Limits II

13.4 Partial Derivatives II

14.2 Double Integrals Over Gen R IV

14.2 Double Integrals Over Gen R III

14.2 Double Integrals Over Gen R II

14.1 Double Integrals Over Rectangles I

Rectangles II

14.1 Double Integrals Over Rectangles II

Show how to determine dependent and independent variables in a function with constrained variables. Find the total differential equations and the corresponding partial derivatives.

13.11 Partials w Constrained Variables II

Show how to develop the procedure for the Lagrange Multiplier. Apply to determine the maximum and minimum of f subject to a constraint. Use a website to demonstrate the geometric and graphical interpretation and a website to check the answers.

13.10 Lagrange Multipliers I

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