Chapter1 - Good and Bad Notation, and Some General Advice...

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Unformatted text preview: Good and Bad Notation, and Some General Advice Appendix 2: Induction Chapter 1: Linear Equations and Matrices MAT188H1F Lec0106 Burbulla Chapter 1 Lecture Notes Fall 2010 Chapter 1 Lecture Notes MAT188H1F Lec0106 Burbulla Good and Bad Notation, and Some General Advice Appendix 2: Induction Chapter 1: Linear Equations and Matrices Good and Bad Notation, and Some General Advice Examples Appendix 2: Induction Examples Chapter 1: Linear Equations and Matrices 1.1 Matrices 1.2 Linear Equations 1.3 Homogeneous Systems 1.4 Matrix Multiplicaton 1.5 Matrix Inverses 1.6 Elementary Matrices Chapter 1 Lecture Notes MAT188H1F Lec0106 Burbulla Good and Bad Notation, and Some General Advice Appendix 2: Induction Chapter 1: Linear Equations and Matrices Examples Notation I Mathematics has its own set of symbols. If you use them, you must use them correctly. I You will lose marks on tests or exams if your notation is incorrect. I Following are some examples of common errors. Chapter 1 Lecture Notes MAT188H1F Lec0106 Burbulla Good and Bad Notation, and Some General Advice Appendix 2: Induction Chapter 1: Linear Equations and Matrices Examples Example 1 Suppose you are differentiating the function y = x 2 . If you write y = x 2 = 2 x it is incorrect, even though most people would know what you are doing. Of course, you should write y = x 2 y = 2 x Or you could simply write dx 2 dx = 2 x . Chapter 1 Lecture Notes MAT188H1F Lec0106 Burbulla Good and Bad Notation, and Some General Advice Appendix 2: Induction Chapter 1: Linear Equations and Matrices Examples Example 2 Dont confuse implication ( ) with equality ( = ) . The symbol is a logical connective and means If ... then ... . For example, if y = x 2 , then y = 2 x , can be written as y = x 2 y = 2 x . But writing something like ax 2 + bx + c x - b b 2- 4 ac 2 a is abuse of notation. Chapter 1 Lecture Notes MAT188H1F Lec0106 Burbulla Good and Bad Notation, and Some General Advice Appendix 2: Induction Chapter 1: Linear Equations and Matrices Examples Example 3 The expressions , , , , 1 , and - are indeterminate. When evaluating limits of this type, which may or may not exist, dont equate the limit to one of the above expressions. For example, writing lim x 1 x 3- 1 x 2- 1 = is incorrect; the limit is actually equal to 3 2 . You can say the limit is of the form ; or that when x = 1 , x 3- 1 x 2- 1 = 1- 1 1- 1 = , which is indeterminate. Chapter 1 Lecture Notes MAT188H1F Lec0106 Burbulla Good and Bad Notation, and Some General Advice Appendix 2: Induction Chapter 1: Linear Equations and Matrices Examples Example 4 When reducing a matrix, dont put equal ( = ) signs between matrices which arent equal: 1 3- 2- 2 3 1 1 2- 1 = 1 3- 2 9- 3- 1 1 is incorrect. Instead, use an arrow ( ) between row equivalent matrices: 1 3- 2- 2 3 1 1 2- 1 1 3- 2 9- 3- 1 1 ....
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This note was uploaded on 12/23/2010 for the course MAT mat 188 taught by Professor Dietrichburbulla during the Spring '10 term at University of Toronto- Toronto.

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Chapter1 - Good and Bad Notation, and Some General Advice...

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