Topic  Name  Description 

Course Introduction  Course Syllabus  
1.1: Preview of Calculus  Preview of Calculus  Read this section for an introduction to calculus. 
Derivatives and Tangent Lines  Watch this video (until 8:12) on how to find the slopes of tangent lines from a graph. 

Find the Area of an Irregular Shape  Watch this video on how to find the area of an irregular shape. 

Practice Problems  Work through the oddnumbered problems 17. Once you have completed the problem set, check your answers. 

1.2: Lines in the Plane  Lines in the Plane  Read this section and work through practice problems 19. 
Find a Slope Given Two Points  Watch this video on how to find the slope of a line given two points on a graph. 

Find the Equation of a Line Given Two Points  Watch this video on how to write the equation of a line through two points using the slopepoint formula, and converting the equation to slopeintersect form. 

Equations of Circles: Radius and Center  Watch this video on how to write an equation of a circle with the given center and radius. 

How to Find the Equation of a Line from a Slope and Point  Watch this video on how to write an equation of a line through a point given the slope. 

Determine the Equation of a Line Parallel to a Line in General Form  Watch this video on how to find the equation of a line going through a point and parallel to another line. 

Determine the Equation of a Line Perpendicular to a Line in SlopeIntercept Form  Watch this video on how to find the equation of a line going through a point and perpendicular to another line. 

Practice Problems  Work through the oddnumbered problems 129. Once you have completed the problem set, check your answers. 

1.3: Functions and Their Graphs  Functions and Their Graphs  Read this section for an introduction to functions and their graphs. Work through practice problems 15. 
Evaluate Function at a Point  Watch this video on evaluating function at a point. 

Practice Problems  Work through the oddnumbered problems 123. Once you have completed the problem set, check your answers. 

1.4: Combinations of Functions  Combinations of Functions  Read this section for an introduction to combinations of functions, then work through practice problems 19. 
More on the Composition of Functions  Watch the first 16 minutes of this video on evaluating composition of functions. 

Combine Functions using Algebraic Operations  Watch this video on combining functions using algebraic operations. 

Evaluating Functions Given Equations, Graphs, and Tables  Watch this video on evaluating functions given equations, graphs and tables. 

Practice Problems  Work through the oddnumbered problems 131. Once you have completed the problem set, check your answers. 

1.5: Mathematical Language  Mathematical Language  Read this section for an introduction to mathematical language, then work through practice problems 14. 
Negating Quantified Statements  Watch this video on how to negate a quantified statement. 

Converse and Contrapositive  Watch this video on converse and contrapositive of a conditional statement and how to write them. 

Practice Problems  Work through the oddnumbered problems 125. Once you have completed the problem set, check your answers for the oddnumbered questions. 

2.1: Tangent Lines, Velocities, and Growth  Tangent Lines, Velocities, and Growth  Read this section for an introduction to connecting derivatives to quantities we can see in the real world. Work through practice problems 14. 
Slope of a Function at a Point  Watch this video on how to find the slope of the line tangent to the graph of a function at a point. 

Practice Problems  Work through the oddnumbered problems 19. Once you have completed the problem set, check your answers for the oddnumbered questions. 

2.2: The Limit of a Function  The Limit of a Function  Read this section for an introduction to connecting derivatives to quantities we can see in the real world. Work through practice problems 14. 
Evaluating Limits Using a Graph  Watch this video on evaluating limits using a graph. 

More on the Limit of a Function  Watch this video on how to evaluate limit of a function. 

The Limit of Laws  Read this section. 

Practice Problems  Work through the oddnumbered problems 119. Once you have completed the problem set, check your answers. 

2.3: Properties of Limits  Properties of Limits  Read this section to learn about the properties of limits. Work through practice problems 16. 
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. 

Calculating Slope of Tangent Line Using the Definition of a Derivative  
Practice Problems  Work through the oddnumbered problems 121. Once you have completed the problem set, check your answers. 

2.4: Continuous Functions  Continuous Functions  Read this section for an introduction to what we mean when we say a function is continuous. Work through practice problems 1 and 2. 
More on Continuous Functions  Watch this video on continuous functions. 

Intermediate Value Theorem  Watch this video on the Intermediate Value Theorem. 

Practice Problems  Work through the oddnumbered problems 123. Once you have completed the problem set, check your answers. 

2.5: Definition of a Limit  Definition of a Limit  Read this section to learn how a limit is defined. Work through practice problems 16. 
EpsilonDelta Limits  Watch this video to learn the epsilondelta definition of a limit. 

Practice Problems  Work through the oddnumbered problems 123. Once you have completed the problem set, check your answers. 

3.1: Introduction to Derivatives  Introduction to Derivatives  Read this section to lay the groundwork for introducing the concept of a derivative. Work through practice problems 15. 
The Tangent Line  Watch this video on the slope of secant lines converging to tangent line slopes. 

Practice Problems  Work through the oddnumbered problems 117. Once you have completed the problem set, check your answers. 

3.2: The Definition of a Derivative  The Definition of a Derivative  Read this section to understand the definition of a derivative. Work through practice problems 18. 
Derivatives from the Definition  Watch this video on how to find a derivative from the definition. 

Practice Problems  Work through the oddnumbered problems 137. Once you have completed the problem set, check your answers. 

3.3: Derivatives, Properties, and Formulas  Derivatives, Properties, and Formulas  Read this section to understand the properties of derivatives. Work through practice problems 111. 
Applying the Product Rule for Derivatives  Watch this video on the product rule for differentiation. 

Practice Problems  Work through the oddnumbered problems 155. Once you have completed the problem set, check your answers. 

3.4: Derivative Patterns  Derivative Patterns  Read this section to learn about patterns of derivatives. Work through practice problems 18. 
The Power Rule for Polynomials  Watch this video on how to find derivatives of polynomial functions using the power rule. 

Derivatives of Exponential Functions  Watch this video on derivatives of exponential functions. 

Derivatives of Trigonometric Functions  Watch this video on how to find the derivatives of trig functions. 

HigherOrdered Derivatives  Watch this video on how to calculate and intepret higher ordered derivatives. 

Practice Problems  Work through the oddnumbered problems 147. Once you have completed the problem set, check your answers. 

3.5: The Chain Rule  The Chain Rule  Read this section to learn about the Chain Rule. Work through practice problems 18. 
Chain Rule Examples  Watch these videos for an introduction to the chain rule for differentiation and examples of the chain rule for differentiation. 

Practice Problems  Work through the oddnumbered problems 183. Once you have completed the problem set, check your answers. 

3.6: Some Applications of the Chain Rule  Some Applications of the Chain Rule  Read this section to learn how to apply the Chain Rule. Work through practice problems 18. 
Solving a Related Rates Problem  Watch this video on using the chain rule to solve rates problems. 

Practice Problems  Work through the oddnumbered problems 149. Once you have completed the problem set, check your answers. 

3.7: Related Rates  Related Rates  Read this section to learn to connect derivatives to the concept of the rate at which things change. Work through practice problems 13. 
Derivatives as Rates of Change  Watch this video on application of derivatives 

Differentiating Parametric Functions  Watch this video on differentiating parametric functions. 

Practice Problems  Work through the oddnumbered problems 121. Once you have completed the problem set, check your answers. 

3.8: Newton's Method for Finding Roots  Newton's Method for Finding Roots  Read this section. Work through practice problems 16. 
Using Newton's Method  Watch this video on Newton's method. 

Determining Differentiability Graphically  Watch this video on how to determine differentiability graphically. 

Continuity on Intervals  Watch this video on continuity of intervals and continuous functions. 

Practice Problems  Work through the oddnumbered problems 121. Once you have completed the problem set, check your answers. 

3.9: Linear Approximation and Differentials  Linear Approximation and Differentials  Read this section to learn how linear approximation and differentials are connected. Work through practice problems 110. 
More on Linear Approximation  Watch this video on linear approximation and differentials. 

The Properties of a Differential of a Function  Watch this video on how to calculate the differential of a function using derivatives. 

Practice Problems  Work through the oddnumbered problems 119. Once you have completed the problem set, check your answers. 

3.10: Implicit and Logarithmic Differentiation  Implicit and Logarithmic Differentiation  Read this section to learn about implicit and logarithmic differentiation. Work through practice problems 16. 
Implicit Differentiation and the Derivative of x^(x^x)  Watch these videos on implicit and logarithmic differentiation. 

Practice Problems  Work through the oddnumbered problems 155. Once you have completed the problem set, check your answers. 

4.1: Finding Maximums and Minimums  Finding Maximums and Minimums  Read this section to learn about maximums, minimums, and extreme values for functions. Work through practice problems 15. 
Maxima and Minima  Watch this video on how to identify minimum/maximum points of a function. 

Practice Problems  Work through the oddnumbered problems 143. Once you have completed the problem set, check your answers. 

4.2: The Mean Value Theorem and Its Consequences  The Mean Value Theorem and Its Consequences  Read this section to learn about the Mean Value Theorem and its consequences. Work through practice problems 13. 
Critical Points and the Mean Value Theorem  Watch this video on local maximums/minimums and proves Rolle's Theorem and the Mean Value Theorem. 

Practice Problems  Work through the oddnumbered problems 135. Once you have completed the problem set, check your answers. 

4.3: The First Derivative and the Shape of a Function f(x)  The First Derivative and the Shape of a Function f(x)  Read this section to learn how the first derivative is used to determine the shape of functions. Work through practice problems 19. 
Examples of the First Derivative Test  Watch both parts of this video on the first derivative test. 

Practice Problems  Work through the oddnumbered problems 129. Once you have completed the problem set, check your answers. 

4.4: The Second Derivative and the Shape of a Function f(x)  The Second Derivative and the Shape of a Function f(x)  Read this section to learn how the second derivative is used to determine the shape of functions. Work through practice problems 19. 
Concavity Across 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. 

Concavity and the Second Derivative  Watch this video, which works through an example of the second derivative test. 

Practice Problems  Work through the oddnumbered problems 117. Once you have completed the problem set, check your answers. 

4.5: Applied Maximum and Minimum Problems  Applied Maximum and Minimum Problems  Read this section to learn how to apply previously learned principles to maximum and minimum problems. Work through practice problems 13. There is no review for this section; instead, make sure to study the problems carefully to become familiar with applied maximum and minimum problems. 
Minimizing Sum of Squares  Watch this video on optimization. 

Minimum Triangle Area  Watch this video on optimization. 

Practice Problems  Work through the oddnumbered problems 133. Once you have completed the problem set, check your answers. 

4.6: Infinite Limits and Asymptotes  Infinite Limits and Asymptotes  Read this section to learn how to use and apply infinite limits to asymptotes. Work through practice problems 18. 
Limits at Infinity and Asymptotes  Watch this video on finding limits at infinite, and graphing using first and second derivative tests. 

Practice Problems  Work through the oddnumbered problems 159. Once you have completed the problem set, check your answer 

4.7: L'Hopital's Rule  L'Hopital's Rule  Read this section to learn how to use and apply L'Hopital's Rule. Work through practice problems 13. 
Introduction to L'Hopital's Rule  Watch this video for an introduction to L'Hopital's Rule. 

Practice Problems  Work through the oddnumbered problems 129. Once you have completed the problem set, check your answers. 

5.1: Introduction to Integration  Introduction to Integration  Read this section to learn about area. Work through practice problems 19. 
Find the Exact and Approximate Area of a Region  Watch this video on finding the exact and approximate area of a region. 

Practice Problems  Work through the oddnumbered problems 115. Once you have completed the problem set, check your answers. 

5.2: Sigma Notation and Riemann Sums  Sigma Notation and Riemann Sums  Read this section to learn about area. Work through practice problems 19. 
Riemann Sums in Summation Notation  Watch this video on riemann sums in summation notation. 

Practice Problems  Work through the oddnumbered problems 161. Once you have completed the problem set, check your answers. 

5.3: The Definite Integral  The Definite Integral  Read this section to learn about the definite integral and its applications. Work through practice problems 16. 
Find the Area between Two Curves Using Definite Integrals  Watch this video on how to find the area between two curves using definite integrals. 

Practice Problems  Work through the oddnumbered problems 129. Once you have completed the problem set, check your answers. 

5.4: Properties of the Definite Integral  Properties of the Definite Integral  Read this section to learn about properties of definite integrals and how functions can be defined using definite integrals. Work through practice problems 15. 
Integrals and the Graph of a Function  Watch this video on definite integral and a function's graph. 

Practice Problems  Work through the oddnumbered problems 151. Once you have completed the problem set, check your answers for the oddnumbered questions against here. 

5.5: Areas, Integrals, and Antiderivatives  Areas, Integrals, and Antiderivatives  Read this section to learn about the relationship among areas, integrals, and antiderivatives. Work through practice problems 15. 
Integration and Antiderivatives  Watch this video on Power Rule of Integration, Antiderivative of Polynomial Functions, Integrating Square Root Functions, and Antiderivatives of Rational Functions. 

Practice Problems  Work through the oddnumbered problems 125. Once you have completed the problem set, check your answers. 

5.6: The Fundamental Theorem of Calculus  The Fundamental Theorem of Calculus  Read this section to see the connection between derivatives and integrals. Work through practice problems 15. 
Integrals and the Fundamental Theorem of Calculus  Watch this video on Integrals and Fundamental theorem of calculus. 

Differentiating an Integral Function  Watch this video on differentiating integral functions. 

Practice Problems  Work through the oddnumbered problems 167. Once you have completed the problem set, check your answers. 

5.7: Finding Antiderivatives  Finding Antiderivatives  Read this section to see how you 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. 
Integrating with USubstitution  Watch these videos on change of variable, also called substitution or Usubstitution. 

Practice Problems  Work through the oddnumbered problems 169. Once you have completed the problem set, check your answers. 

5.8: First Application of Definite Integral  First Application of Definite Integral  Read this section to see how some applied problems can be reformulated as integration problems. Work through practice problems 14. 
Practice Problems  Work through the oddnumbered problems 141. Once you have completed the problem set, check your answers. 

5.9: Using Tables to Find Antiderivatives  Using Tables to Find Antiderivatives  Read this section to learn how to use tables to find antiderivatives. See the Calculus Reference Facts for the table of integrals. Work through practice problems 15. 
Practice Problems  Work through the oddnumbered problems 155. Once you have completed the problem set, check your answers. 

Study Guide  MA005 Study Guide  
Course Feedback Survey  Course Feedback Survey 