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.

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MATH 221: Calculus III

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

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 II

Show how to evaluate the triple integrals.

14.6 Triple Integrals I

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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