diff --git a/source/linear-algebra/source/01-LE/main.ptx b/source/linear-algebra/source/01-LE/main.ptx index c36034be5..bf655c49b 100644 --- a/source/linear-algebra/source/01-LE/main.ptx +++ b/source/linear-algebra/source/01-LE/main.ptx @@ -2,6 +2,22 @@ Systems of Linear Equations (LE) Systems of Linear Equations + +

One of the fundamental lessons of calculus is that many complicated problems + can be solved by taking linear approximations to complicated functions. This + often produces several linear equations for which we want to know when they are simultaneously + true; that is, we would like to solve this system of linear equations. + This chapter centers around that fundamental question, building off of your intuition + for what happens in the simplest case of two equations in two variables. Geometrically, + this corresponds to finding the intersection of two lines in the plane. As we introduce more + variables, we quickly lose our ability to visualize this process geometrically, so we will + introduce a tool called a matrix to help us solve these. +

+ + Motivating Question + + +
diff --git a/source/linear-algebra/source/01-LE/outcomes/main.ptx b/source/linear-algebra/source/01-LE/outcomes/main.ptx index 190833bbe..84dd96b45 100644 --- a/source/linear-algebra/source/01-LE/outcomes/main.ptx +++ b/source/linear-algebra/source/01-LE/outcomes/main.ptx @@ -1,7 +1,6 @@ -

By the end of this chapter, you should be able to...

diff --git a/source/linear-algebra/source/02-EV/main.ptx b/source/linear-algebra/source/02-EV/main.ptx index a69c1329d..9594111a3 100644 --- a/source/linear-algebra/source/02-EV/main.ptx +++ b/source/linear-algebra/source/02-EV/main.ptx @@ -2,6 +2,20 @@ Euclidean Vectors (EV) Euclidean Vectors + +

+ In , we saw how matrices and vectors were useful tools in solving + systems of linear equations. In this chapter, we will explore the structure of + the space of vectors, and in particular see how solving systems + of linear equations helps us understand this structure. Finally, in + we will see how our newfound knowledge of this structure applies back to more + fully understanding solution sets of linear systems. +

+ + Motivating Question + + +
diff --git a/source/linear-algebra/source/02-EV/outcomes/main.ptx b/source/linear-algebra/source/02-EV/outcomes/main.ptx index f7dd87c17..3cfb71de7 100644 --- a/source/linear-algebra/source/02-EV/outcomes/main.ptx +++ b/source/linear-algebra/source/02-EV/outcomes/main.ptx @@ -1,7 +1,6 @@ -

By the end of this chapter, you should be able to...

diff --git a/source/linear-algebra/source/03-AT/main.ptx b/source/linear-algebra/source/03-AT/main.ptx index 0e4434ae3..7327b0e1e 100644 --- a/source/linear-algebra/source/03-AT/main.ptx +++ b/source/linear-algebra/source/03-AT/main.ptx @@ -2,6 +2,20 @@ Algebraic Properties of Linear Maps (AT) Algebraic Properties of Linear Maps + +

+ In this chapter, we deepen our exploration of vector spaces through + a widespread technique in mathematics: in order to understand the structure + of mathematical objects, we study functions between those objects. In this case, + we introduce linear transformations as structure-preserving functions + between spaces of vectors. We begin here by taking a mostly algebraic approach, + deferring geometric explorations for later chapters. +

+ + Motivating Question + + +
diff --git a/source/linear-algebra/source/03-AT/outcomes/main.ptx b/source/linear-algebra/source/03-AT/outcomes/main.ptx index baf2a08c7..174c4f5a3 100644 --- a/source/linear-algebra/source/03-AT/outcomes/main.ptx +++ b/source/linear-algebra/source/03-AT/outcomes/main.ptx @@ -1,7 +1,6 @@ -

By the end of this chapter, you should be able to...

diff --git a/source/linear-algebra/source/04-MX/main.ptx b/source/linear-algebra/source/04-MX/main.ptx index c22b2aedb..1a992ee17 100644 --- a/source/linear-algebra/source/04-MX/main.ptx +++ b/source/linear-algebra/source/04-MX/main.ptx @@ -2,6 +2,18 @@ Matrices (MX) Matrices + +

+ In Chapter , we saw that matrices are fundamentally just + a representation of linear transformations (with respect to a choice of basis). + Here, we explore the algebraic structure of the set of matrices of a given size, + which will provide us further tools for understanding linear transformations. +

+ + Motivating Question + + +
diff --git a/source/linear-algebra/source/04-MX/outcomes/main.ptx b/source/linear-algebra/source/04-MX/outcomes/main.ptx index 60798603d..8e7f16f9d 100644 --- a/source/linear-algebra/source/04-MX/outcomes/main.ptx +++ b/source/linear-algebra/source/04-MX/outcomes/main.ptx @@ -1,7 +1,6 @@ > -

By the end of this chapter, you should be able to...

diff --git a/source/linear-algebra/source/05-GT/main.ptx b/source/linear-algebra/source/05-GT/main.ptx index ae61c984d..6ba8b977b 100644 --- a/source/linear-algebra/source/05-GT/main.ptx +++ b/source/linear-algebra/source/05-GT/main.ptx @@ -2,6 +2,20 @@ Geometric Properties of Linear Maps (GT) Geometric Properties of Linear Maps + +

+ In this chapter, we continue our study of linear transformations by studying + them from a geometric perspective. The tools we explore in this chapter, + namely determinants and eigenvectors are incredibly + pervasive in mathematics and applications thereof (in fact, it is likely you + have already used determinants as a computational tool in other courses prior + to fully understanding them). +

+ + Motivating Question + + +
diff --git a/source/linear-algebra/source/05-GT/outcomes/main.ptx b/source/linear-algebra/source/05-GT/outcomes/main.ptx index 26af63627..7ae8acae6 100644 --- a/source/linear-algebra/source/05-GT/outcomes/main.ptx +++ b/source/linear-algebra/source/05-GT/outcomes/main.ptx @@ -1,7 +1,6 @@ > -

By the end of this chapter, you should be able to...

diff --git a/source/linear-algebra/source/future-ON/main.ptx b/source/linear-algebra/source/future-ON/main.ptx index 1b285e228..432602cfb 100644 --- a/source/linear-algebra/source/future-ON/main.ptx +++ b/source/linear-algebra/source/future-ON/main.ptx @@ -1,6 +1,13 @@ Orthogonal and Orthonormal Vectors (ON - Coming Soon!) +

TODO: Add introductory text

+ + + Motivating Question + + + diff --git a/source/linear-algebra/source/future-ON/outcomes/main.ptx b/source/linear-algebra/source/future-ON/outcomes/main.ptx index a10c1c771..997c5fd0e 100644 --- a/source/linear-algebra/source/future-ON/outcomes/main.ptx +++ b/source/linear-algebra/source/future-ON/outcomes/main.ptx @@ -1,7 +1,6 @@ > -

By the end of this chapter, you should be able to...

diff --git a/xsl/print.xsl b/xsl/print.xsl index 7896f9507..73de79412 100644 --- a/xsl/print.xsl +++ b/xsl/print.xsl @@ -49,6 +49,26 @@ fonttitle=\bfseries, + + + size=normal, colback=white, colbacktitle=white, coltitle=black, colframe=black, rounded corners, center title, fonttitle=\blocktitlefont\bfseries, blockspacingstyle, + titlerule=-1pt, + + + + + colframe=black, + colback=white, + coltitle=black, + colbacktitle=white, + fonttitle=\bfseries, + halign title=flush center, + + boxrule=-1pt, + titlerule=2pt, + + +