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Table of Contents

Introduction to Calculus

Volume II

Chapter 6 Introduction to Vectors...................................... 1

Vectors and Scalars, Vector Addition and Subtraction, UnitVectors, Scalar or Dot

Product (inner product), Direction Cosines Associated with Vectors, Component Form

for Dot Product, The Cross Product or Outer Product, Geometric Interpretation,

Vector Identities, Moment Produced by a Force, Moment AboutArbitrary Line,

Differentiation of Vectors, Differentiation Formulas, Kinematics of Linear Motion,

Tangent Vector to Curve, Angular Velocity, Two-Dimensional Curves, Scalar and

Vector Fields, Partial Derivatives, Total Derivative, Notation, Gradient, Divergence

and Curl, Taylor Series for Vector Functions, Differentiation of Composite Functions,

Integration of Vectors, Line Integrals of Scalar and VectorFunctions, Work Done,

Representation of Line Integrals

Chapter 7 Vector Calculus I............................................. 81

Curves, Tangents to Space Curve, Normal and Binormal to Space Curve, Surfaces, The

Sphere, The Ellipsoid, The Elliptic Paraboloid, The Elliptic Cone, The Hyperboloid

of One Sheet, The Hyperboloid of Two Sheets, The Hyperbolic Paraboloid, Surfaces

of Revolution, Ruled Surfaces, Surface Area, Arc Length, The Gradient, Divergence

and Curl, Properties of the Gradient, Divergence and Curl, Directional Derivatives,

Applications for the Gradient, Maximum and Minimum Values,Lagrange Multipliers,

Generalization of Lagrange Multipliers, Vector Fields andField Lines, Surface and

Volume Integrals, Normal to a Surface, Tangent Plane to Surface, Element of Surface

Area, Surface Placed in a Scalar Field, Surace Placed in a Vector Field, Summary,

Volume Integrals, Other Volume Elements, Cylindrical Coordinates (r, θ, z), Spherical

Coordinates (ρ, θ, φ)

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