This course is a continuation of Calculus II. Topics include vectors, vector valued functions, partial differentiation, multiple integrals, space geometry, and vector calculus. Podcast items include both video lectures and handouts in PDF format. Use of technology such as graphing calculators and w…
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Apply dot product to find angles in a triangle. Introduce the projection vector. Demonstrate the use of website.
Define dot product apply to find the angle between two vectors. Demonstrate the use of website.
Introduce vectors. Show how to find components, lengths, unit vectors, vector sums, and scalar multiples. Demonstrate vectors graphically.
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.
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.
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.
Show how to find the centroid and center of mass using double integrals.
Show how to determine the absolute maximum and absolute minimum of f with a given domain, bounded region. Use the website to check answers.
Show how to change from Cartesian integral to polar integral, set up region of integration, and limits. Evaluate the polar integrals. Use websites and graphing utility to graph polar plots and check answers.
Show how to set up the region of integration, limits, and the double integral for the volume of the solid. Evaluate the integral. Use a graphing utility to get different views of the solids and a website to check the answers.
Given the double integral, show how to sketch the region of integration, reverse the order of integration, and evaluate. Use a website to check the answers.
Show how to sketch the region of integration, reverse the order of integration, set up the limits, and evaluate the double integral. Show how to find the average value of f and use a website to check the answers.
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.
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.
Show how to apply second derivative test to determine the local maximum, local minimum, and saddle point(s) of z = f(x, y). Use the website to demonstrate and enhance the understanding of the concepts.
Show how to determine dependent and independent variables in a function with constrained variables. Find the total differential equations and the corresponding partial derivatives.
Show how to determine dependent and independent variables in a function with constrained variables. Find the total differential equations and the corresponding partial derivatives.
Show how to set up dxdy or dydx to evaluate iterated integrals and find the volume of a solid. Use a website to check answers.
Introduce double integrals. Use Riemann sum for estimation. Show how to evaluate iterated integrals. Use a website to check answers.
Show how to find absolute maximum and absolute minimum of z = f(x, y) with given domain. Use the website to demonstrate and enhance the understanding of the concepts.
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