Students will apply the rules of integration to functions
Integration
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Apply the definition of the integral to model problems in physics, economics, etc, obtaining results in terms of integrals
Demonstrate knowledge of the Fundamental Theorem of Calculus, and use it to interpret integrals as anti-derivatives.
Use definite integrals in problems involving area, velocity, acceleration, and the volume of a solid
Compute, by hand, the integrals of a wide variety of functions using substitution.
Students will integrate functions of the form z = f(x, y) or w = f(x, y, z)
Define, use, and interpret double and triple integrals in terms of volume and mass.
Represent integrals of vectors as double and triple integrals.
Integrate functions through various techniques such as changing the order of integration, substituting variables, or changing to polar coordinates.
Students will apply and interpret the theorems of Green, Stokes, and Gauss.
Apply line and surface integrals to functions representing real world phenomena
Recognize, understand, and use line integrals that are independence of path.
Define and apply the gradient, the divergence, and the curl in terms of integrals of vectors.
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