Multivariable Calculus with MATLAB

This is the table of contents for Multivariable Calculus with MATLAB, with Applications to Geometry and Physics, to be published by Springer, 2017, ISBN 978-3-319-65069-2.

Contents

  1. Introduction
    1. Benefits of Mathematical Software
    2. What's in This Book
    3. What's Not in This Book
    4. How to Use This Book
    5. The MATLAB Interface
    6. Software Versions
  2. Vectors and Graphics
    1. Vectors
    2. Parametric Curves
    3. Graphing Surfaces
    4. Parametric Surfaces
  3. Geometry of Curves
    1. Parametric Curves
    2. Geometric Invariants
    3. Differential Geometry of Curves
  4. Kinematics
    1. Newton's Laws of Motion
    2. Kepler's Laws of Planetary Motion
    3. Studying Equations of Motion with MATLAB
  5. Directional Derivatives
    1. Visualizing Functions of Two Variables
    2. The Gradient of a Function of Two Variables
    3. Functions of Three or More Variables
  6. Geometry of Surfaces
    1. The Concept of a Surface
    2. The Implicit Function Theorem
    3. Geometric Invariants
    4. Curvature Calculations with MATLAB
  7. Optimization in Several Variables
    1. The One-Variable Case
    2. Functions of Two Variables
    3. Three or More Variables
    4. Constrained Optimization and Lagrange Multipliers
  8. Multiple Integrals
    1. Automation and Integration
    2. Algorithms for Numerical Integration
    3. Viewing Solid Regions
    4. A More Complicated Example
    5. Cylindrical Coordinates
    6. More General Changes of Coordinates
  9. Multidimensional Calculus
    1. The Fundamental Theorem of Line Integrals
    2. Green's Theorem
    3. Stokes' Theorem
    4. The Divergence Theorem
    5. Vector Calculus and Physics
  10. Physical Applications of Vector Calculus
    1. Motion in a Central Force Field
    2. Newtonian Gravitation
    3. Electricity and Magnetism
    4. Fluid Flow
    5. Heat and Wave Equations
  11. MATLAB Tips
  12. Sample Solutions