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Solutions to Vector Calculus 6e
by J. E. Marsden
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155 of 1487 listed exercises currently have solution PDFs.
Chapter 1: The Geometry of Euclidean Space
Chapter 2: Differentiation
Chapter 3: Higher-Order Derivatives: Maxima and Minima
Chapter 4: Vector-Valued Functions
Chapter 5: Double and Triple Integrals
Chapter 6: The Change of Variables Formula and Applications of Integration
Chapter 7: Integrals Over Paths and Surfaces
Chapter 8: The Integral Theorems of Vector Analysis
Section 1.1: Vectors in Two- and Three-Dimensional Space
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Section 1.2: The Inner Product, Length, and Distance
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Section 1.3: Matrices, Determinants, and the Cross Product
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Section 1.4: Cylindrical and Spherical Coordinates
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Section 1.5: n-Dimensional Euclidean Space
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Section 2.1: The Geometry of Real-Valued Functions
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Section 2.2: Limits and Continuity
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Section 2.3: Differentiation
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Section 2.4: Introduction to Paths and Curves
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Section 2.5: Properties of the Derivative
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Section 2.6: Gradients and Directional Derivatives
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Section 3.1: Iterated Partial Derivatives
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Section 3.2: Taylor's Theorem
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Section 3.3: Extrema of Real-Valued Functions
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Section 3.4: Constrained Extrema and Lagrange Multipliers
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Section 3.5: The Implicit Function Theorem (Optional)
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Section 4.1: Acceleration and Newton's Second Law
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Section 4.2: Arc Length
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Section 4.3: Vector Fields
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Section 4.4: Divergence and Curl
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Section 5.1: Introduction
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Section 5.2: The Double Integral Over a Rectangle
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Section 5.3: The Double Integral Over More General Regions
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Section 5.4: Changing the Order of Integration
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Section 5.5: The Triple Integral
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Section 6.1: The Geometry of Maps from R2 to R2
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Section 6.2: The Change of Variables Theorem
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Section 6.3: Applications
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Section 6.4: Improper Integrals (Optional)
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Section 7.1: The Path Integral
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Section 7.2: Line Integrals
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Section 7.3: Parametrized Surfaces
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Section 7.4: Area of a Surface
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Section 7.5: Integrals of Scalar Functions Over Surfaces
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Section 7.6: Surface Integrals of Vector Fields
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Section 7.7: Applications of Differential Geometry, Physics, and Forms of Life
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Section 8.1: Green's Theorem
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Section 8.2: Stokes' Theorem
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Section 8.3: Conservative Fields
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Section 8.4: Gauss' Theorem
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Section 8.5: Differential Forms
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