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Title: Multivariable Calculus
Description: These notes are aimed at first year students who need to study Advanced mathematics as part of their course requirement.
Description: These notes are aimed at first year students who need to study Advanced mathematics as part of their course requirement.
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Multivariable Calculus
15 November 2023
19:42
Real Numbers
• Real numbers can be positive, zero, or negative, and they can be rational or irrational
...
Representation in 1 Dimension (R)
• Real numbers can be thought of as points on a line when an origin and unit length are
chosen
...
Representation in 2 Dimensions (R2)
• Pairs of real numbers ((x1,x2)) form elements of R2
...
• These elements are also called 2-dimensional vectors and can be represented as arrows
...
• These elements label points in space when an origin and three orthogonal axes are chosen
...
Generalizing to Rn
• Rn represents all n-tuples of real numbers ((x1,x2,
...
• These elements are points in n-dimensional space and are called n-dimensional vectors
...
• Vectors (x and y) can be added (x + y) or subtracted (x − y)
...
Geometric Interpretation
• Scalar multiplication (αx) changes the length and direction of a vector
...
• Vector subtraction (x − y) can be visualized as completing a parallelogram or
connecting the heads of vectors
Title: Multivariable Calculus
Description: These notes are aimed at first year students who need to study Advanced mathematics as part of their course requirement.
Description: These notes are aimed at first year students who need to study Advanced mathematics as part of their course requirement.