Ch1and2

Ch1and2 - Notes for Math 152 Linear Systems Spring 2010...

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Unformatted text preview: Notes for Math 152: Linear Systems Spring, 2010 Richard Froese and Brian Wetton © 2009 Richard Froese and Brian Wetton. Permission is granted to make and distribute copies of this document provided the copyright notice and this permission notice are preserved on all copies. Contents 1 Introduction 5 1.1 Course Goals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2 About the Subject . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.1 Connection to Geometry . . . . . . . . . . . . . . . . . . . 6 1.2.2 Linear Systems . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.3 Eigen-analysis . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 About These Notes . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 About The Computer Labs . . . . . . . . . . . . . . . . . . . . . 9 2 Vectors and Geometry 10 2.1 Chapter Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2 Vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 2.2.1 Multiplication by a number and vector addition . . . . . . 11 2.2.2 Co-ordinates . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.3 Properties of vector addition and scalar multiplication . . 16 2.2.4 MATLAB: basic scalar and vector operations . . . . . . . 17 2.2.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.3 Geometrical Aspects of Vectors . . . . . . . . . . . . . . . . . . . 19 2.3.1 Length of a vector . . . . . . . . . . . . . . . . . . . . . . 19 2.3.2 The dot product . . . . . . . . . . . . . . . . . . . . . . . 19 2.3.3 Projections . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2.3.4 MATLAB: norm and dot commands . . . . . . . . . . . . 23 2.3.5 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.4 Determinants and the Cross Product . . . . . . . . . . . . . . . . 25 2.4.1 The determinant in two and three dimensions . . . . . . . 25 2.4.2 The cross product . . . . . . . . . . . . . . . . . . . . . . 27 2.4.3 The triple product and the determinant in three dimensions 30 2.4.4 MATLAB: assigning matrices and det and cross commands 31 2.4.5 MATLAB: generating scripts with the MATLAB editor . 31 2.4.6 MATLAB: floating point representation of real numbers . 32 2.4.7 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.5 Lines and Planes . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.5.1 Describing linear sets . . . . . . . . . . . . . . . . . . . . 34 2.5.2 Lines in two dimensions: Parametric form . . . . . . . . . 34 1 CONTENTS CONTENTS 2.5.3 Lines in two dimensions: Equation form . . . . . . . . . . 35 2.5.4 Lines in three dimensions: Parametric form . . . . . . . . 35 2.5.5 Lines in three dimensions: Equation form . . . . . . . . . 36 2.5.6 Planes in three dimensions: Parametric form . . . . . . . 37 2.5.7 Planes in three dimensions: Equation form . . . . . . . . 37 2.5.8 Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 2.6 Introduction to Linear Systems . . . . . . . . . . . . . . . . . . .Introduction to Linear Systems ....
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Ch1and2 - Notes for Math 152 Linear Systems Spring 2010...

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