MATH162A

Use substitution to find anti-derivatives

Use substitution to find definite integrals

Use algebraic substitutions

Find the exact area between curves using dx and dy integrals

Find the exact average value of a function on an interval

Find volumes of rotation using discs and washers using dx and dy integrals

Find volumes of rotation using cylindrical shells using dx and dy integrals

Work backwards and explain the solid represented by a given volume integral

Apply integration by parts to product rule integration problems

Use integration by parts to find the anti-derivative of inverse functions whose derivatives are known

Use integration by parts to derive and prove reduction formulas

Evaluate definite and indefinite trigonometric integrals by using trigonometric identities and substitution

Evaluate certain trigonometric integrals by using trigonometric identities and fold-back integration by parts

Use trigonometric substitutions when necessary

Rewrite rational functions using long division and partial fractions

Find definite and indefinite integrals of rational functions, including exact values

Employ useful strategies for finding integrals, including integrals that require multiple methods

Effectively use tables of integrals when so instructed

Use the midpoint rule and Simpsons Rule to approximate integrals

Find upper bounds for errors in approximating integrals and the required number of subintervals for a given degree of accuracy

Evaluate improper integrals at infinity and improper integrals with a vertical asymptote as a boundary

Evaluate improper integrals with asymptotes inside the domain

Evaluate improper integrals that require substitution or LHospitals Rule

Apply improper integrals to certain area, volume, and average value problems

Find arc length using dx and dy integrals

Find areas of surfaces of revolutions using dx and dy integrals

Understand probability distribution functions, determine unknown coefficients, and estimate probabilities

Find the median and various percentiles of a given probability distribution function

Find the mean of a given probability distribution function

Find the centroid of a given region in quadrant I, including infinite regions

Use the centroid and Pappas Theorem to find exact volumes of revolution

Find the pressure and total force applied in hydrostatic pressure problems

Use the market equilibrium price, demand curve, and supply curve to find producers and consumers surplus

Use integrals to solve certain biology and ecology problems, including average values

Sketch parametric curves and find points with horizontal tangents

Find points on parametric curves with vertical tangents or undefined slopes

Find concavity at various points on a parametric curve

Use parametric equations to find areas and volumes

Find the arc length of parametric equations

Sketch accurate graphs of polar equations, including equations with negative radii

Convert polar equations to rectangular equations and vice versa

Find the exact area enclosed by various polar graphs

Find the exact area between two polar graphs

Sketch conic sections, including foci and asymptotes

Identify conic sections by completing squares

Identify conic sections in polar form

Understand the difference between sequences and series

Understand the differences among divergence, convergence, and absolute convergence

Use a calculator (and recursion) to approximate infinite series

Use the rules for geometric series

Apply the integral test to a given series

Use improper integrals to estimate the value of a convergent series

Use the limit comparison test and other comparisons to investigate the convergence or divergence of positive series

Understand and apply the Alternating Series Test

Understand and apply the Ratio Test and Root Test

Apply convergence tests to find the radius and interval of convergence for a given power series

Find the exact value of function defined by a power series for a given x value

Become familiar with the power series representations of certain transcendental functions, including hyperbolics

Use power series to rewrite composite functions and products of polynomials and transcendentals

Use power series to find derivatives anti-derivatives of transcendental functions and various products of functions

Construct a Taylor Series for an analytic function

Construct a Maclaurin Series for an analytic function

Use properties and identities to evaluate transcendental functions outside the domain of their power series