Calculus Course Structure

• Corequisite: Rational Expressions
• Corequisite: Difference Quotient
• Graphs and Limits
• When Limits Fail to Exist
• Limit Laws
• The Squeeze Theorem
• Limits using Algebraic Tricks
• When the Limit of the Denominator is 0
• Corequisite: Lines: Graphs and Equations
• Corequisite: Rational Functions and Graphs
• Limits at Infinity and Graphs
• Limits at Infinity and Algebraic Tricks
• Continuity at a Point
• Continuity on Intervals
• Intermediate Value Theorem
• Corequisite: Right Angle Trigonometry
• Corequisite: Sine and Cosine of Special Angles
• Corequisite: Unit Circle Definition of Sine and Cosine
• Corequisite: Properties of Trig Functions
• Corequisite: Graphs of Sine and Cosine
• Corequisite: Graphs of Sinusoidal Functions
• Corequisite: Graphs of Tan, Sec, Cot, Csc
• Corequisite: Solving Basic Trig Equations
• Derivatives and Tangent Lines
• Computing Derivatives from the Definition
• Interpreting Derivatives
• Derivatives as Functions and Graphs of Derivatives
• Proof that Differentiable Functions are Continuous
• Power Rule and Other Rules for Derivatives
• Corequisite: Trig Identities
• Corequisite: Pythagorean Identities
• Corequisite: Angle Sum and Difference Formulas
• Corequisite: Double Angle Formulas
• Higher Order Derivatives and Notation
• Derivative of e^x
• Proof of the Power Rule and Other Derivative Rules
• Product Rule and Quotient Rule
• Proof of Product Rule and Quotient Rule
• Special Trigonometric Limits
• Corequisite: Composition of Functions
• Corequisite: Solving Rational Equations
• Derivatives of Trig Functions
• Proof of Trigonometric Limits and Derivatives
• Rectilinear Motion
• Marginal Cost
• Corequisite: Logarithms: Introduction
• Corequisite: Log Functions and Their Graphs
• Corequisite: Combining Logs and Exponents
• Corequisite: Log Rules
• The Chain Rule
• More Chain Rule Examples and Justification
• Justification of the Chain Rule
• Implicit Differentiation
• Derivatives of Exponential Functions
• Derivatives of Log Functions
• Logarithmic Differentiation
• Corequisite: Inverse Functions
• Inverse Trig Functions
• Derivatives of Inverse Trigonometric Functions
• Related Rates - Distances
• Related Rates - Volume and Flow
• Related Rates - Angle and Rotation
• Corequisite: Solving Right Triangles
• Maximums and Minimums
• First Derivative Test and Second Derivative Test
• Extreme Value Examples
• Mean Value Theorem
• Proof of Mean Value Theorem
• Corequisite: Solving Right Triangles
• Derivatives and the Shape of the Graph
• Linear Approximation
• The Differential
• L'Hospital's Rule
• L'Hospital's Rule on Other Indeterminate Forms
• Newtons Method
• Antiderivatives
• Finding Antiderivatives Using Initial Conditions
• Any Two Antiderivatives Differ by a Constant
• Summation Notation
• Approximating Area
• The Fundamental Theorem of Calculus, Part 1
• The Fundamental Theorem of Calculus, Part 2
• Proof of the Fundamental Theorem of Calculus
• The Substitution Method
• Why U-Substitution Works
• Average Value of a Function
• Proof of the Mean Value Theorem for Integrals