Calculus
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  • List of Lessons
  • Version #1
    • Unit 0 >
      • 0.1 Summer Packet
      • 0.2 Calculator Skillz
    • Unit 1 >
      • 1.1 Can Change Occur at an instant
      • 1.2 Defining Limits and Using Limit Notation
      • 1.3 Limit Values from Graphs
      • 1.4 Limit Values from Tables
      • 1.5 Determining Limits Using Algebraic Properties
      • 1.6 Determining Limits Using Algebraic Manipulation
      • 1.7 Selecting Procedures for Determining Limits
      • 1.8 Determining Limits Using the Squeeze Theorem
      • 1.9 Connecting Multiple Representations of Limits
      • mid-Unit 1 Review
      • 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 Infinite Limits and Vertical Asymptotes
      • 1.15 Limits at Infinity and Horizontal Asymptotes
      • 1.16 Intermediate Value Theorem
      • End of Unit 1 Review
    • Unit 2 >
      • 2.1 Defining Average and Instantaneous Rate of Change at a Point
      • 2.2 Defining the Derivative of a Function and Using Derivative Notation
      • 2.3 Estimating Derivatives of a Function at a Point
      • 2.4 Connecting Differentiability and Continuity
      • 2.5 Applying the Power Rule
      • 2.6 Derivative Rules: Constant, Sum, Difference, and Constant Multiple
      • 2.7 Derivatives of cos(x), sin(x), e^x, and ln(x)
      • 2.8 The Product Rule
      • 2.9 The Quotient Rule
      • 2.10 Derivatives of tan(x), cot(x), sec(x), csc(x)
      • Unit 2 Review
    • Unit 3 >
      • 3.1 The Chain Rule
      • 3.2 Implicit Differentiation
      • 3.3 Differentiating Inverse Functions
      • 3.4 Differentiating Inverse Trigonometric Functions
      • 3.5 Selecting Procedures for Calculating Derivatives
      • 3.6 Calculating Higher-Order Derivatives
      • Unit 3 Review
    • Unit 4 >
      • 4.1 Interpreting the Meaning of the Derivative in Context
      • 4.2 Straight-Line Motion: Connecting Position, Velocity, and Acceleration
      • 4.3 Rates of Change in Applied Contexts Other Than Motion
      • 4.4 Introduction to Related Rates
      • 4.5 Solving Related Rates Problems
      • 4.6 Approximating Values of a Function Using Local Linearity and Linearization
      • 4.7 Using L'Hopital's Rule for Determining Limits of Indeterminate Forms
      • Unit 4 Review
    • Unit 5 >
      • 5.1 Using the Mean Value Theorem
      • 5.2 Extreme Value Theorem, Global Versus Local Extrema, and Critical Points
      • 5.3 Determining Intervals on Which a Function is Increasing or Decreasing.
      • 5.4 Using the First Derivative Test to Determine Relative Local Extrema
      • 5.5 Using the Candidates Test to Determine Absolute (Global) Extrema
      • 5.6 Determining Concavity of Functions over Their Domains
      • 5.7 Using the Second Derivative Test to Determine Extrema
      • mid-Unit 5 Review
      • 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
      • End of Unit 5 Review
    • Unit 6 >
      • 6.1 Exploring Accumulation of Change
      • 6.2 Approximating Areas with Riemann Sums
      • 6.3 Riemann Sums, Summation Notation, and Definite Integral Notation
      • 6.4 The Fundamental Theorem of Calculus and Accumulation Functions
      • 6.5 Interpreting the Behavior of Accumulation Functions Involving Area
      • Mid-Unit 6 Review
      • 6.6 Applying Properties of Definite Integrals
      • 6.7 The Fundamental Theorem of Calculus and Definite Integrals
      • 6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation
      • 6.9 Integrating Using Substitution
      • 6.10 Integrating Functions Using Long Division and Completing the Square
      • 6.11 Integration by Parts
      • 6.12 Integrating Using Linear Partial Fractions
      • 6.13 Evaluating Improper Integrals
      • 6.14 Selecting Techniques for Antidifferentiation
      • End of Unit 6 Review
    • Unit 7 >
      • 7.1 Modeling Situations with Differential Equations
      • 7.2 Verifying Solutions for Differential Equations
      • 7.3 Sketching Slope Fields
      • 7.4 Reasoning Using Slope Fields
      • 7.5 Approximating Solutions Using Euler’s Method
      • 7.6 General Solutions Using Separation of Variables
      • 7.7 Particular Solutions using Initial Conditions and Separation of Variables
      • 7.8 Exponential Models with Differential Equations
      • 7.9 Logistic Models with Differential Equations
      • Unit 7 Review
    • Unit 8 >
      • 8.1 Average Value of a Function on an Interval
      • 8.2 Connecting Position, Velocity, and Acceleration of Functions Using Integrals
      • 8.3 Using Accumulation Functions and Definite Integrals in Applied Contexts
      • 8.4 Finding the Area Between Curves Expressed as Functions of x
      • 8.5 Finding Area Between Curves Expressed as Functions of y
      • 8.6 Finding the Area Between Curves That Intersect at More Than Two Points
      • Mid-Unit 8 Review
      • 8.7 Volumes with Cross Sections: Squares and Rectangles
      • 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
      • 8.13 The Arc Length of a Smooth, Planar Curve and Distance Traveled
      • End of Unit 8 Review
    • Unit 9 >
      • 9.1 Defining and Differentiating Parametric Equations
      • 9.2 Second Derivatives of Parametric Equations
      • 9.3 Finding Arc Lengths of Curves Given by Parametric Equations
      • 9.4 Defining and Differentiating Vector-Valued Functions
      • 9.5 Integrating Vector-Valued Functions
      • 9.6 Solving Motion Problems using Parametric and Vector-Valued Functions
      • 9.7 Defining Polar Coordinates and Differentiating 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
      • Unit 9 Review
    • Unit 10 >
      • 10.1 Defining Convergent and Divergent Infinite Series
      • 10.2 Working with Geometric Series
      • 10.3 The nth Term Test for Divergence
      • 10.4 Integral Test for Convergence
      • 10.5 Harmonic Series and p-series
      • 10.6 Comparison Tests for Convergence
      • 10.7 Alternating Series Test for Convergence
      • 10.8 Ratio Test for Convergence
      • 10.9 Determining Absolute or Conditional Convergence
      • Mid-Unit 10 Review
      • 10.10 Alternating Series Error Bound
      • 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 a Power Series
      • End of Unit 10 Review
  • Version #2
    • Derivatives >
      • Unit 0 - Calc Prerequisites >
        • 0.1 Things to Know for Calc
        • 0.2 Summer Packet
        • 0.3 Calculator Skillz
      • Unit 1 - Limits >
        • 1.1 Limits Graphically
        • 1.2 Limits Analytically
        • 1.3 Asymptotes
        • 1.4 Continuity
        • Review - Unit 1
      • Unit 2 - The Derivative >
        • 2.1 Average Rate of Change
        • 2.2 Definition of the Derivative
        • 2.3 Differentiability
        • Review - Unit 2
      • Unit 3 - Basic Differentiation >
        • 3.1 Power Rule
        • 3.2 Product & Quotient Rule
        • 3.3 Velocity/Rates of Change
        • 3.4 Chain Rule
        • 3.5 Trig Derivatives
        • Review - Unit 3
      • Unit 4 - More Derivatives >
        • 4.1 Exp and Log Derivatives
        • 4.2 Inverse Derivatives
        • 4.3 L'Hopitals Rule
        • Review - Unit 4
      • Unit 5 - Curve Sketching >
        • 5.1 Extreme Values
        • 5.2 First Derivative Test
        • 5.3 Second Derivative Test
        • Review - Unit 5
      • Unit 6 - Implicit Differentiation >
        • 6.1 Implicit Differentiation
        • 6.2 Related Rates
        • 6.3 Optimization
        • Review - Unit 6
      • SEMESTER REVIEW
    • Integrals >
      • Unit 7 - Approximation Methods >
        • 7.1 Rectangular Approximation
        • 7.2 Trapezoidal Approximation
      • Unit 8 - Integration >
        • 8.1 Definite Integral
        • 8.2 First Fundamental Theorem of Calculus
        • 8.3 Antiderivatives
        • Review - Unit 8
      • Unit 9 - FTC Part 2 >
        • 9.1 The 2nd FTC
        • 9.2 Trig Integrals
        • 9.3 Average Value
        • 9.4 Net Change
        • Review - Unit 9
      • Unit 10 - More Integrals >
        • 10.1 Slope Fields
        • 10.2 u Sub Indefinite Integral
        • 10.3 u Sub Definite Integral
        • 10.4 Separation of Variables
        • Review - Unit 10
      • Unit 11 - Area and Volume >
        • 11.1 Area Between Curves
        • 11.2 Solids of Revolution (Discs)
        • 11.3 Solids of Revolution (Washers)
        • 11.4 Perpendicular Cross Sections
        • Review - Unit 11
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