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Vector Calculus and Multiple Integrals
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  • Course
  • Mathematics (KNF2033)
  • Institution
  • UNIMAS

This course covers i) vector calculus (Matrix Addition , Scalar Multiplication, Matrix multiplication, Transposition, Linear systems of Equation, Gauss elimination technique) ii)Line integrals ( Line Integral of a Scalar Field, Line Integral of a Vector Field, Line Integral Independent of Pa...

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Document information

  • August 26, 2021
  • 115
  • 2018/2019
  • Class notes
  • Hazrul mohamed basri
  • All classes

Subjects

  • vector calculus
  • line integrals
  • doble integral
  • surface integrals

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  • UNIMAS
  • Mathematics (KNF2033)
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ENGINEERING MATHEMATICS
SYSTEM OF LINEAR ALGEBRAIC
EQUATIONS

, Matrix Addition

Scalar Multiplication
OUTLINES
Matrix multiplication

Transposition

, INTRODUCTION
𝑎11 𝑎12 … 𝑎1𝑛
• Matrices are rectangular arrays of numbers treated 𝐴𝑚𝑛 =
𝑎21 𝑎22 𝑎1𝑛
as mathematical entities in themselves and ⋮ ⋮
satisfying an algebra that suits their particular 𝑎𝑚1 𝑎𝑚2 … 𝑎𝑚𝑛
application.
• In this respect they are similar to vectors, but
𝑎𝑚𝑛
whereas vectors are designed to reflect the
behaviour of physical quantities that have a
direction associated with them, matrices are row colu
designed to enable us to handle systems of linear Element a matrix, the subsc
equations j, denoting the ith row and
• An mxn matrix A is an array of mn numbers with column.
mrows and ncolumns denoted by

, INTRODUCTION

• EXAMPLE:
The main diagonal of a matrix A are the entries aIJ where i = j.
(a) Write down the three-by-three matrix with ones on the diagonal and zeros
elsewhere.
(b) Write down the three-by-four matrix with ones on the diagonal and zeros
elsewhere.
(c) Write down the four-by-three matrix with ones on the diagonal and zeros
elsewhere.

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