MATH212

Evaluate definite integrals and antiderivatives by using a variety of techniques of integration including substitution, integration by parts, and partial fractions.

Differentiate and integrate functions that are the product, quotient, and composition of trigonometric and inverse trigonometric functions with other functions.

Approximate solutions using numerical techniques including the Newton-Raphson Method, Euler's Method, and numerical integration techniques.

Set up and solve applications of the definite integral including finding volumes of solids and calculating work and hydrostatic force.

Calculate partial derivatives of functions of several variables and interpret the results.

Find extrema of functions of several variables using the Second Derivative Test, the Extreme Value Theorem (extended to functions of two variables), and Lagrange Multipliers.

Set up and evaluate double integrals to find the volume under a surface and above the x-y plane.

Derive Taylor Polynomials and Maclaurin Series for variations of familiar functions.

Sketch solutions to the differential equation for various initial values (given a slope field).

Solve first-order, separable differential equations with and without initial values.

Sketch a qualitative solution to a differential equation without solving that equation explicitly.

Determine whether a differential is exact and if so find the function of two variables that generates such a differential.