Calc 2 Final

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30 Terms

1

Integration by Parts

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

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2

Trigonometric Integrals

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

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3

Trigonometric Substitution

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

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4

Integration of Rational Functions by Partial Fractions

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

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5

Improper Integrals

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

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6

Approximate Integration

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

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7

Arc Length

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

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8

Area of a Surface of Revolution

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

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9

Modeling with Differential Equations

Using differential equations to represent real-world phenomena mathematically.

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10

Direction Fields

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

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11

Euler's Method

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

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12

Separable Equations

Differential equations that can be separated into two integrable parts.

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13

Exponential Growth and Decay Models

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

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14

Logistic Models

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

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15

First-Order Linear Differential Equations

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

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16

Curves Defined by Parametric Equations

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

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17

Calculus with Parametric Curves

Calculating derivatives and integrals involving parametric equations.

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18

Polar Coordinates

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

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19

Areas and Lengths in Polar Coordinates

Calculating areas and lengths of curves represented in polar coordinates.

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20

Conic Sections

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

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21

Sequences

Ordered lists of numbers defined by a specific rule.

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22

Series

The sum of the terms of a sequence.

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23

Integral Test

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

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24

Comparison Tests

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

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25

Alternating Series

Series whose terms alternate in sign.

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26

Absolute Convergence

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

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27

Conditional Convergence

A series that converges, but does not converge absolutely.

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28

Ratio and Root Tests

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

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29

Power Series Representations of Functions

Expressing functions as infinite sums of powers of a variable.

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30

Taylor and MacLaurin Series

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

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