Topic | Name | Description |
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Course Introduction | ||
1.1: Preview of Calculus | Read this section for an introduction to calculus. |
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Watch this video (until 8:12) on how to find the slopes of tangent lines from a graph. |
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Watch this video on how to find the area of an irregular shape. |
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Work through the odd-numbered problems 1-7. Once you have completed the problem set, check your answers. |
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1.2: Lines in the Plane | Read this section and work through practice problems 1-9. |
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Watch this video on how to find the slope of a line given two points on a graph. |
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Watch this video on how to write the equation of a line through two points using the slope-point formula, and converting the equation to slope-intersect form. |
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Watch this video on how to write an equation of a circle with the given center and radius. |
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Watch this video on how to write an equation of a line through a point given the slope. |
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Watch this video on how to find the equation of a line going through a point and parallel to another line. |
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Watch this video on how to find the equation of a line going through a point and perpendicular to another line. |
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Work through the odd-numbered problems 1-29. Once you have completed the problem set, check your answers. |
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1.3: Functions and Their Graphs | Read this section for an introduction to functions and their graphs. Work through practice problems 1-5. |
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Watch this video on evaluating function at a point. |
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Work through the odd-numbered problems 1-23. Once you have completed the problem set, check your answers. |
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1.4: Combinations of Functions | Read this section for an introduction to combinations of functions, then work through practice problems 1-9. |
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Watch the first 16 minutes of this video on evaluating composition of functions. |
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Watch this video on combining functions using algebraic operations. |
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Watch this video on evaluating functions given equations, graphs and tables. |
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Work through the odd-numbered problems 1-31. Once you have completed the problem set, check your answers. |
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1.5: Mathematical Language | Read this section for an introduction to mathematical language, then work through practice problems 1-4. |
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Watch this video on how to negate a quantified statement. |
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Watch this video on converse and contrapositive of a conditional statement and how to write them. |
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Work through the odd-numbered problems 1-25. Once you have completed the problem set, check your answers for the odd-numbered questions. |
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2.1: 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 1-4. |
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Watch this video on how to find the slope of the line tangent to the graph of a function at a point. |
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Work through the odd-numbered problems 1-9. Once you have completed the problem set, check your answers for the odd-numbered questions. |
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2.2: 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 1-4. |
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Watch this video on evaluating limits using a graph. |
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Watch this video on how to evaluate limit of a function. |
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Read this section. |
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Work through the odd-numbered problems 1-19. Once you have completed the problem set, check your answers. |
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2.3: Properties of Limits | Read this section to learn about the properties of limits. Work through practice problems 1-6. |
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Watch this video on finding limits algebraically. Be warned that removing |
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Work through the odd-numbered problems 1-21. Once you have completed the problem set, check your answers. |
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2.4: 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. |
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Watch this video on continuous functions. |
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Watch this video on the Intermediate Value Theorem. |
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Work through the odd-numbered problems 1-23. Once you have completed the problem set, check your answers. |
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2.5: Definition of a Limit | Read this section to learn how a limit is defined. Work through practice problems 1-6. |
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Watch this video to learn the epsilon-delta definition of a limit. |
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Work through the odd-numbered problems 1-23. Once you have completed the problem set, check your answers. |
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3.1: Introduction to Derivatives | Read this section to lay the groundwork for introducing the concept of a derivative. Work through practice problems 1-5. |
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Watch this video on the slope of secant lines converging to tangent line slopes. |
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Work through the odd-numbered problems 1-17. Once you have completed the problem set, check your answers. |
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3.2: The Definition of a Derivative | Read this section to understand the definition of a derivative. Work through practice problems 1-8. |
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Watch this video on how to find a derivative from the definition. |
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Work through the odd-numbered problems 1-37. Once you have completed the problem set, check your answers. |
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3.3: Derivatives, Properties, and Formulas | Read this section to understand the properties of derivatives. Work through practice problems 1-11. |
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Watch this video on the product rule for differentiation. |
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Work through the odd-numbered problems 1-55. Once you have completed the problem set, check your answers. |
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3.4: Derivative Patterns | Read this section to learn about patterns of derivatives. Work through practice problems 1-8. |
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Watch this video on how to find derivatives of polynomial functions using the power rule. |
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Watch this video on derivatives of exponential functions. |
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Watch this video on how to find the derivatives of trig functions. |
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Watch this video on how to calculate and intepret higher ordered derivatives. |
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Work through the odd-numbered problems 1-47. Once you have completed the problem set, check your answers. |
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3.5: The Chain Rule | Read this section to learn about the Chain Rule. Work through practice problems 1-8. |
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Watch these videos for an introduction to the chain rule for differentiation and examples of the chain rule for differentiation. |
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Work through the odd-numbered problems 1-83. Once you have completed the problem set, check your answers. |
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3.6: Some Applications of the Chain Rule | Read this section to learn how to apply the Chain Rule. Work through practice problems 1-8. |
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Watch this video on using the chain rule to solve rates problems. |
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Work through the odd-numbered problems 1-49. Once you have completed the problem set, check your answers. |
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3.7: Related Rates | Read this section to learn to connect derivatives to the concept of the rate at which things change. Work through practice problems 1-3. |
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Watch this video on application of derivatives |
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Watch this video on differentiating parametric functions. |
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Work through the odd-numbered problems 1-21. Once you have completed the problem set, check your answers. |
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3.8: Newton's Method for Finding Roots | Read this section. Work through practice problems 1-6. |
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Watch this video on Newton's method. |
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Watch this video on how to determine differentiability graphically. |
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Watch this video on continuity of intervals and continuous functions. |
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Work through the odd-numbered problems 1-21. Once you have completed the problem set, check your answers. |
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3.9: Linear Approximation and Differentials | Read this section to learn how linear approximation and differentials are connected. Work through practice problems 1-10. |
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Watch this video on linear approximation and differentials. |
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Watch this video on how to calculate the differential of a function using derivatives. |
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Work through the odd-numbered problems 1-19. Once you have completed the problem set, check your answers. |
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3.10: Implicit and Logarithmic Differentiation | Read this section to learn about implicit and logarithmic differentiation. Work through practice problems 1-6. |
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Watch these videos on implicit and logarithmic differentiation. |
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Work through the odd-numbered problems 1-55. Once you have completed the problem set, check your answers. |
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4.1: Finding Maximums and Minimums | Read this section to learn about maximums, minimums, and extreme values for functions. Work through practice problems 1-5. |
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Watch this video on how to identify minimum/maximum points of a function. |
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Work through the odd-numbered problems 1-43. Once you have completed the problem set, check your answers. |
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4.2: The Mean Value Theorem and Its Consequences | Read this section to learn about the Mean Value Theorem and its consequences. Work through practice problems 1-3. |
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Watch this video on local maximums/minimums and proves Rolle's Theorem and the Mean Value Theorem. |
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Work through the odd-numbered problems 1-35. Once you have completed the problem set, check your answers. |
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4.3: 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 1-9. |
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Watch both parts of this video on the first derivative test. |
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Work through the odd-numbered problems 1-29. Once you have completed the problem set, check your answers. |
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4.4: 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 1-9. |
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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. |
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Watch this video, which works through an example of the second derivative test. |
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Work through the odd-numbered problems 1-17. Once you have completed the problem set, check your answers. |
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4.5: 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 1-3. There is no review for this section; instead, make sure to study the problems carefully to become familiar with applied maximum and minimum problems. |
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Watch this video on optimization. |
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Watch this video on optimization. |
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Work through the odd-numbered problems 1-33. Once you have completed the problem set, check your answers. |
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4.6: Infinite Limits and Asymptotes | Read this section to learn how to use and apply infinite limits to asymptotes. Work through practice problems 1-8. |
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Watch this video on finding limits at infinite, and graphing using first and second derivative tests. |
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Work through the odd-numbered problems 1-59. Once you have completed the problem set, check your answer |
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4.7: L'Hopital's Rule | Read this section to learn how to use and apply L'Hopital's Rule. Work through practice problems 1-3. |
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Watch this video for an introduction to L'Hopital's Rule. |
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Work through the odd-numbered problems 1-29. Once you have completed the problem set, check your answers. |
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5.1: Introduction to Integration | Read this section to learn about area. Work through practice problems 1-9. |
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Watch this video on finding the exact and approximate area of a region. |
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Work through the odd-numbered problems 1-15. Once you have completed the problem set, check your answers. |
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5.2: Sigma Notation and Riemann Sums | Read this section to learn about area. Work through practice problems 1-9. |
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Watch this video on riemann sums in summation notation. |
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Work through the odd-numbered problems 1-61. Once you have completed the problem set, check your answers. |
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5.3: The Definite Integral | Read this section to learn about the definite integral and its applications. Work through practice problems 1-6. |
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Watch this video on how to find the area between two curves using definite integrals. |
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Work through the odd-numbered problems 1-29. Once you have completed the problem set, check your answers. |
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5.4: 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 1-5. |
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Watch this video on definite integral and a function's graph. |
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Work through the odd-numbered problems 1-51. Once you have completed the problem set, check your answers for the odd-numbered questions against here. |
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5.5: Areas, Integrals, and Antiderivatives | Read this section to learn about the relationship among areas, integrals, and antiderivatives. Work through practice problems 1-5. |
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Watch this video on Power Rule of Integration, Antiderivative of Polynomial Functions, Integrating Square Root Functions, and Antiderivatives of Rational Functions. |
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Work through the odd-numbered problems 1-25. Once you have completed the problem set, check your answers. |
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5.6: The Fundamental Theorem of Calculus | Read this section to see the connection between derivatives and integrals. Work through practice problems 1-5. |
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Watch this video on Integrals and Fundamental theorem of calculus. |
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Watch this video on differentiating integral functions. |
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Work through the odd-numbered problems 1-67. Once you have completed the problem set, check your answers. |
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5.7: 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 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. |
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Watch these videos on change of variable, also called substitution or U-substitution. |
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Work through the odd-numbered problems 1-69. Once you have completed the problem set, check your answers. |
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5.8: First Application of Definite Integral | Read this section to see how some applied problems can be reformulated as integration problems. Work through practice problems 1-4. |
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Work through the odd-numbered problems 1-41. Once you have completed the problem set, check your answers. |
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5.9: 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 1-5. |
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Work through the odd-numbered problems 1-55. Once you have completed the problem set, check your answers. |
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Study Guide | ||
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