Topic  Name  Description 

Course Introduction  Course Syllabus  
Course Terms of Use  
Unit 1: Preview and Review  Unit 1 Learning Outcomes  
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 oddnumbered problems 1  7 on page 5 and page 6. Once you have completed the problem set, check your answers for the oddnumbered 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 19. 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 oddnumbered problems 129 on pages 1014. 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 15. For solutions to the practice problems, see pages 1314. 
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 oddnumbered problems 123 on pages 813. 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 111 for an introduction to combinations of functions, then work through practice problems 19. For solutions to the practice problems, see pages 1820. 
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 oddnumbered problems 131 on pages 1116. 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 15 for an introduction to mathematical language, then work through practice problems 14. For the solutions to the practice problems, see pages 78. 
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 oddnumbered problems 125 on pages 57. Once you have completed the problem set, check your answers for the oddnumbered questions here. 
Unit 2: Functions, Graphs, Limits, and Continuity  Unit 2 Learning Outcomes  
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 17 for an introduction to connecting derivatives to quantities we can see in the real world. Work through practice problems 14. For the solutions to these practice problems, see page 1011. 
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 oddnumbered problems 19 on pages 79. Once you have completed the problem set, check your answers for the oddnumbered 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 17 for an introduction to connecting derivatives to quantities we can see in the real world. Work through practice problems 14. 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 oddnumbered problems 119 on pages 79. Once you have completed the problem set, check your answers for the oddnumbered 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 18 to learn about the properties of limits. Work through practice problems 16. For the solutions to these problems, see page 14. 
RootMath: "Solving Limits (Rationalization)"  Watch this video on finding limits algebraically. Be warned that removing from the numerator and denominator in Step 4 of this video is only legal inside this limit. The function is not defined at ; however, when is not 4, it simplifies to 1. Because the limit as approaches 4 depends only on values of different from 4, inside that limit 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"  
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 oddnumbered problems 121 on pages 914. Once you have completed the problem set, check your answers for the oddnumbered 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 111 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 oddnumbered problems 123 on pages 1215. Once you have completed the problem set, check your answers for the oddnumbered 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 111 to learn how a limit is defined. Work through practice problems 16. For solutions to these problems, see pages 1416. 
Khan Academy: "EpsilonDelta Limit Definition 1"  Watch this video to learn the epsilondelta 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 oddnumbered problems 123 on pages 1214. Once you have completed the problem set, check your answers for the oddnumbered questions here. 
Unit 3: Derivatives  Unit 3 Learning Outcomes  
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 15 to lay the groundwork for introducing the concept of a derivative. Work through practice problems 15. For solutions to these problems, see pages 89. 
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 oddnumbered problems 117 on pages 57. Once you have completed the problem set, check your answers for the oddnumbered 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 110 to understand the definition of a derivative. Work through practice problems 18. For solutions to these problems, see pages 1415. 
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 oddnumbered problems 137 on pages 1114. Once you have completed the problem set, check your answers for the oddnumbered 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 19 to understand the properties of derivatives. Work through practice problems 111. For solutions to these problems, see pages 1617. 
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 oddnumbered problems 155 on pages 1015. Once you have completed the problem set, check your answers for the oddnumbered 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 19 to learn about patterns of derivatives. Work through practice problems 18. For solutions to these problems, see pages 1214. 
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 oddnumbered problems 147 on pages 914. Once you have completed the problem set, check your answers for the oddnumbered 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 17 to learn about the Chain Rule. Work through practice problems 18. For solutions to these problems, see pages 1112. 
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 oddnumbered problems 183 on pages 711. Once you have completed the problem set, check your answers for the oddnumbered 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 18 to learn how to apply the Chain Rule. Work through practice problems 18. For solutions to these problems, see pages 1314. 
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 oddnumbered problems 149 on pages 911. Once you have completed the problem set, check your answers for the oddnumbered 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 17 to learn to connect derivatives to the concept of the rate at which things change. Work through practice problems 13. For solutions to these problems, see pages 1213. 
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 oddnumbered problems 121 on pages 812. Once you have completed the problem set, check your answers for the oddnumbered 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 18. Work through practice problems 16. For solutions to these problems, see pages 1011. 
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 oddnumbered problems 121 on pages 89. Once you have completed the problem set, check your answers for the oddnumbered 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 110 to learn how linear approximation and differentials are connected. Work through practice problems 110. For the solutions to these problems, see pages 1415. 
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 oddnumbered problems 119 on pages 1013. Once you have completed the problem set, check your answers for the oddnumbered 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 15 to learn about implicit and logarithmic differentiation. Work through practice problems 16. For solutions to these problems, see pages 89. 
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 oddnumbered problems 155 on pages 58. Once you have completed the problem set, check your answers for the oddnumbered questions here. 
Unit 4: Derivatives and Graphs  Unit 4 Learning Outcomes  
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 19 to learn about maximums, minimums, and extreme values for functions. Work through practice problems 15. For solutions to these problems, see pages 1314. 
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 oddnumbered problems 143 on pages 913. Once you have completed the problem set, check your answers for the oddnumbered 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 16 to learn about the Mean Value Theorem and its consequences. Work through practice problems 13. 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 oddnumbered problems 135 on pages 69. Once you have completed the problem set, check your answers for the oddnumbered 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 18 to learn how the first derivative is used to determine the shape of functions. Work through practice problems 19. For the solution to these problems, see pages 1012. 
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 oddnumbered problems 129 on pages 810. Once you have completed the problem set, check your answers for the oddnumbered 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 16 to learn how the second derivative is used to determine the shape of functions. Work through practice problems 19. For solutions to these problems, see pages 89. 
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 oddnumbered problems 117 on pages 68. Once you have completed the problem set, check your answers for the oddnumbered 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 16 to learn how to apply previously learned principles to maximum and minimum problems. Work through practice problems 13. For solutions to these problems, see pages 1516. 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 oddnumbered problems 133 on pages 615. Once you have completed the problem set, check your answers for the oddnumbered 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 110 to learn how to use and apply infinite limits to asymptotes. Work through practice problems 18. For solutions to these problems, see pages 1314. 
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 oddnumbered problems 159 on pages 1012. Once you have completed the problem set, check your answers for the oddnumbered 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 16 to learn how to use and apply L'Hopital's Rule. Work through practice problems 13. 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 oddnumbered problems 129 on pages 67. Once you have completed the problem set, check your answers for the oddnumbered questions here. 
Unit 5: The Integral  Unit 5 Learning Outcomes  
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 17 to learn about area. Work through practice problems 19. 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 oddnumbered problems 115 on pages 89. Once you have completed the problem set, check your answers for the oddnumbered 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 110 to learn about area. Work through practice problems 19. For solutions to these problems, see pages 1516. 
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 oddnumbered problems 161 on pages 1015. Once you have completed the problem set, check your answers for the oddnumbered 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 16 to learn about the definite integral and its applications. Work through practice problems 16. 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 oddnumbered problems 129 on pages 610. Once you have completed the problem set, check your answers for the oddnumbered 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 18 to learn about properties of definite integrals and how functions can be defined using definite integrals. Work through practice problems 15. 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 oddnumbered problems 151 on pages 911. Once you have completed the problem set, check your answers for the oddnumbered 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 16 to learn about the relationship among areas, integrals, and antiderivatives. Work through practice problems 15. For solutions to these problems, see pages 1011. 
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 oddnumbered problems 125 on pages 79. Once you have completed the problem set, check your answers for the oddnumbered 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 19 to see the connection between derivatives and integrals. Work through practice problems 15. For solutions to these problems, see pages 1415. 
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 oddnumbered problems 167 on pages 1013. Once you have completed the problem set, check your answers for the oddnumbered 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 19 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 usubstitution (for the most commonlyused 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 14. For solutions to these problems, see pages 1213. 
RootMath: "Integration: USubstitution"  Watch these videos on change of variable, also called substitution or usubstitution. 

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 oddnumbered problems 169 on pages 1012. Once you have completed the problem set, check your answers for the oddnumbered 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 18 to see how some applied problems can be reformulated as integration problems. Work through practice problems 14. For solutions to these problems, see pages 1011. 
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 oddnumbered problems 141 on pages 810. Once you have completed the problem set, check your answers for the oddnumbered 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 13 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 15. 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 oddnumbered problems 155 on pages 45. Once you have completed the problem set, check your answers for the oddnumbered questions here. 
Optional Course Evaluation Survey  Optional Course Evaluation Survey  Please take a few moments to provide some feedback about this course. Consider completing the survey whether you have completed the course, you are nearly at that point, or you have just come to study one unit or a few units of this course. Your feedback will focus our efforts to continually improve our course design, content, technology, and general easeofuse. Additionally, your input will be considered alongside our consulting professors' evaluation of the course during its next round of peer review. As always, please report urgent course experience concerns to [email protected] and/or our discussion forums. 