notes_2212_L1.pdf - DMFM 2212 Engineering Mathematics Sem 1...

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DMFM 2212: Engineering Mathematics Sem 1 2018/2019 Lecture 1: Week 1 Lecturer: Mohd Shahrizan bin Othman 1.1 Functions of Several Variables In Elementary Mathematics, we have studied the differentiation and integration for function which involves one independent variable (normally x ) only, i.e. function of single variable . For function of single variable, we normally regard x as independent variable and y (or f ( x )) as dependent variable . For example, the equation y = 5 x is equivalent to f ( x ) = 5 x , where y = f ( x ). In this chapter, we extend our discussion to the functions which have two and three independent variables. 1.1.1 Functions of Two Variables For example, z = x + y or equivalent to f ( x, y ) = x + y , where z is dependent variable and x, y are independent variables. In this case, we have the subject of formula, z = f ( x, y ) and it is known as function of two variables. 1.1.2 Functions of Three Variables For instance, w = x + y + z or equivalent to f ( x, y, z ) = x + y + z , where w is dependent variable and x, y, z are independent variables.

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