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Unit 1 - Limits and Continuity

§1.1 Can Change Occur at an Instant?

§1.2 Defining Limits and Using Limit Notation

§1.3 Estimating Limit Values from Graphs

§1.4 Estimating 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

§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 (IVT)


Unit 2 - Differentiation: Definition and Fundamental Properties

§2.1 Average and Instantaneous Rate of Change

§ 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 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), and csc(x)


Unit 3 - Differentiation: Composite, Implicit, and Inverse Functions

§3.1 The Chain Rule

§3.2 Implicit Differentiation

§3.3 Differentiating Inverse Functions

§3.4 Differentiating Inverse Trig Functions

§3.5 Selecting Procedures for Derivatives

§3.6 Calculating Higher Order Derivatives

Unit 4 - Contextual Applications of Differentiation

§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'Hôpital's Rule for Determining Limits of Indeterminate Forms


Unit 5 - Analytical Applications of Differentiation

§5.1 Using the Mean Value Theorem

§5.2 Extrreme Value Theorem, Global vs. 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 Deterine Absolute (Global) Extrema

§5.6 Determining Concavity of Functions over Their Domains

§5.7 Using the Second Derivative Test to Determine Extrema

§5.8 Sketching Graphs of Functions and Their Derivatives

§5.9 Connecting a Function, It's First Derivative, and It's Second Derivative

§5.10 Introduction to Optimization Problems

§5.11 Solving Optimization Problems

§5.12 Exploring Behaviors of Implicit Relations


Unit 6 - Analytical Applications of Differentiation

§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 Acculmlation Functions

§6.5 Interpreting the Behavior of Accumulation Functions Involving Area

§6.6 Applying Properties of Definitel Integrals

§6.7 The Fundamental Theorem of Calculus and Definite Integrals

§6.8 Finding Antiderivatives and Indefinite Integrals: Basic Rules and Notation

§6.9 Integration Using Substitution

§6.10 Integrating Functions Using Long Division and Completing the Square

§6.11 Integration Using Integration by Parts

§6.12 Integrating Using Linear Partial Fractions

§6.14 Selecting Techniques for Antidifferentiation

Unit 7 - Differential Equations

§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

§7.6 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 8 - Applications of Integration

§8.1 Average Value of a Function on an Interval

§8.2 Position, Velocity and Acceleration Using Integrals

§8.3 Using Accumulation Functions...

§8.4 Area Between Curves (with respect to x)

§8.5 Area Between Curves (with respect to y)

§8.6 Area Between Curves - More than Two Intersections

§8.7 Cross Sections: Squares and Rectangles

§8.8 Cross Sections: Triangles and Semicircles

§8.9 Disc Method: Revolving Around the x or y Axis

§8.10 Disc Method: Revolving Around Other Axes

§8.11 Washer Method: Revolving Around the x or y Axis

§8.12 Washer Method: Revolving Around Other Axes

(updated 2/24/22)