Calc 2 Final

Integration by Parts

A technique for integrating the product of two functions, based on the product rule for differentiation.

Trigonometric Integrals

Integrals that involve trigonometric functions, often requiring specific techniques for evaluation.

Trigonometric Substitution

A method used to simplify integrals by substituting trigonometric functions for algebraic expressions.

Integration of Rational Functions by Partial Fractions

A technique that expresses a rational function as a sum of simpler fractions to facilitate integration.

Improper Integrals

Integrals with infinite limits or integrands that approach infinity within the integration limits.

Approximate Integration

Techniques to estimate the value of definite integrals when an exact form is difficult to obtain.

Arc Length

The length of a curve defined by a function over a given interval.

Area of a Surface of Revolution

The area of a 3D surface generated by rotating a curve around an axis.

Modeling with Differential Equations

Using differential equations to represent real-world phenomena mathematically.

Direction Fields

A graphical representation of the slopes of solutions to a differential equation.

Euler's Method

A numerical method for approximating solutions to first-order differential equations.

Separable Equations

Differential equations that can be separated into two integrable parts.

Exponential Growth and Decay Models

Mathematical models representing populations or quantities that grow or decay exponentially.

Logistic Models

A type of growth model that accounts for carrying capacity in a population.

First-Order Linear Differential Equations

Differential equations of the form dy/dx + P(x)y = Q(x), where P and Q are continuous functions.

Curves Defined by Parametric Equations

Curves that are described using parameters instead of a single function.

Calculus with Parametric Curves

Calculating derivatives and integrals involving parametric equations.

Polar Coordinates

A coordinate system where points are defined by a distance from a reference point and an angle from a reference direction.

Areas and Lengths in Polar Coordinates

Calculating areas and lengths of curves represented in polar coordinates.

Conic Sections

The curves obtained by intersecting a plane with a cone, including ellipses, parabolas, and hyperbolas.

Sequences

Ordered lists of numbers defined by a specific rule.

Series

The sum of the terms of a sequence.

Integral Test

A method for determining the convergence of a series by comparing it to an integral.

Comparison Tests

Techniques to determine the convergence of a series by comparing it to another series.

Alternating Series

Series whose terms alternate in sign.

Absolute Convergence

A series is absolutely convergent if the series of absolute values of its terms converges.

Conditional Convergence

A series that converges, but does not converge absolutely.

Ratio and Root Tests

Tests used to determine the convergence of series based on the ratio or root of terms.

Power Series Representations of Functions

Expressing functions as infinite sums of powers of a variable.

Taylor and MacLaurin Series

Specific types of power series that represent functions as an infinite sum of derivatives evaluated at a point.