What You will Learn?

• [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