Readings

1.1 Reading: Whitman College: David Guichard’s Calculus: Chapter 1: Analytic Geometry: “Section 1.1: Lines”
Link: Whitman College: David Guichard’s Calculus: Chapter 1: Analytic Geometry: “Section 1.1: Lines” (PDF)
Instructions: Please click on the link above and read Section 1.1 (pages 1417) in its entirety. Working with lines should be familiar to you, and this section serves as a review of the notions of points, lines, slope, intercepts, and graphing.
This reading should take you approximately 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
1.2 Reading: Whitman College: David Guichard’s Calculus: Chapter 1: Analytic Geometry: “Section 1.2: Distance Between Two Points; Circles”
Link: Whitman College: David Guichard’s Calculus: Chapter 1: Analytic Geometry: “Section 1.2: Distance Between Two Points; Circles” (PDF)
Instructions: Please click on the link above and read Section 1.2 (pages 19 and 20) in its entirety. This reading reviews the notions of distance in the plane and the equations and graphs of circles.
This reading should take approximately 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
1.3 Reading: Whitman College: David Guichard’s Calculus: Chapter 1: Analytic Geometry: “Section 1.3: Functions”
Link: Whitman College: David Guichard’s Calculus: Chapter 1: Analytic Geometry: “Section 1.3: Functions” (PDF)
Instructions: Please click on the link above and read Section 1.3 (pages 2024) in its entirety. This reading reviews the notion of functions, linear functions, domain, range, and dependent and independent variables.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
1.4 Reading: Whitman College: David Guichard’s Calculus: Chapter 1: Analytic Geometry: “Section 1.4: Shifts and Dilations”
Link: Whitman College: David Guichard’s Calculus: Chapter 1: Analytic Geometry: “Section 1.4: Shifts and Dilations” (PDF)
Instructions: Please click on the link above and read Section 1.4 (pages 2528) in its entirety. This reading will review graph transformations associated with some basic ways of manipulating functions like like shifts and dilations.
This reading should take you approximately 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
2.1 Reading: Whitman College: David Guichard’s Calculus: Chapter 2: Instantaneous Rate of Change: The Derivative: “Section 2.1: The Slope of a Function”
Link: Whitman College: David Guichard’s Calculus: Chapter 2: Instantaneous Rate of Change: The Derivative: “Section 2.1: The Slope of a Function” (PDF)
Instructions: Please click on the link above and read Section 2.1 (pages 2933) in its entirety. You will be introduced to the notion of a derivative through studying a specific example. The example will also reveal the necessity of having a precise definition for the limit of a function.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
2.2 Reading: Whitman College: David Guichard’s Calculus: Chapter 2: Instantaneous Rate of Change: The Derivative: “Section 2.2: An Example”
Link: Whitman College: David Guichard’s Calculus: Chapter 2: Instantaneous Rate of Change: The Derivative: “Section 2.2: An Example” (PDF)
Instructions: Please click on the link above and read Section 2.2 (pages 3436) in its entirety. This reading discusses the derivative in the context of studying the velocity of a falling object.
This reading should take you approximately 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
2.3.1 Reading: Whitman College: David Guichard’s Calculus: Chapter 2: Instantaneous Rate of Change: The Derivative: “Section 2.3: Limits”
Link: Whitman College: David Guichard’s Calculus: Chapter 2: Instantaneous Rate of Change: The Derivative: “Section 2.3: Limits” (PDF)
Instructions: Please click on the link above and read Section 2.3 (pages 3645) in its entirety. Read this section carefully and pay close attention to the definition of the limit and the examples that follow. You should also closely examine the algebraic properties of limits as you will need to take advantage of these in the exercises.
This reading should take you approximately two hours to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
2.3.2 Reading: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.3: A Hard Limit”
Link: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.3: A Hard Limit” (PDF)
Instructions: Please click on the link above and read Section 4.3 (pages 7577) in its entirety. The Squeeze Theorem is an important application of the limit and is useful in many limit computations.
This reading should take you approximately 30 minute to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
2.4 Reading: Whitman College: David Guichard’s Calculus: Chapter 2: Instantaneous Rate of Change: The Derivative: “Section 2.4: The Derivative Function”
Link: Whitman College: David Guichard’s Calculus: Chapter 2: Instantaneous Rate of Change: The Derivative: “Section 2.4: The Derivative Function” (PDF)
Instructions: Please click on the link above and read Section 2.4 (pages 4650) in its entirety. In this reading, you will see how limits are used to compute derivatives. A derivative is a description of how a function changes as its input varies. In the case of a straight line, this description is the same at every point, which is why we can describe the slope of an entire function when it is linear. You can also describe the slope of nonlinear functions. The slope, however, will not be constant; it will change as the independent variable changes.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
2.5 Reading: Whitman College: David Guichard’s Calculus: Chapter 2: Instantaneous Rate of Change: The Derivative: “Section 2.5: Adjectives for Functions”
Link: Whitman College: David Guichard’s Calculus: Chapter 2: Instantaneous Rate of Change: The Derivative: “Section 2.5: Adjectives for Functions” (PDF)
Instructions: Please click on the link above and read Section 2.5 (pages 5154) in its entirety. This reading covers the topics outlined in subsubunits 2.5.1 through 2.5.3. The intuitive notion of a continuous function is made precise using limits. Additionally, you will be introduced to the Intermediate Value Theorem, which rigorously captures the intuitive behavior of continuous realvalued functions.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
3.1 Reading: Whitman College: David Guichard’s Calculus: Chapter 3: Rules for Finding Derivatives: “Section 3.1: The Power Rule”
Link: Whitman College: David Guichard’s Calculus: Chapter 3: Rules for Finding Derivatives: “Section 3.1: The Power Rule” (PDF)
Instructions: Please click on the link above and read Section 3.1 (pages 5557) in its entirety. This section will show you a simple rule for how to find the derivative of a power function without explicitly computing a limit.
This reading should take you approximately 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
3.2 Reading: Whitman College: David Guichard’s Calculus: Chapter 3: Rules for Finding Derivatives: “Section 3.2: Linearity of the Derivative”
Link: Whitman College: David Guichard’s Calculus: Chapter 3: Rules for Finding Derivatives: “Section 3.2: Linearity of the Derivative” (PDF)
Instructions: Please click on the link above and read Section 3.2 (pages 5859) in its entirety. In this reading, you will see how the derivative behaves with regards to addition and subtraction of functions and with scalar multiplication. That is, you will see that the derivative is a linear operation.
This reading should take you approximately 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. (PDF) 
3.3 Reading: Whitman College: David Guichard’s Calculus: Chapter 3: Rules for Finding Derivatives: “Section 3.3: The Product Rule”
Link: Whitman College: David Guichard’s Calculus: Chapter 3: Rules for Finding Derivatives: “Section 3.3: The Product Rule” (PDF)
Instructions: Please click on the link above and read Section 3.3 (pages 6061) in its entirety. The naïve assumption is that the derivative of a product of two functions is the product of the derivatives of the two functions. This assumption is false. In this reading, you will see that the derivative of a product is slightly more complicated, but that it follows a definite rule called the product rule.
This reading should take you approximately 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. (PDF) 
3.4 Reading: Whitman College: David Guichard’s Calculus: Chapter 3: Rules for Finding Derivatives: “Section 3.4: The Quotient Rule”
Link: Whitman College: David Guichard’s Calculus: Chapter 3: Rules for Finding Derivatives: “Section 3.4: The Quotient Rule” (PDF)
Instructions: Please click on the link above and read Section 3.4 (pages 6265) in its entirety. As with product of two functions, the derivative of a quotient of two functions is not simply the quotient of the two derivatives. This reading will introduce you to the quotient rule for differentiating a quotient of two functions. In particular, it will allow you to find the derivative of any rational function.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
3.5 Reading: Whitman College: David Guichard’s Calculus: Chapter 3: Rules for Finding Derivatives: “Section 3.5: The Chain Rule”
Link: Whitman College: David Guichard’s Calculus: Chapter 3: Rules for Finding Derivatives: “Section 3.5: The Chain Rule” (PDF)
Instructions: Please click on the link above and read Section 3.5 (pages 6569) in its entirety. The chain rule explains how the derivative applies to the composition of functions. Pay particular attention to Example 3.11, which works through a derivative computation where all of the differentiation rules of this unit are applied in finding the derivative of one function.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
4.1 Reading: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.1: Trigonometric Functions”
Link: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.1: Trigonometric Functions” (PDF)
Instructions: Please click on the link above and read Section 4.1 (pages 7174) in its entirety. This reading will review the definition of trigonometric functions.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
4.2 Reading: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.2: The Derivative of sin x”
Link: Whitman College: Professor David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.2: The Derivative of sin x” (PDF)
Instructions: Please click on the link above and read Section 4.2 (pages 7475) in its entirety. This reading begins the computation of the derivative of the sine function. Two specific limits will need to be evaluated in order to complete this computation. These limits are addressed in the following section.
This reading should take you approximately 15 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
4.3 Reading: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.3: A Hard Limit”
Link: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.3: A Hard Limit” (PDF)
Instructions: Please click on the link above and read Section 4.3 (pages 7577) in its entirety. You have read this section previously to become acquainted with the Squeeze Theorem. When you read the section the second time, pay particular attention to the geometric argument used to set up the application of the Squeeze Theorem.
This reading should take you approximately 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
4.4 Reading: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.4: The Derivative of sin x, continued”
Link: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.4: The Derivative of sin x, continued” (PDF)
Instructions: Please click on the link above and read Section 4.4 (pages 7778) in its entirety. This reading completes the computation of the derivative of the sine function. Be sure to review all of the concepts involved in this computation.
This reading should take you approximately 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
4.5 Reading: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.5: Derivatives of the Trigonometric Functions”
Link: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.5: Derivatives of the Trigonometric Functions” (PDF)
Instructions: Please click on the link above and read Section 4.5 (pages 78 and 79) in its entirety. Building on the work done to compute the derivative of the sine function and the rules of differentiation from previous readings, the derivatives of the remaining trigonometric functions are computed.
This reading should take you approximately 15 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
4.6 Reading: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.6: Exponential and Logarithmic Functions”
Link: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.6: Exponential and Logarithmic Functions” (PDF)
Instructions: Please click on the link above and read Section 4.6 (pages 8081) in its entirety. This reading reviews the exponential and logarithmic functions, their properties, and their graphs.
This reading should take you approximately 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
4.7 Reading: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.7: Derivatives of the Exponential and Logarithmic Functions”
Link: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.7: Derivatives of the Exponential and Logarithmic Functions” (PDF)
Instructions: Please click on the link above and read Section 4.7 (pages 8286) in its entirety. In this reading, the derivatives of the exponential and logarithmic functions are computed. Notice that the number e is defined in terms of a particular limit.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
4.8 Reading: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.8: Implicit Differentiation”
Link: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.8: Implicit Differentiation” (PDF)
Instructions: Please click on the link above and read Section 4.8 (pages 8790) in its entirety. As a result of the chain rule, we have a method for computing derivatives of curves which are not explicitly described by a function. This method, called implicit differentiation, allows us to find tangent lines to such curves.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
4.9 Reading: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.9: Inverse Trigonometric Functions”
Link: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.9: Inverse Trigonometric Functions” (PDF)
Instructions: Please click on the link above and read Section 4.9 (pages 9194) in its entirety. In this reading, implicit differentiation and the Pythagorean identity are used to compute the derivatives of inverse trigonometric functions. You should notice that the same techniques can be used to find derivatives of other inverse functions as well.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
4.10 Reading: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.10: Limits Revisited”
Link: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.10: Limits Revisited” (PDF)
Instructions: Please click on the link above and read Section 4.10 (pages 9497) in its entirety. In this section, you will learn how derivatives relate back to limits. Limits of Indeterminate Forms (or limits of functions that, when evaluated, tend to 0/0 or ∞/∞) have previously been beyond our grasp. Using L’Hopital’s Rule, you will find that these limits are attainable with derivatives.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
4.11 Reading: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.11: Hyperbolic Functions”
Link: Whitman College: David Guichard’s Calculus: Chapter 4: Transcendental Functions: “Section 4.11: Hyperbolic Functions” (PDF)
Instructions: Please click on the link above and read Section 4.11 (pages 99102) in its entirety. In this reading, you are introduced to the hyperbolic trigonometric functions. These functions, which appear in many engineering and physics applications, are specific combinations of exponential functions which have properties similar to those that the ordinary trigonometric functions have.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
5.1 Reading: Whitman College: David Guichard’s Calculus: Chapter 5: Curve Sketching: “Section 5.1: Maxima and Minima”
Link: Whitman College: David Guichard’s Calculus: Chapter 5: Curve Sketching: “Section 5.1: Maxima and Minima” (PDF)
Instructions: Please click on the link above and read Section 5.1 (pages 103106) in its entirety. Fermat's Theorem indicates how derivatives can be used to find where a function reaches its highest or lowest points.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
5.2 Reading: Whitman College: David Guichard’s Calculus: Chapter 5: Curve Sketching: “Section 5.2: The First Derivative Test”
Link: Whitman College: David Guichard’s Calculus: Chapter 5: Curve Sketching: “Section 5.2: The First Derivative Test” (PDF)
Instructions: Please click on the link above and read Section 5.2 (page 107) in its entirety. In this reading, you will see how to use information about the derivative of a function to find local maxima and minima.
This reading should take you approximately 15 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
5.3 Reading: Whitman College: David Guichard’s Calculus: Chapter 5: Curve Sketching: “Section 5.3: The Second Derivative Test”
Link: Whitman College: David Guichard’s Calculus: Chapter 5: Curve Sketching: “Section 5.3: The Second Derivative Test” (PDF)
Instructions: Please click on the link above and read Section 5.3 (pages 108109) in its entirety. In this reading, you will see how to use information about the second derivative (that is, the derivative of the derivative) of a function to find local maxima and minima.
This reading should take you approximately 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
5.4 Reading: Whitman College: David Guichard’s Calculus: Chapter 5: Curve Sketching: “Section 5.4: Concavity and Inflection Points”
Link: Whitman College: David Guichard’s Calculus: Chapter 5: Curve Sketching: “Section 5.4: Concavity and Inflection Points” (PDF)
Instructions: Please click on the link above and read Section 5.4 (pages 109110) in its entirety. In this reading, you will see how the second derivative relates to the concavity of the graph of a function and use this information to find the points where the concavity changes, i.e. the inflection points of the graph.
This reading should take you approximately 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
5.5 Reading: Whitman College: David Guichard’s Calculus: Chapter 5: Curve Sketching: “Section 5.5: Asymptotes and Other Things to Look For”
Link: Whitman College: David Guichard’s Calculus: Chapter 5: Curve Sketching: “Section 5.5: Asymptotes and Other Things to Look For” (PDF)
Instructions: Please click on the link above and read Section 5.5 (pages 111112) in its entirety. In this reading, you will see how limits can be used to find any asymptotes the graph of a function may have.
This reading should take you approximately 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
6.1 Reading: Whitman College: David Guichard’s Calculus: Chapter 6: Applications of the Derivative: “Section 6.1: Optimization”
Link: Whitman College: David Guichard’s Calculus: Chapter 6: Applications of the Derivative: “Section 6.1: Optimization” (PDF)
Instructions: Please click on the link above and read Section 6.1 (pages 115124) in its entirety. An important application of the derivative is to find the global maximum and global minimum of a function. The Extreme Value Theorem indicates how to approach this problem. Pay particular attention to the summary at the end of the section.
This reading should take you approximately three hours to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
6.2 Reading: Whitman College: David Guichard’s Calculus: Chapter 6: Applications of the Derivative: “Section 6.2: Related Rates”
Link: Whitman College: David Guichard’s Calculus: Chapter 6: Applications of the Derivative: “Section 6.2: Related Rates” (PDF)
Instructions: Please click on the link above and read Section 6.2 (pages 127132) in its entirety. Another application of the chain rule, related rates problems apply to situations where multiple dependent variables are changing with respect to the same independent variable. Make note of the summary in the middle of page 128.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
6.3 Reading: Whitman College: David Guichard’s Calculus: Chapter 6: Applications of the Derivative: “Section 6.3: Newton's Method”
Link: Whitman College: David Guichard’s Calculus: Chapter 6: Applications of the Derivative: “Section 6.3: Newton's Method” (PDF)
Instructions: Please click on the link above and read Section 6.3 (pages 135138) in its entirety. In this section, you will be introduced to a numerical approximation technique called Newton's Method. This method is useful for finding approximate solutions to equations which cannot be solved exactly.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
6.4 Reading: Whitman College: David Guichard’s Calculus: Chapter 6: Applications of the Derivative: “Section 6.4: Linear Approximations”
Link: Whitman College: David Guichard’s Calculus: Chapter 6: Applications of the Derivative: “Section 6.4: Linear Approximations” (PDF)
Instructions: Please click on the link above and read Section 6.4 (pages 139140) in its entirety. In this reading, you will see how tangent lines can be used to locally approximate functions.
This reading should take you approximately 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
6.5 Reading: Whitman College: David Guichard’s Calculus: Chapter 6: Applications of the Derivative: “Section 6.5: The Mean Value Theorem”
Link: Whitman College: David Guichard’s Calculus: Chapter 6: Applications of the Derivative: “Section 6.5: The Mean Value Theorem” (PDF)
Instructions: Please click on the link above and read Section 6.5 (pages 141144) in its entirety. The Mean Value Theorem is an important application of the derivative which is used most often in developing further mathematical theories. A special case of the Mean Value Theorem, called Rolle's Theorem, leads to a characterization of antiderivatives.
This reading should take you approximately 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
7.1 Reading: Whitman College: David Guichard’s Calculus: Chapter 7: Integration: “Section 7.1: Two Examples”
Link: Whitman College: David Guichard’s Calculus: Chapter 7: Integration: “Section 7.1: Two Examples” (PDF)
Instructions: Please click on the link above and read Section 7.1 (pages 145149) in its entirety. This reading introduces the integral through two examples. The first example addresses the question of how to determine the distance traveled based only on information about velocity. The second example addresses the question of how to determine the area under the graph of a function. Surprisingly, these two questions are closely related to each other and to the derivative.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
7.2 Reading: Whitman College: David Guichard’s Calculus: Chapter 7: Integration: “Section 7.2: The Fundamental Theorem of Calculus”
Link: Whitman College: David Guichard’s Calculus: Chapter 7: Integration: “Section 7.2: The Fundamental Theorem of Calculus” (PDF)
Instructions: Please click on the link above and read Section 7.2 (pages 149155) in its entirety. Pay close attention to the treatment of Riemann sums, which lead to the definite integral. The Fundamental Theorem of Calculus explicitly describes the relationship between integrals and derivatives.
This reading should take you approximately one hour and 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
7.3 Reading: Whitman College: David Guichard’s Calculus: Chapter 7: Integration: “Section 7.3: Some Properties of Integrals”
Link: Whitman College: David Guichard’s Calculus: Chapter 7: Integration: “Section 7.3: Some Properties of Integrals” (PDF)
Instructions: Please click on the link above and read Section 7.3 (pages 156160) in its entirety. In particular, note that the definite integral enjoys the same linearity properties that the derivative does, in addition to some others. In its application to velocity functions, pay particular attention to the distinction between distance traveled and net distance traveled.
This reading should take you approximately one hour to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here. 
7.4 Reading: Whitman College: David Guichard’s Calculus: Chapter 8: Techniques of Integration: “Section 8.1: Substitution”
Link: Whitman College: David Guichard’s Calculus: Chapter 8: Techniques of Integration: “Section 8.1: Substitution” (PDF)
Instructions: Please click on the link above and read Section 8.1 (pages 161166) in its entirety. This section explains the process of taking the integral of slightly more complicated functions. We do this by implementing a “change of variables,” or rewriting a complicated integral in terms of elementary functions that we already know how to integrate. Simply put, integration by substitution is merely the act of taking the chain rule in reverse.
This reading should take approximately one hour and 30 minutes to complete.
Terms of Use: This resource is licensed under a Creative Commons AttributionNonCommercialShareAlike 3.0 License. This text was originally written by Professor David Guichard. It has since been modified to include edited material from Neal Koblitz of the University of Washington, H. Jerome Keisler of the University of Wisconsin, Albert Schueller, Barry Balof, and Mike Wills. You can access the original version here.