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Calculus I
Click on chapters.
Chapter 2 - Limits and Derivatives
§1: 1. The Tangent Problem
§1: 2. The Velocity Problem
§2: 1. Limits: Introduction
§2: 2. Limits: Infinite Limits
§2: 3. Limits: Example Calculations
§2: 4. Limits: Vertical Asymptotes
§3: 1. The Limit Laws: Introduction Laws
§3: 2. The Limit Laws, Worked Examples
§3: 3. The Limit Laws, Further Examples
§3: 4. The Limit Laws, Conclusions
§5: 1. Continuity: Introduction
§5: 2. Continuity Exercises: Making A Function Continuous
§6: 1. Limits at Infinity: Introduction
§6: 2. Limits at Infinity: Worked Examples
§6: 3. Limits at Infinity: Further Examples
§6: 4. Limits at Infinity: Horizontal Asymptotes
§7: 1. Derivatives: Definition
§7: 2. Derivatives: Example Calculations
§7: 3. Derivatives: Velocity
§8: 1. Derivative as a Function: Introduction
§8: 2. Derivative as a Function: Example Calculations
§8: 2. Derivative as a Function: Non-Differentiability
Chapter 3 - Differentiation Rules
§1: 1. Derivatives of Polynomials
§1: 2. The Derivative of the Exponential Function
§1: 3. Derivatives of Polynomials and the Natural Exponential Function
§2: 1. The Product and Quotient Rules: Introduction
§2: 2. The Product and Quotient Rules: Examples, Part 1
§2: 3. The Product and Quotient Rules: Examples, Part 2
§3: 1. Derivatives of Trigonometric Functions: Introducton
§3: 2. Exercises with the Derivatives of Sine and Cosine
§3: 3. The Derivative of Tangent and Other Trig Functions
§4: 1. The Chain Rule: Introduction
§4: 2. The Chain Rule: Examples
§4: 3. The Chain Rule: Iteration
§4: 4. The Chain Rule: Other Exponentials
§5: 1. Implicit Differentiation: First Example
§5: 2. Implicit Differentiation: An Involved Example
§5: 3. Derivatives of Inverse Trigonometric Functions
§6: 1. Derivative of Logarithms: Introduction
§6: 2. Derivatives of Logarithms: Intermediate Examples
§6: 3. Derivatives of Logarithms: A New Technique
§7: 1. Applications of Differentiation: Velocity
§7: 2. Applications of Differentiation: More on Motion
§7: 3. Applications of Differentiation: Distance Traveled
§9: 1. Related Rates: Introduction
§9: 2. Related Rates: Lamp Post Example
§9: 3. Related Rates: Trigonometric Example
§10: 1. Linearization: Introduction
§10: 2. Linearization: Worked Example
Chapter 4 - Applications of Differentiation
§1: 1. Maximum and Minimum Values: Introduction
§1: 2. Maximum and Minimum Values: Critical Numbers
§1: 3. Maximum and Minimum Values: Exercises
§2: 1. The Mean Value Theorem: Introduction
§2: 2. The Mean Value Theorem: An Example
§2: 3. The Mean Value Theorem: A Second Example
§2: 4. The Mean Value Theorem: Optional
§3: 1. Derivatives and the Shape of a Graph: Increasing and Decreasing
§3: 2. Derivatives and the Shape of a Graph: Concavity and Points of Inflection
§3: 3. Interpreting the Graph of the Derivative
§4: 1. L'Hospital's Rule: Introduction and First Examples
§4: 2. L'Hospital's Rule: Intermediate Examples
§4: 3. L'Hospital's Rule: Limits as x Approaches Infinity
§7: 1. Optimization:
§7: 2. Optimization:
§7: 3. Optimization:
§9: 1. Antiderivatives: Introduction
§9: 2. Antiderivatives: Examples
Chapter 5 - Integration
§2: 1. The Definite Integral: Introduction
§2: 2. The Definite Integral: Exercises
§3: 1. The Fundamental Theorem of Calculus: Introduction
§3: 2. The Fundamental Theorem of Calculus: Exercises
§3: 3. The Fundamental Theorem of Calculus: Further Examples
§4: 1. Indefinite Integrals: Introduction
§4: 2. Indefinite Integrals: Worked Examples
§4: 3. Indefinite Integrals: A Step in Evaluating Definite Integrals
§5: 1. Integration by Substitution: Introduction
§5: 2. Integration by Substitution: Worked Examples
§5: 3. Integration by Substitution: Further Examples