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Recent Notes

August 21, 2017

Matrix Inverse

Example 1. We want to find inverse of the matrix (1)   This means we want to find a matrix such that (2)   We start […]
August 18, 2017

Matrix & Basic Operations

Suppose (1)   and we would like to compute when possible.   Let’s begin with the first one (2)     Next, we know multiplying two […]
August 12, 2017

Linear System and Matrix

Example 1. We are given the system (1)   The matrix associated to this system is (2)   We want to find the solution set of […]
August 12, 2017

More Examples, Linear Systems

Observation 1. Suppose we have a system of linear equations (1)   We are looking for all real numbers such that this system has exactly one […]
August 12, 2017

System of Linear Equations

Observation 1. Consider two lines with equations and in -plane. There are three possible cases: 1. The two lines could intersect in one point. 2. The […]
August 1, 2017

Playing with a Dataset in R

Please upload the data set from this page and let us start editing this data set in R. To begin, we may want to see the first […]
July 31, 2017

Upload a Dataset to R

In this section, we want to start to work with an example in R. We will upload a data set and start to perform basic operations. […]
July 17, 2017

Integration by Substitution

Example 1. Suppose we want to evaluate the following integral     Of course, one way to do this is to expand and integrate each term. […]
July 12, 2017

Definite Integrals

In this section, we go over a few elementary examples of evaluating a definite integral. Example 1.     Example 2.     Example 3.   […]
July 9, 2017

Antiderivatives

Observation 1. Suppose we are asked to find a function such that if we differentiate it, we get . Anyone who has studied differentiation will suggest […]
July 8, 2017

Exponential & Logarithmic Differentiation

Example 1. Suppose we are given and want to differentiate . We write     Example 2. Suppose we are given and want to differentiate . […]
July 8, 2017

Related Rates

Example 1. Suppose we are given a cone with height equal times radius at any given height. Assume that we know the rate of change of […]