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AP Calculus

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Course Content

Lesson Content

0% Complete 0/16 Steps

[1.1] Concept of Instantaneous Rate of Change

[1.2] Understanding Limits Graphically and Numerically

[1.3] Properties of Limits

[1.4] Limits of Composite Functions

[1.5] Finding Limits by Analytic Methods

[1.6] Limits of Transcendental Functions

[1.7] Limits and Continuity

[1.8] Infinite Limits and Limits at Infinity

[1.9] Intermediate Value Theorem

[1.10] Exploring Types of Discontinuities

[1.11] Defining Continuity at a Point

[1.12] Confirming Continuity over an Interval

[1.13] Removing Discontinuities

[1.14] Connecting Infinite Limits and Vertical Asymptotes

[1.15] Connecting Limits at Infinity and Horizontal Asymptotes

[1.16] Working with the Intermediate Value Theorem (IVT)

Lesson Content

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[2.1] Rates of Change and the Tangent Line Problem

[2.2] Tangent Lines and the Derivative

[2.3] Understanding the Derivative and Linear Approximations

[2.4] Differentiability and Continuity

[2.5] Basic Differentiation Rules

[2.6] Product and Quotient Rules

[2.7] Velocity and Other Rates of Change

[2.8] The Product Rule

[2.9] The Quotient Rule

[2.10] Finding the Derivatives of Tangent, Cotangent, Secant, and/or Cosecant Functions

Lesson Content

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[3.1] The Chain Rule

[3.2] Symbolic Differentiation

[3.3] Implicit Differentiation

[3.4] Derivatives of Inverse Functions

[3.5] Derivatives of Inverse Trig Functions

[3.6] Calculating Higher-Order Derivatives

Lesson Content

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[4.1] Interpretations of the Derivative in Context

[4.2] Straight Line Motion: Connecting Position, Velocity & Acceleration

[4.3] Rates of Change in Other Applications

[4.4] Related Rates

[4.5] Local Linearity and Linearization

[4.6] L’Hospital’s Rule

[4.7] Using L’Hospital’s Rule for Determining Limits of Indeterminate Forms

Lesson Content

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[5.1] The Mean Value Theorem

[5.2] Extrema on an Interval

[5.3] Increasing, Decreasing & First Derivative Test

[5.4] Concavity & Second Derivative Test

[5.5] Sketching Graphs of Functions F, F’ and F”

[5.6] Optimization

[5.7] Using the Second Derivative Test to Determine Extrema

[5.8] Sketching Graphs of Functions and Their Derivatives

[5.9] Connecting a Function, Its First Derivative, and Its Second Derivative

[5.10] Introduction to Optimization Problems

[5.11] Solving Optimization Problems

[5.12] Exploring Behaviors of Implicit Relations

Lesson Content

0% Complete 0/11 Steps

[6.1] Approximating Area with Riemann Sums

[6.2] Sigma Notation and Riemann Sums

[6.3] Accumulation Functions

[6.4] Properties of Definite Integrals

[6.5] Antiderivatives and Indefinite Integrals

[6.6] The Fundamental Theorem of Calculus

[6.7] Integration by Substitution

[6.8] Integrals of Transcendental Functions

[6.9] Integrating Using Substitution

[6.10] Integrating Functions Using Long Division and Completing the Square

[6.14] Selecting Techniques for Antidifferentiation

Lesson Content

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[7.1] Introduction to Differential Equations

[7.2] Slope Fields

[7.3] Separation of Variables

[7.4] Growth and Decay

[7.6] Finding General Solutions Using Separation of Variables

[7.7] Finding Particular Solutions Using Initial Conditions and Separation of Variables

[7.8] Exponential Models with Differential Equations

Lesson Content

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[8.1] Finding Average Value for Integrals

[8.2] Another Look at Particle Motion

[8.3] Accumulation Functions in Applied Contexts

[8.4] Area Between Two Curves

[8.5] Volumes by Cross Sections

[8.6] Volume of Revolution: Disc and Washer Methods

[8.7] Volumes-Revolving Around Other Axes

[8.8] Volumes with Cross Sections: Triangles and Semicircles

[8.9] Volume with Disc Method: Revolving Around the x- or y-Axis

[8.10] Volume with Disc Method: Revolving Around Other Axes

[8.11] Volume with Washer Method: Revolving Around the x- or y-Axis

[8.12] Volume with Washer Method: Revolving Around Other Axes

Lesson Content

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[9.1] Parametric Equations and Calculus

[9.2] Parametric Equations and Arc Length

[9.3] Vector-Valued Functions

[9.4] Velocity Acceleration of Vector Functions

[9.5] Polar Coordinates

[9.6] Area and Arc Length of Polar Coordinates

[9.7] Defining Polar Coordinates and Differentiation in Polar Form

[9.8] Find the Area of a Polar Region or the Area Bounded by a Single Polar Curve

[9.9] Finding the Area of the Region Bounded by Two Polar Curves

Lesson Content

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[10.1] Series and Convergence

[10.2] Integral Test p-Series

[10.3] Comparison of Series

[10.4] Alternating Series

[10.5] Ratio and Root Tests

[10.6] Taylor Polynomials

[10.7] Lagrange Error Bound

[10.8] Power Series & Intervals of Convergence

[10.9] Taylor and MacLaurin Series

[10.10] Representing Functions by Power Series

[10.11] Finding Taylor Polynomial Approximations of Functions

[10.12] Lagrange Error Bound

[10.13] Radius and Interval of Convergence of Power Series

[10.14] Finding Taylor or Maclaurin Series for a Function

[10.15] Representing Functions as Power Series

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