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Calculus AB Review
Review of material covered in calculus AB, including basic integrals, finding integrals through u-substitution, and the trapezoidal rule. -
Differential Equations
Differential equations can be modeled by a slope field and are solved using the seperation of variables. The constant should always be kept with the dx term. When the rate of change is proportional to the amount present, the function is exponential. Logistic growth functions have a carrying capacity and grow the fastest at half of the carrying capacity, -
Taylor Polynomials
Taylor polynomials can be used to approximate a function. They are useful for expressing transcendental functions as a sum of polynomials. A first degree taylor polynomial is a tangent line, and a taylor polynomial centered at zero is a Maclaurin polynomial. -
Advanced Integration Techniques
After regular integration techniques cannot be used, techniques such as integration by parts can be used. Integration by parts splits up the integral into u and dv and uses the product rule. In addition, trig substitution allow for the solving of integrals such as sqrt(1+x^2) -
Solids of Revolution
By using the formula for the area of a cylinder, the disk method can be obtained. Using the integral from a to b of pi*f(x)dx (for a curve revolved around the x-axis), the volume of the solid can be obtained. If the solid is revolved around the y-axis, the two possible methods are changing the limits of integration and solving for y, or using the shell method. -
Polar Equations Review
On this date, a review of polar equations was completed for the test. Topics included were c=polar coordinates, conversion between polar and rectangular equations, derivatives (which can also be used for arc length), and area. In order to convert between polar and rectangular, y=r*sin(theta) and x=r*cos(theta) can be used.
