Introduction to Linear Algebra and Differential Equations
MATH 287

Fall 2016
CHAPTER
3
Determinants
Mathematics is the gate and key to the sciences. Roger Bacon
In this chapter, we introduce a basic tool in applied mathematics, namely the determinant of a square matrix. The determinant is a number, associated with an n n matrix
A,
Introduction to Linear Algebra and Differential Equations
MATH 287

Fall 2016
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CHAPTER
2
Matrices and Systems
of Linear Equations
Algebra is the intellectual instrument which has been created for rendering clear
the quantitive aspects of the world Alfred North Whitehead
We will see in the later chapters
Introduction to Linear Algebra and Differential Equations
MATH 287

Fall 2016
CHAPTER
6
Linear Differential
Equations of Order n
There is no branch of mathematics, however abstract, which may not someday be
applied to the phenomena of the real world. Nicolai Lobachevsky
In Chapter 1 we developed a technique that enabled us to solve
Introduction to Linear Algebra and Differential Equations
MATH 287

Fall 2016
CHAPTER
7
Systems of Differential
Equations
Go down deep enough into anything and you will find mathematics.
Dean Schlicter
In practice, most applied problems involve more than one unknown function for
their formulation and hence require the solution to
Introduction to Linear Algebra and Differential Equations
MATH 287

Fall 2016
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CHAPTER
1
FirstOrder Differential
Equations
Among all of the mathematical disciplines the theory of differential equations is the
most important. It furnishes the explination of all those elementary manifestations
of nature wh