List of all pages
- A line or a plane or a point?
Examples showing how the graph of an equation depends on the underlying dimension, becoming a line or a point or a plane. - Linear approximations: approximation by differentials
Approximating the value of a function near a point by its tangent line formula. - The multivariable linear approximation
Introduction to the linear approximation in multivariable calculus and why it might be useful. - The linear function
Overview of the linear function of one variable and a few of its properties. - Solutions to linear and quadratic Taylor polynomial problems
Solutions to sample problems involving first and second order Taylor polynomials. - Linear and quadratic Taylor polynomial problems
Sample problems involving first and second order Taylor polynomials. - Linear transformations
Definition of a linear transformation of Euclidean spaces. - How linear transformations map parallelograms and parallelepipeds
Why linear transformations map parallelograms onto parallelograms and parallelepipeds onto parallelepipeds. - Lines (and other items in Analytic Geometry)
How to describe the equation for a line in terms of horizontal and vertical coordinates. - Two variable local extrema examples
Examples of calculating the critical points and local extrema of two variable functions. - Introduction to local extrema of functions of two variables
Introduction to the idea of critical points and local extrema of two variable functions. - Local minima and maxima (First Derivative Test)
How to calculate the local maxima and minima of a differentiable function. - Basic idea and rules for logarithms
A brief overview of the basic idea and rules for logarithms. - Definition: Magnitude of a vector definition
The magnitude of a vector is the length of the vector. - The master stability function approach to determine the synchronizability of a network
The master stability function approach allows one to analyze how network structure influences the stability of the completely synchronous state.. - 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. - Introduction to matrices
A brief introduction to matrices. - The transpose of a matrix
Definition of the transpose of a matrix or a vector. - Multiplying matrices and vectors
How to multiply matrices with vectors and other matrices.
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