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lec3-3 - Chapter 4 Partial dierentiation It is generally...

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Chapter 4: Partial differentiation It is generally the case that derivatives are introduced in terms of functions of a single variable. For example, y = f ( x ), then dy dx = df dx = f 0 . However, most of the time we are dealing with quantities that are functions of several variables. For example, we usually want physical quantities in three dimensional space. For example, the electric field at each point in space might depend on x , y , and z , ~ E ~ E ( x , y , z ). Or, it might be convenient in some cases to use spherical coordinates, and then ~ E ~ E ( r , φ, θ ). We hence have to think about partial differentiation in physics. Patrick K. Schelling Introduction to Theoretical Methods
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Chapter 4 goals By the end of this chapter, you should be able to: I Work with power series in two or more variables Patrick K. Schelling Introduction to Theoretical Methods
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Chapter 4 goals By the end of this chapter, you should be able to: I Work with power series in two or more variables I Use total differentials Patrick K. Schelling Introduction to Theoretical Methods
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Chapter 4 goals By the end of this chapter, you should be able to: I Work with power series in two or more variables I Use total differentials I Use total differentials for approximation Patrick K. Schelling Introduction to Theoretical Methods
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Chapter 4 goals By the end of this chapter, you should be able to: I Work with power series in two or more variables I Use total differentials I Use total differentials for approximation I Use the chain rule for differentiation of a function of a function Patrick K. Schelling Introduction to Theoretical Methods
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Chapter 4 goals By the end of this chapter, you should be able to: I Work with power series in two or more variables I Use total differentials I Use total differentials for approximation I
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