Math Insight

Pages similar to: Introduction to matrices

• Multiplying matrices and vectors
  How to multiply matrices with vectors and other matrices.
• The derivative matrix
  The derivative matrix is presented as a natural generalization of the single variable derivative to multivariable functions.
• Matrices and determinants for multivariable calculus
  Brief description of matrices and determinants, at the level needed for multivariable calculus.
• Matrices and linear transformations
  A description of how every matrix can be associated with a linear transformation.
• The transpose of a matrix
  Definition of the transpose of a matrix or a vector.
• Dot product in matrix notation
  How to view the dot product between two vectors as a product of matrices.
• Matrix and vector multiplication examples
  Examples demonstrating how to multiply matrices and vectors.
• Determinants and linear transformations
  A description of how a determinant describes the geometric properties of a linear transformation.
• An introduction to ordinary differential equations
  An introduction using simple examples explaining what an ordinary differential equation is and how one might solve them.
• An introduction to networks
  An overview of a network as a collection of connected elements. Different types of networks are illustrated as well as a way to represent them mathematically.
• The absurd high dimensionality of random graphs
  The space of random networks is so ridiculously large that one needs to take drastic measures to make it manageable.
• How linear transformations map parallelograms and parallelepipeds
  Why linear transformations map parallelograms onto parallelograms and parallelepipeds onto parallelepipeds.
• Discrete dynamical systems as function iteration
  The simplest versions of discrete dynamical systems can be viewed as evolving due to iterating a function repeatedly.
• Solving linear ordinary differential equations using an integrating factor
  Illustration of the procedure to find an integrating factor that allows integration of a first order linear ordinary differential equation.
• Special cases of the multivariable chain rule
  Illustrations of different special cases of the multivariable chain rule and their relationship to the general case.
• Initial dynamical systems exploration
  Exploring models of anteater population growth and lead decay in the bloodstream using interactive applets.
• Introduction to the multivariable chain rule
  Introduction to the multivariable chain rule. The basic concepts are illustrated through a simple example.
• Introduction to changing variables in double integrals
  Introduction to the concepts behind a change of variables in double integrals. The transformation is illustrated with interactive graphics.
• Vectors in two- and three-dimensional Cartesian coordinates
  A introduction to representing vectors using the standard Cartesian coordinate systems in the plane and in three-dimensional space.
• The idea of a dynamical system
  The basic concept of a dynamical system as the evolution of something over time. The fundamental ideas of the state space and temporal evolution rules are illustrated with examples featuring interactive graphics.

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