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Introduction to Calculus I - Table of Contents

Offering: Introduction to Calculus I

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  • 1. Unit 0: Introduction and References
    • 1.1 - Objectives and Requirements
    • 1.2 - Algebra
    • 1.3 - Trigonometry
    • 1.4 - Finishing This Unit
    • 1.5 - Assignment for Credit
    • 1.6 - Learning from Mistakes
  • 2. Unit 1: Brief Review of Algebra and Trigonometry for Calculus
    • 2.1 - Objectives
    • 2.2 - Relations and Functions
    • 2.3 - The Graph of a Function
    • 2.4 - Transformations
    • 2.5 - Finishing This Unit
    • 2.6 - Learning from Mistakes
  • 3. Unit 2: Functions
    • 3.1 - Objectives
    • 3.2 - Evaluating Limits Visually
    • 3.3 - Continuous Functions
    • 3.4 - Using Algebra to Evaluate Limits
    • 3.5 - Infinite Limits: Vertical Asymptotes
    • 3.6 - The Squeeze Theorem
    • 3.7 - Laws of Limits
    • 3.8 - Limits at Infinity: Horizontal Asymptotes
    • 3.9 - The Definition of a Limit
    • 3.10 - Finishing This Unit
    • 3.11 - Assignment for Credit
    • 3.12 - Procedure to Evaluate Limit at a Number
    • 3.13 - Procedure to Evaluate Limit at Infinity
    • 3.14 - Learning from Mistakes
  • 4. Unit 3: Limits
    • 4.1 - Objectives
    • 4.2 - The Average Rate of Change and the Slope of the Secant Line
    • 4.3 - The Instantaneous Rate of Change and the Slope of the Tangent Line
    • 4.4 - The Graph of the Derivative Function
    • 4.5 - The Derivative Function
    • 4.6 - Rules of Differentiation
    • 4.7 - Derivatives of the Trigonometric Functions
    • 4.8 - The Chain Rule
    • 4.9 - Applications of the Derivative
    • 4.10 - Implicit Differentiation
    • 4.11 - Related Rates
    • 4.12 - Higher-order Derivatives
    • 4.13 - Finishing This Unit
    • 4.14 - Learning from Mistakes
  • 5. Unit 4: Differentiation
    • 5.1 - Objectives
    • 5.2 - Domain, x-y Intercepts, and Symmetries
    • 5.3 - Asymptotes
    • 5.4 - Intervals of Increase and Decrease
    • 5.5 - Local and Absolute Extreme Values
    • 5.6 - Concavity and Points of Inflection
    • 5.7 - Graph Sketching
    • 5.8 - Optimization Problems
    • 5.9 - Newton's Method
    • 5.10 - Finishing This Unit
    • 5.11 - Assignment for Credit
    • 5.12 - Learning from Mistakes
  • 6. Unit 5: Applications of Derivative
    • 6.1 - Objectives
    • 6.2 - Antiderivatives
    • 6.3 - The Antiderivative and the General Power Rule
    • 6.4 - Change of Variable: u - identification
    • 6.5 - The u - substitution
    • 6.6 - The Mean Value Theorem
    • 6.7 - The Fundamental Theorem of Calculus
    • 6.8 - Finishing This Unit
    • 6.9 - Learning from Mistakes
  • 7. Unit 6: Integration
    • 7.1 - Objectives
    • 7.2 - Rectilinear Motion
    • 7.3 - Net Change
    • 7.4 - Area Between Curves
    • 7.5 - Work
    • 7.6 - Average Value of a Function
    • 7.7 - Finishing This Unit
    • 7.8 - Assignment for Credit
    • 7.9 - Learning from Mistakes
  • 8. Unit 7: Applications of the Definite Integral
  • 10. Algebra of Numbers
  • 11. Geometry
  • 12. Trigonometry
  • 13. The Concept of Functions
  • 14. Limits and Continuity
  • 15. Differentiation
  • 16. Analyzing Functions and Curves
  • 17. Indefinite Integrals
  • 18. Definite Integrals and Its Applications
  • 19. Help Documents