Limits and Continuity - Introducing Calculus: Can Change Occur at an Instant? - Defining Limits and Using Limit Notation - Estimating Limit Values from Graphs - Estimating Limit Values from Tables - Determining Limits Using Algebraic Properties of Limits - Determining Limits Using Algebraic Manipulation - Selecting Procedures for Determining Limits - Determining Limits Using the Squeeze Theorem - Connecting Multiple Representations of Limits - Exploring Types of Discontinuities - Defining Continuity at a Point - Confirming Continuity Over an Interval - Removing Discontinuities - Connecting Infinite Limits and Vertical Asymptotes - Connecting Limits at Infinity and Horizontal Asymptotes - Working With the Intermediate Value Theorem (IVT) - Limits and Continuity - Assignment Differentiation: Definition and Basic Derivative Rules - Defining Average and Instantaneous Rates of Change at a Point - Defining the Derivative of a Function and Using Derivative Notation - Estimating Derivatives of a Function at a Point - Connecting Differentiability and Continuity: Determining When Derivatives Do and Do Not Exist - Applying the Power Rule - Derivative Rules: Constant, Sum, Difference, and Constant Multiple - Derivatives of Cos X, Sin X, E^x, and Ln x - The Product Rule - The Quotient Rule - Finding the Derivatives of Tangent, Cotangent, Secant, And/or Cosecant Functions - Differentiation: Assignments Differentiation:composite, Implicit, and Inverse Functions - The Chain Rule - Implicit Differentiation - Differentiating Inverse Functions - Differentiating Inverse Trigonometric Functions - Selecting Procedures for Calculating Derivatives - Calculating Higher- Order Derivatives - Inverse Function Differentiation Assignment Contextual Applications of Differentiation - Interpreting the Meaning of the Derivative in Context - Straight-line Motion: Connecting Position, Velocity, and Acceleration - Rates of Change in Applied Contexts Other Than Motion - Introduction to Related Rates - Solving Related Rates Problems - Approximating Values of a Function Using Local Linearity and Linearization - Using L'hospital's Rule for Determining Limits of Indeterminate Forms - Contextual Applications of Differentiation : Assignment Analytical Applications of Differentiation - Using the Mean Value Theorem - Extreme Value Theorem, Global Versus Local Extreme, and Critical Points - Determining Intervals on Which a Function Is Increasing or Decreasing - Using the First Derivative Test to Determine Relative (Local) Extrema - Using the First Derivative Test to Determine Absolute (Global) Extrema - Determining Concavity of Functions Over Their Domains - Using the Second Derivative Test to Determine Extrema - Sketching Graphs of Functions and Their Derivatives - Connecting a Function, Its First Derivative, and Its Second Derivative - Introduction to Optimization Problems - Solving Optimization Problems - Exploring Behaviors of Implicit Relations - Analytical Applications of Differentiation : Assignment