Class Notes (835,581)
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MATH 215 (39)
Lecture

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Department
Mathematics
Course
MATH 215
Professor
Collin Roberts
Semester
Winter

Description
Contents 1 Introduction 7 2 Complex Numbers 9 2.1 De▯nitions . . . . . . . . . . . . . . . . . . . . . . . . . .9. . 2.2 The Complex Plane . . . . . . . . . . . . . . . . . . . . . . . 10 2.3 The Polar Form of a Complex Number . . . . . . . . . . . . . 11 2.3.1 Multiplication in Polar Form . . . . . . . . . . . . . . 13 2.3.2 Roots of Complex Numbers . . . . . . . . . . . . . . . 14 2.4 Complex Numbers as Field . . . . . . . . . . . . . . . . . . . 15 3 Vector Algebra 17 3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.2 Direction Cosines . . . . . . . . . . . . . . . . . . . . . . . . . 17 3.3 De▯nitions and Operations . . . . . . . . . . . . . . . . . . . 18 3.4 Vector Addition . . . . . . . . . . . . . . . . . . . . . . . . . 20 3.5 Vector Products . . . . . . . . . . . . . . . . . . . . . . . . . 21 3.6 Lines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.7 Planes - Vector Equations . . . . . . . . . . . . . . . . . . . . 25 3.8 Planes - Scalar Equations . . . . . . . . . . . . . . . . . . . . 26 4 Systems of Linear Equations 29 4.1 Systems of Linear Equations . . . . . . . . . . . . . . . . . . 29 4.2 Solutions to Systems of Linear Equations . . . . . . . . . . . 31 4.3 Elementary Operations . . . . . . . . . . . . . . . . . . . . . 33 4.4 Gaussian Elimination (MEM pp362-367) . . . . . . . . . . . . 34 5 Matrix Algebra 39 5.1 Terminology . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3
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