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Department of Mathematics
Real Analysis III
Lecture notes
- Introduction to n-Dimensional Space
- Open Sets
- Limits and Continuity
- The Derivative of a Scalar Field with Respect to a Vector
- Directional Derivatives and Partial Derivatives
- The Total Derivative
- The Gradient of a Scalar Field
- A Chain Rule for Derivatives of Scalar Fields
- Derivatives of Vector Fields
- Sufficient Conditions for the Equality of Mixed Partial Derivatives
- Derivatives of Functions De?ned Implicitly
- Maxima, Minima, and Saddle Points