Vector Calculus

Vector Calculus is calculus which uses vectors

Vectorize components to solve unique solutions

Prerequisites: Precalculus, Algebra, Geometry, Trigonometry, Calculus I, Calculus II, Calculus III, Differential Equations, Linear Algebra

The main book used in colleges today is Vector Calculus by Marsden


[expand title=”1.-THE GEOMETRY OF EUCLIDEAN SPACE” rel=”Functions and Models”]

[expandsub2 title=”1.1-Vectors in Two- and Three-Dimensional Space”]

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[expandsub2 title=”1.2-The inner Product, Length, and Distance”]

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[expandsub2 title=”1.3-Matrices, Determinants, and the Cross Product”]

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[expandsub2 title=”1.4-Cylindrical and Spherical Coordinates”]

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[expandsub2 title=”1.5-n-Dimensional Euclidean Space”]

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[expand title=”2.-DIFFERENTIATION” rel=”Functions and Models”]

[expandsub2 title=”2.1-The Geometry of Real-Valued Functions”]

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[expandsub2 title=”2.2-Limits and Continuity”]

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[expandsub2 title=”2.3-Differentiation”]

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[expandsub2 title=”2.4-Introduction to Paths and Curves”]

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[expandsub2 title=”2.5-Properties of the Derivative”]

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[expandsub2 title=”2.6-Gradients and Directional Derivatives”]

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[expand title=”3.-HIGHER-ORDER DERIVATIVES: MAXIMA AND MINIMA” rel=”Functions and Models”]

[expandsub2 title=”3.1-Iterated Partial Derivatives”]

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[expandsub2 title=”3.2-Taylor’s Theorem”]

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[expandsub2 title=”3.3-Extrema of Real-Valued Functions”]

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[expandsub2 title=”3.4-Constrained Extrema and Lagrange Multipliers”]

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[expandsub2 title=”3.5-The Implicit Function Theorem”]

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[expand title=”4.-VECTOR-VALUED FUNCTIONS” rel=”Functions and Models”]

[expandsub2 title=”4.1-Acceleration and Newton’s Second Law”]

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[expandsub2 title=”4.2-Arc Length”]

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[expandsub2 title=”4.3-Vector Fields”]

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[expandsub2 title=”4.4-Divergence and Curl”]

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[expand title=”5.-DOUBLE AND TRIPLE INTEGRALS” rel=”Functions and Models”]

[expandsub2 title=”5.1-Introduction”]

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[expandsub2 title=”5.2-The Double Integral Over a Rectangle”]

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[expandsub2 title=”5.3-The Double Integral Over More General Regions”]

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[expandsub2 title=”5.4-Changing the Order of Integration”]

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[expandsub2 title=”5.5-The Triple Integral”]

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[expand title=”6.-THE CHANGE OF VARIABLES FORMULA AND APPLICATIONS OF INTEGRATION” rel=”Functions and Models”]

[expandsub2 title=”6.1-The Geometry of Maps from R^2 to R^3″]

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[expandsub2 title=”6.2-The Change of Variables Theorem”]

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[expandsub2 title=”6.3-Applications”]

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[expandsub2 title=”6.4-Improper Integrals”]

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[expand title=”7.-INTEGRALS OVER PATHS AND SURFACES” rel=”Functions and Models”]

[expandsub2 title=”7.1-The Path Integral”]

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[expandsub2 title=”7.2-Line Integrals”]

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[expandsub2 title=”7.3-Parametrized Surfaces”]

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[expandsub2 title=”7.4-Area of a Surface”]

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[expandsub2 title=”7.5-Integrals of Scalar Functions Over Surfaces”]

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[expandsub2 title=”7.6-Surface Integrals of Vector Fields”]

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[expandsub2 title=”7.7-Applications to Differential Geometry, Physics, and Forms of Life”]

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[expand title=”8.-THE INTEGRAL THEOREMS OF VECTOR ANALYSIS” rel=”Functions and Models”]

[expandsub2 title=”8.1-Green’s Theorem”]

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[expandsub2 title=”8.2-Stokes’ Theorem”]

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[expandsub2 title=”8.3-Conservative Fields”]

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[expandsub2 title=”8.4-Gauss’ Theorem”]

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[expandsub2 title=”8.5-Differential Forms”]

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