Lecture Notes for Math 4013
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Lecture 1: Vectors and Vector Spaces
Lecture 2: Vectors and Vector Spaces, Cont'd
Lecture 3: Vectors and Vector Spaces, Cont'd
Lecture 4: Real-Valued Functions
Lecture 5: Limits of Real-Valued Functions
Lecture 6: Partial Derivatives and Differentiability
Lecture 7: Differentials and the Chain Rule
Lecture 8: Directional Derivatives and the Gradient
Lecture 9: Paths and Curves in
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Lecture 10: Higher Order Derivatives and Taylor Expansions
Lecture 11: Maxima and Minima
Lecture 12: Arc Length
Lecture 13: Vector Fields
Lecture 14: The Divergence and Curl of a Vector Field
Lecture 15: Identities of Vector Analysis
Lecture 16: Double Integrals over Rectangles
Lecture 17: Double Integrals over More General Regions
Lecture 18: Reversing the Order of Integration
Lecture 19: Integrals over 3-Dimensional Regions
Lecture 20: Integration by a Change of Variables
Lecture 21: Integration by a Change of Variables, Cont'd
Lecture 22: Integrals over Curves
Lecture 23: Integrals over Surfaces
Lecture 24: The Integral Theorems of Vector Analysis