Math 142, Chapter 8 Spring 2011 Zarestky Chapter 8 Reading Notes In this chapter, we will learn about functions of more than one variable and apply our calculus skills to analyze these functions. Section 8.1: Functions of Several Variables By the end of this section, you should be able to: • Evaluate a function of two or more variables. • Plot points in the three-dimensional coordinate system. • Sketch a graph of a function in the three-dimensional coordinate system. • Evaluate a difference quotient for a function of two variables. • Apply business models involving more than one independent variable. The first few examples are to get you comfortable with multivariate functions. Read Examples 1-5. Attempt the Matched Problems. What questions do you have?Math 142, Chapter 8 Spring 2011 Zarestky Graphs in three dimensions can be tougher to visualize than in two dimensions. In example 6, you will learn about three-dimensional coordinates. Read Example 6. Attempt the Matched Problem. What questions do you have? Skim the remainder of the section. We will discuss graphs of three-dimensional curves as a class. Check your understanding of this section by working a few problems from the exercises on your own. Focus on 1-33(odd), 37, 39, 43, 45, 49, 51, 53, 57, 59, 61. Do you have any questions?Math 142, Chapter 8 Spring 2011 Zarestky Section 8.2: Partial Derivatives By the end of this section, you should be able to: • Calculate first- and second-order partial derivatives. • Apply business models involving more than one independent variable. In this section, you will take derivatives of multivariate functions. Note that it is only possible to take a derivative with respect to one variable at a time! Work Examples 1-4 and attempt the Matched Problems. Compare your answers to the book’s solution. What questions do you have?Math 142, Chapter 8 Spring 2011 Zarestky In the next example, you will calculate higher-order derivatives, analogous to the second derivative for a function of a single variable. Work Example 5 and attempt the Matched Problem. Compare your answers to the book’s solution. What questions do you have? Check your understanding of this section by working a few problems from the exercises on your own. Focus on 1-69(odd), 79, 81, 83, 85, 93, 95. What questions do you still have?Math 142, Chapter 8 Spring 2011 Zarestky Section 8.3: Maxima and Minima By the end of this section, you should be able to: • Determine if a critical point in three dimensions is a local maximum, local minimum, or a saddle point by using the second derivative test. In this section, you will identify the maximum and minimum values of multivariate functions. Read pp. 467-469 and make notes regarding the vocabulary. How are the terms used the same or differently than in our previous contexts? Work Examples 1-2 and attempt the Matched Problems. Compare your answers to the book’s solution. What questions do you have?Math 142, Chapter 8 Spring 2011 Zarestky Work Example 3 and attempt the Matched Problem. Compare your answers to the book’s solution. What questions do you have? Work Example 4 and attempt the Matched Problem. Compare your answers to the book’s solution. What questions do you have? Check your understanding of this section by working a few problems from the exercises on your own. Focus on 1, 5-21(odd), 29, 31, 35. What questions do you still have?Math 142, Chapter 8 Spring 2011 Zarestky Section 8.5: Method of Least Squares By the end of this section, you should be able to: • Apply the method of least-squares to model a data set. Skim this section and we’ll save it for an in-class discussion. Check your understanding of this section by working a few problems from the exercises on your own. Focus on 1-11(odd), 15. What questions do you still