Multivariable Calculus with Mathematica

✍ Scribed by Michael Shoushani, Robert P Gilbert, and Yvonne Ou

• Year: 2020
• Tongue: English
• Leaves: 431
• Category: Library

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
Preface
Author Bios
1 Vectors in R3
1.1 Vector algebra in R3
1.2 The inner product
1.3 The vector product
1.4 Lines and planes in space
2 Some Elementary Curves and Surfaces in R3
2.1 Curves in space and curvature
2.2 Quadric surfaces
2.3 Cylindrical and spherical coordinates
3 Functions of Several Variables
3.1 Surfaces in space, functions of two variables
3.2 Partial derivatives
3.3 Gas thermodynamics
3.4 Higher order partial derivatives
3.5 Differentials
3.6 The chain rule for several variables
3.7 The implicit function theorem
3.8 Implicit differentiation
3.9 Jacobians
4 Directional Derivatives and Extremum Problems
4.1 Directional derivatives and gradients
4.2 A Taylor theorem for functions of two variables
4.3 Unconstrained extremum problems
4.4 Second derivative test for extrema
4.5 Constrained extremal problems and Lagrange multipliers
4.6 Several constraints
4.7 Least squares
5 Multiple Integrals
5.1 Introduction
5.2 Iterated double integrals
5.3 Double integrals
5.4 Volume by double integration
5.5 Centroids and moments of inertia
5.6 Areas of surfaces in R3
5.7 Triple integrals
5.8 Change of variables in multiple integration
6 Vector Calculus
6.1 Fields, potentials and line integrals
6.2 Green’s theorem
6.3 Gauss’ divergence theorem
6.4 The curl
6.5 Stokes’ theorem
6.6 Applications of Gauss’ theorem and Stokes’ theorem
7 Elements of Tensor Analysis
7.1 Introduction to tensor calculus
7.1.1 Covariant and contravariant tensors
7.1.2 Raising and lowering indices
7.1.3 Geodesics
7.1.4 Derivatives of tensors
7.1.5 Frenet formulas
7.1.6 Curvature
8 Partial Differential Equations
8.1 First order partial differential equations
8.1.1 Linear, equations
8.1.2 The method of characteristics for a first order partial differential equation
8.2 Second order partial differential equations
8.2.1 Heat equation
8.2.2 The Laplace equation
8.2.3 MATHEMATICA package for solving Laplace’s equation
8.2.4 The wave equation
8.2.5 The Fourier method for the vibrating string
8.2.6 Vibrating membrane
8.2.7 The reduced wave equation
8.3 Series methods for ordinary differential equations
8.4 Regular-singular points
8.4.1 Project
Bibliography
Index