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Index
Preface
Contents
1 Vectors and matrices
1.1 Two-dimensional vectors
1.2 The norm and dot product of vectors
1.3 Bilinear functions
1.4 n-dimensional vectors
1.5 Norm and dot product in n dimensions
1.6 The determinant
1.7 Signed volume
1.8 Linear functions and their representation by matrices
1.9 Geometric applications
2 Functions
2.1 Functions of several variables
2.2 Continuity
2.3 Other coordinate systems
3 Differentiation
3.1 Differentiable functions
3.2 The tangent plane and partial derivatives
3.3 The Chain Rule
3.4 Inverse functions
3.5 Divergence and curl
4 More about differentiation
4.1 Higher derivatives of functions of several variables
4.2 Extrema of functions of two variables
4.3 Extrema of functions of several variables
4.4 Extrema on level sets
5 Applications to motion
5.1 Motion in space
5.2 Planetary motion
6 Integration
6.1 Introduction to area, volume, and integral
6.2 The integral of a continuous function of two variables
6.3 Double integrals as iterated single integrals
6.4 Change of variables in a double integral
6.5 Integration over unbounded sets
6.6 Triple and higher integrals
7 Line and surface integrals
7.1 Line integrals
7.2 Conservative vector fields
7.3 Surfaces and surface integrals
8 Divergence and Stokes' Theorems and conservation laws
8.1 Green's Theorem and the Divergence Theorem in mathbbR2
8.2 The Divergence Theorem in mathbbR3
8.3 Stokes' Theorem
8.4 Conservation laws
8.5 Conservation laws and one-dimensional flows
9 Partial differential equations
9.1 Vibration of a string
9.2 Vibration of a membrane
9.3 The conduction of heat
9.4 Equilibrium
9.5 The Schrödinger equation
Answers to selected problems
Index
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