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Calculus BC

Calculus BC

Mastering additional advanced topics in calculus, such as infinite series, sequences, parametric equations, and vectors.

Limits & Continuity

Meaning of Limits
Properties of Limits
Direct Substitution
Algebraic Manipulation
Squeeze Theorem
Limits from Graphs
Limits from Tables
Continuity
Infinite Limits
Limits at Infinity
Application of Limits

Derivatives

Meaning of Derivatives
Differentiability & Continuity
Intermediate and Mean Value Theorem
Rules for Differentiation
Transcendental Functions
Trigonometric Functions
Implicit Differentiation
Inverse Function
Higher Order Derivatives

Applications of Derivatives

Meaning of a Derivative in Context
Position, Velocity, & Acceleration
Rates of Change
Related Rates
Approximating Values of a Function
Extreme Value Theorem
Increasing & Decreasing Functions
Mean Value Theorem
Points of Inflection
L’Hopital’s Rule
Graphs of Functions
Connecting First & Second Derivatives
Optimization
Implicit Relations

Definite Integral

Riemann Sums
Definite Integral
Properties of Definite Integrals
Connecting Integral & Differential Calculus
Antiderivatives and Indefinite Integrals
Integration Using Substitution
Long Division & Completing the Square
Integration by Parts
Linear Partial Fractions
Improper Integrals

Differential Equations

Modeling with Differential Equations
Solutions for Differential Equations
Slope Fields
Euler’s Method
General Solutions
Particular Solutions
Exponential Models
Logistic Models

Applications of Integrals

Average Value
Position, Velocity, & Acceleration
Accumulation Functions & Definite Integrals
Area under a Curve
Volume of a Solid
Disc Method
Washer Method
Planar Curve

Parametric Equations

Differentiating Parametric Equations
Second Derivatives
Arc Length of Curves

Vector-Valued Functions

Differentiating Vector-Valued Functions
Integrating Vector-Valued Functions
Motion Problems

Polar Coordinates

Differentiating in Polar Form
Area Problems

Infinite Sequences and Series

Convergent & Divergent Infinite Series
Geometric Series
Test for Divergence
Test for Convergence
Harmonic Series and p-Series
Comparison Tests for Convergence
Alternating Series Test for Convergence
Ratio Test for Convergence
Conditional Convergence
Alternating Series
Taylor Polynomial
Lagrange Error Bound
Radius & Interval of Convergence
Taylor & Maclaurin Series
Power Series