18.02SC | Fall 2010 | Undergraduate
Multivariable Calculus
2. Partial Derivatives

Part A: Functions of Two Variables, Tangent Approximation and Optimization

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We start this unit by learning to visualize functions of several variables using graphs and level curves. Following this we will study partial derivatives. These will be used in the tangent approximation formula, which is one of the keys to multivariable calculus. It ties together the geometric and algebraic sides of the subject and is the higher dimensional analog of the equation for the tangent line found in single variable calculus. We will use it in part B to develop the chain rule.

We will apply our understanding of partial derivatives to solving unconstrained optimization problems. (In part C we will solve constrained optimization problems.)

» Session 24: Functions of Two Variables: Graphs
» Session 25: Level Curves and Contour Plots
» Session 26: Partial Derivatives
» Session 27: Approximation Formula
» Session 28: Optimization Problems
» Session 29: Least Squares
» Session 30: Second Derivative Test
» Session 31: Example
» Problem Set 4

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Fall 2010
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