Topic Name Description
Course Introduction Course Syllabus Course Terms of Use
1.1: Preview of Calculus Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 1.1: Preview of Calculus"

Read this section for an introduction to calculus.

1.1.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 1.1: Practice Problems"

Work through the odd-numbered problems 1 - 7 on page 5 and page 6. Once you have completed the problem set, check your answers for the odd-numbered questions here.

1.2: Lines in the Plane Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 1.2: Lines in the Plane"

Read this section and work through practice problems 1-9. For solutions to the practice problems, see page 15.

1.2.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 1.2: Practice Problems"

Work through the odd-numbered problems 1-29 on pages 10-14. Once you have completed the problem set, check your answers here.

1.3: Functions and Their Graphs Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 1.3: Functions and Their Graphs"

Read this section for an introduction to functions and their graphs. Work through practice problems 1-5. For solutions to the practice problems, see pages 13-14.

1.3.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 1.3: Practice Problems"

Work through the odd-numbered problems 1-23 on pages 8-13. Once you have completed the problem set, check your answers here.

1.4: Combinations of Functions Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 1.4: Combinations of Functions"

Read this section on pages 1-11 for an introduction to combinations of functions, then work through practice problems 1-9. For solutions to the practice problems, see pages 18-20.

1.4.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 1.4: Practice Problems"

Work through the odd-numbered problems 1-31 on pages 11-16. Once you have completed the problem set, check your answers here.

1.5: Mathematical Language Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 1.5: Mathematical Language"

Read this section on pages 1-5 for an introduction to mathematical language, then work through practice problems 1-4. For the solutions to the practice problems, see pages 7-8.

1.5.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 1.5: Practice Problems"

Work through the odd-numbered problems 1-25 on pages 5-7. Once you have completed the problem set, check your answers for the odd-numbered questions here.

2.1: Tangent Lines, Velocities, and Growth Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 2.1: Tangent Lines, Velocities, and Growth"

Read this section on pages 1-7 for an introduction to connecting derivatives to quantities we can see in the real world. Work through practice problems 1-4. For the solutions to these practice problems, see page 10-11.

2.1.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 2.1: Practice Problems"

Work through the odd-numbered problems 1-9 on pages 7-9. Once you have completed the problem set, check your answers for the odd-numbered questions here.

2.2: The Limit of a Function Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 2.2: The Limit of a Function"

Read this section on pages 1-7 for an introduction to connecting derivatives to quantities we can see in the real world. Work through practice problems 1-4. For solutions to these practice problems, see page 10.

2.2.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 2.2: Practice Problems"

Work through the odd-numbered problems  1-19 on pages 7-9. Once you have completed the problem set, check your answers for the odd-numbered questions here.

2.3: Properties of Limits Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 2.3: Properties of Limits"

Read this section on pages 1-8 to learn about the properties of limits. Work through practice problems 1-6. For the solutions to these problems, see page 14. RootMath: "Solving Limits (Rationalization)"

Watch this video on finding limits algebraically. Be warned that removing $x-4$ from the numerator and denominator in Step 4 of this video is only legal inside this limit. The function $\frac{x - 4}{x - 4}$ is not defined at $x = 4$; however, when $x$ is not 4, it simplifies to 1. Because the limit as $x$ approaches 4 depends only on values of $x$ different from 4, inside that limit $\frac{x - 4}{x - 4}$ and 1 are interchangeable. Outside that limit, they are not! However, this kind of cancellation is a key technique for finding limits of algebraically complicated functions. Khan Academy: "Calculating Slope of Tangent Line Using Derivative Definition"

Watch this video on limits as the slopes of tangent lines.

An earlier Khan Academy video (not used in this course) defined the limit that gives the slope of the tangent line to a curve as $y = f(x)$ at a point $x = a$ and called it the derivative of $f(x)$ at $a$. The text will introduce this term in Unit 3.

2.3.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 2.3: Practice Problems"

Work through the odd-numbered problems 1-21 on pages 9-14. Once you have completed the problem set, check your answers for the odd-numbered questions here.

2.4: Continuous Functions Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 2.4: Continuous Functions"

Read this section on pages  1-11 for an introduction to what we mean when we say a function is continuous. Work through practice problems 1 and 2. For solutions to these problems, see page 16.

2.4.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 2.4: Practice Problems"

Work through the odd-numbered problems 1-23 on pages 12-15. Once you have completed the problem set, check your answers for the odd-numbered questions here.

2.5: Definition of a Limit Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 2.5: Definition of a Limit"

Read this section on pages 1-11 to learn how a limit is defined. Work through practice problems 1-6. For solutions to these problems, see pages 14-16. Khan Academy: "Epsilon-Delta Limit Definition 1"

Watch this video to learn the epsilon-delta definition of a limit.

2.5.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 2.5: Practice Problems"

Work through the odd-numbered problems 1-23 on pages 12-14. Once you have completed the problem set, check your answers for the odd-numbered questions here.

3.1: Introduction to Derivatives Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.1: Introduction to Derivatives"

Read this section on pages 1-5 to lay the groundwork for introducing the concept of a derivative. Work through practice problems 1-5. For solutions to these problems, see pages 8-9.

3.1.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.1: Practice Problems"

Work through the odd-numbered problems 1-17 on pages 5-7. Once you have completed the problem set, check your answers for the odd-numbered questions here.

3.2: The Definition of a Derivative Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.2: The Definition of a Derivative"

Read this section on pages 1-10 to understand the definition of a derivative. Work through practice problems 1-8. For solutions to these problems, see pages 14-15.

3.2.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.2: Practice Problems"

Work through the odd-numbered problems 1-37 on pages 11-14. Once you have completed the problem set, check your answers for the odd-numbered questions here.

3.3: Derivatives, Properties and Formulas Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.3: Derivatives, Properties and Formulas"

Read this section on pages 1-9 to understand the properties of derivatives. Work through practice problems 1-11. For solutions to these problems, see pages 16-17. Khan Academy: "Applying the Product Rule for Derivatives"

Watch this video on the product rule for differentiation.

3.3.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.3: Practice Problems"

Work through the odd-numbered problems 1-55 on pages 10-15. Once you have completed the problem set, check your answers for the odd-numbered questions here.

3.4: Derivative Patterns Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.4: More Differentiation Problems"

Read this section on pages 1-9 to learn about patterns of derivatives. Work through practice problems 1-8. For solutions to these problems, see pages 12-14.

3.4.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.4: Practice Problems"

Work through the odd-numbered problems 1-47 on pages 9-14. Once you have completed the problem set, check your answers for the odd-numbered questions here.

3.5: The Chain Rule Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.5: The Chain Rule"

Read this section on pages 1-7 to learn about the Chain Rule. Work through practice problems 1-8. For solutions to these problems, see pages 11-12. Khan Academy: "Chain Rule Introduction" and "Chain Rule Definition and Example"

Watch these videos for an introduction to the chain rule for differentiation and examples of the chain rule for differentiation.

3.5.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.5: Practice Problems"

Work through the odd-numbered problems 1-83 on pages 7-11. Once you have completed the problem set, check your answers for the odd-numbered questions here.

3.6: Some Applications of the Chain Rule Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.6: Some Applications of the Chain Rule"

Read this section on pages 1-8 to learn how to apply the Chain Rule. Work through practice problems 1-8. For solutions to these problems, see pages 13-14.

3.6.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.6: Practice Problems"

Work through the odd-numbered problems 1-49 on pages 9-11. Once you have completed the problem set, check your answers for the odd-numbered questions here.

3.7: Related Rates Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.7: Related Rates: An Application of Derivatives"

Read this section on pages 1-7 to learn to connect derivatives to the concept of the rate at which things change. Work through practice problems 1-3. For solutions to these problems, see pages 12-13.

3.7.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.7: Practice Problems"

Work through the odd-numbered problems 1-21 on pages 8-12. Once you have completed the problem set, check your answers for the odd-numbered questions here.

3.8: Newton's Method for Finding Roots Washington State Board for Community and Technical Colleges: Dale Hoffman's Contemporary Calculus: "Section 3.8: Newton's Method for Finding Roots"

Read this section on pages 1-8. Work through practice problems 1-6. For solutions to these problems, see pages 10-11. Massachusetts Institute of Technology: Christine Breiner's "Using Newton's Method"

Watch this video on Newton's method.

3.8.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.8: Practice Problems"

Work through the odd-numbered problems 1-21 on pages 8-9. Once you have completed the problem set, check your answers for the odd-numbered questions here.

3.9: Linear Approximation and Differentials Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.9: Linear Approximation and Differentials"

Read this section on pages 1-10 to learn how linear approximation and differentials are connected. Work through practice problems 1-10. For the solutions to these problems, see pages 14-15. RootMath: "Linear Approximation"

Watch this video on linear approximation and differentials.

3.9.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.9: Practice Problems"

Work through the odd-numbered problems 1-19 on pages 10-13. Once you have completed the problem set, check your answers for the odd-numbered questions here.

3.10: Implicit and Logarithmic Differentiation Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.10: Implicit and Logarithmic Differentiation"

Read this section on pages 1-5 to learn about implicit and logarithmic differentiation. Work through practice problems 1-6. For solutions to these problems, see pages 8-9. Khan Academy: "Implicit Differentiation" and "Derivative of x^(x^x)"

Watch these videos on implicit and logarithmic differentiation.

3.10.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 3.10: Practice Problems"

Work through the odd-numbered problems 1-55 on pages 5-8. Once you have completed the problem set, check your answers for the odd-numbered questions here.

4.1: Finding Maximums and Minimums Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 4.1: Finding Maximums and Minimums"

Read this section on pages 1-9 to learn about maximums, minimums, and extreme values for functions. Work through practice problems 1-5. For solutions to these problems, see pages 13-14.

4.1.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 4.1: Practice Problems"

Work through the odd-numbered problems 1-43 on pages 9-13. Once you have completed the problem set, check your answers for the odd-numbered questions here.

4.2: The Mean Value Theorem and Its Consequences Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 4.2: The Mean Value Theorem and Its Consequences"

Read this section on pages 1-6 to learn about the Mean Value Theorem and its consequences. Work through practice problems 1-3. For solutions to these problems, see pages 9 and 10.

4.2.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 4.2: Practice Problems"

Work through the odd-numbered problems 1-35 on pages 6-9. Once you have completed the problem set, check your answers for the odd-numbered questions here.

4.3: The First Derivative and the Shape of a Function f(x) Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 4.3: The First Derivative and the Shape of f"

Read this section on pages 1-8 to learn how the first derivative is used to determine the shape of functions. Work through practice problems 1-9. For the solution to these problems, see pages 10-12. RootMath: "First Derivative Test, Example 2"

Watch both parts of this video on the first derivative test.

4.3.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 4.3: Practice Problems"

Work through the odd-numbered problems 1-29 on pages 8-10. Once you have completed the problem set, check your answers for the odd-numbered questions here.

4.4: The Second Derivative and the Shape of a Function f(x) Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 4.4: Second Derivative and the Shape of f"

Read this section on pages 1-6 to learn how the second derivative is used to determine the shape of functions. Work through practice problems 1-9. For solutions to these problems, see pages 8-9. Khan Academy: "Concavity, Concave upwards and Concave downwards Intervals"

Watch this video on the second derivative test. This video describes a way to identify critical points as minima or maxima other than the first derivative test, using the second derivative. RootMath: "Concavity and the Second Derivative"

Watch this video, which works through an example of the second derivative test.

4.4.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 4.4: Practice Problems"

Work through the odd-numbered problems 1-17 on pages 6-8. Once you have completed the problem set, check your answers for the odd-numbered questions here.

4.5: Applied Maximum and Minimum Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 4.5: Applied Maximum and Minimum Problems"

Read this section on pages 1-6 to learn how to apply previously learned principles to maximum and minimum problems. Work through practice problems 1-3. For solutions to these problems, see pages 15-16. There is no review for this section; instead, make sure to study the problems carefully to become familiar with applied maximum and minimum problems. Khan Academy: "Minimizing Sum of Squares"

Watch this video on optimization. Massachusetts Institute of Technology: Christine Breiner's "Minimum Triangle Area"

Watch this video on optimization. Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 4.5: Practice Problems"

Work through the odd-numbered problems 1-33 on pages 6-15. Once you have completed the problem set, check your answers for the odd-numbered questions here.

4.6: Infinite Limits and Asymptotes Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 4.6: Infinite Limits and Asymptotes"

Read this section on pages 1-10 to learn how to use and apply infinite limits to asymptotes. Work through practice problems 1-8. For solutions to these problems, see pages 13-14.

4.6.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 4.6: Practice Problems"

Work through the odd-numbered problems 1-59 on pages 10-12. Once you have completed the problem set, check your answers for the odd-numbered questions here.

4.7: L'Hopital's Rule Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 4.7: L'Hopital's Rule"

Read this section on pages 1-6 to learn how to use and apply L'Hopital's Rule. Work through practice problems 1-3. For solutions to these problems, see page 8. Khan Academy: "Introduction to L'Hopital's Rule"

Watch this video for an introduction to L'Hopital's Rule.

4.7.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 4.7: Practice Problems"

Work through the odd-numbered problems 1-29 on pages 6-7. Once you have completed the problem set, check your answers for the odd-numbered questions here.

5.1: Introduction to Integration Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.1: Introduction to Integration"

Read this section on pages 1-7 to learn about area. Work through practice problems 1-9. For solutions to these problems, see page 10.

5.1.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.1: Practice Problems"

Work through the odd-numbered problems 1-15 on pages 8-9. Once you have completed the problem set, check your answers for the odd-numbered questions against here.

5.2: Sigma Notation and Riemann Sums Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.2: Sigma Notation and Riemann Sums"

Read this section on pages 1-10 to learn about area. Work through practice problems 1-9. For solutions to these problems, see pages 15-16.

5.2.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.2: Practice Problems"

Work through the odd-numbered problems 1-61 on pages 10-15. Once you have completed the problem set, check your answers for the odd-numbered questions here.

5.3: The Definite Integral Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.3: The Definite Integral"

Read this section on pages 1-6 to learn about the definite integral and its applications. Work through practice problems 1-6. For solutions to these problems, see page 11.

5.3.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.3: Practice Problems"

Work through the odd-numbered problems 1-29 on pages 6-10. Once you have completed the problem set, check your answers for the odd-numbered questions here.

5.4: Properties of the Definite Integral Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.4: Properties of the Definite Integral"

Read this section on pages 1-8 to learn about properties of definite integrals and how functions can be defined using definite integrals. Work through practice problems 1-5. For solutions to these problems, see page 11.

5.4.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.4: Practice Problems"

Work through the odd-numbered problems 1-51 on pages 9-11. Once you have completed the problem set, check your answers for the odd-numbered questions against here.

5.5: Areas, Integrals, and Antiderivatives Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.5: Areas, Integrals, and Antiderivatives"

Read this section on pages 1-6 to learn about the relationship among areas, integrals, and antiderivatives. Work through practice problems 1-5. For solutions to these problems, see pages 10-11.

5.5.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.5: Practice Problems"

Work through the odd-numbered problems 1-25 on pages 7-9. Once you have completed the problem set, check your answers for the odd-numbered questions here.

5.6: The Fundamental Theorem of Calculus Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.6: The Fundamental Theorem of Calculus"

Read this section on pages 1-9 to see the connection between derivatives and integrals. Work through practice problems 1-5. For solutions to these problems, see pages 14-15.

5.6.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.6: Practice Problems"

Work through the odd-numbered problems 1-67 on pages 10-13. Once you have completed the problem set, check your answers for the odd-numbered questions here.

5.7: Finding Antiderivatives Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.7: Finding Antiderivatives"

Read this section on pages 1-9 to see how one can (sometimes) find an antiderivative. In particular, we will discuss the change of variable technique. Change of variable, also called substitution or u-substitution (for the most commonly-used variable), is a powerful technique that you will use time and again in integration. It allows you to simplify a complicated function to show how basic rules of integration apply to the function. Work through practice problems 1-4. For solutions to these problems, see pages 12-13. RootMath: "Integration: U-Substitution"

Watch these videos on change of variable, also called substitution or u-substitution.

5.7.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.7: Practice Problems"

Work through the odd-numbered problems 1-69 on pages 10-12. Once you have completed the problem set, check your answers for the odd-numbered questions here.

5.8: First Application of Definite Integral Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.8: First Application of Definite Integrals"

Read this section on pages 1-8 to see how some applied problems can be reformulated as integration problems. Work through practice problems 1-4. For solutions to these problems, see pages 10-11.

5.8.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.8: Practice Problems"

Work through the odd-numbered problems 1-41 on pages 8-10. Once you have completed the problem set, check your answers for the odd-numbered questions here.

5.9: Using Tables to Find Antiderivatives Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.9: Using Tables to Find Antiderivatives"

Read this section on pages 1-3 to learn how to use tables to find antiderivatives. See the Calculus Reference Facts for the table of integrals mentioned in the reading. Work through practice problems 1-5. For solutions to these problems, see page 6.

5.9.1: Practice Problems Washington State Board for Community and Technical Colleges: Dale Hoffman's "Contemporary Calculus, Section 5.9: Practice Problems"

Work through the odd-numbered problems 1-55 on pages 4-5. Once you have completed the problem set, check your answers for the odd-numbered questions here.

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