Topic outline

  • CALCULUS VOLUME 1 COURSE


    This comprehensive course contains 6 sections with 51 self-grading lessons, including final assessments. The first section is available to try for free.

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  • Functions and Graphs


    • 1.1 Review of Functions SCORM package

      • Use functional notation to evaluate a function.
      • Determine the domain and range of a function.
      • Draw the graph of a function.
      • Find the zeros of a function.
      • Recognize a function from a table of values.
      • Make new functions from two or more given functions.
      • Describe the symmetry properties of a function.

    • 1.2 Basic Classes of Functions SCORM package

      • Calculate the slope of a linear function and interpret its meaning.
      • Recognize the degree of a polynomial.
      • Find the roots of a quadratic polynomial.
      • Describe the graphs of basic odd and even polynomial functions.
      • Identify a rational function.
      • Describe the graphs of power and root functions.
      • Explain the difference between algebraic and transcendental functions.
      • Graph a piecewise-defined function.
      • Sketch the graph of a function that has been shifted, stretched, or reflected from its initial graph position.


      1.3. Trigonometric Functions
      1.4. Inverse Functions
      1.5. Exponential and Logarithmic Functions

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  • Functions and Graphs - Final Assessment


    This is the final assessment for Functions and Graphs. (Available when you subscribe.)

    • This topic

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      • Limits


        2.1. A Preview of Calculus
        2.2. The Limit of a Function
        2.3. The Limit Laws
        2.4. Continuity
        2.5. The Precise Definition of a Limit
        Final Assessment


        • Derivatives


          3.1. Defining the Derivative
          3.2. The Derivative as a Function
          3.3. Differentiation Rules
          3.4. Derivatives as Rates of Change
          3.5. Derivatives of Trigonometric Functions
          3.6. The Chain Rule
          3.7. Derivatives of Inverse Functions
          3.8. Implicit Differentiation
          3.9. Derivatives of Exponential and Logarithmic Functions
          Final Assessment

          • Applications of Derivatives


            4.1. Related Rates
            4.2. Linear Approximations and Differentials
            4.3. Maxima and Minima
            4.4. The Mean Value Theorem
            4.5. Derivatives and the Shape of a Graph
            4.6. Limits at Infinity and Asymptotes
            4.7. Applied Optimization Problems
            4.8. L’Hôpital’s Rule
            4.9. Newton’s Method
            4.10. Antiderivatives
            Final Assessment

            • Integration


              5.1. Approximating Areas
              5.2. The Definite Integral
              5.3. The Fundamental Theorem of Calculus
              5.4. Integration Formulas and the Net Change Theorem
              5.5. Substitution
              5.6. Integrals Involving Exponential and Logarithmic Functions
              5.7. Integrals Resulting in Inverse Trigonometric Functions
              Final Assessment

              • Applications of Integration


                6.1. Areas between Curves
                6.2. Determining Volumes by Slicing
                6.3. Volumes of Revolution: Cylindrical Shells
                6.4. Arc Length of a Curve and Surface Area
                6.5. Physical Applications
                6.6. Moments and Centers of Mass
                6.7. Integrals, Exponential Functions, and Logarithms
                6.8. Exponential Growth and Decay
                6.9. Calculus of the Hyperbolic Functions
                Final Assessment

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