This unit starts with an investigation of linearity: linear functions, general principles relating to the solution sets of homogeneous and inhomogeneous linear equations (including differential equations), linear independence and the dimension of a linear space. The study of eigenvalues and eigenvectors, begun in junior level linear algebra, is extended and developed. The unit then moves on to topics from vector calculus, including vectorvalued functions (parametrised curves and surfaces; vector fields; div, grad and curl; gradient fields and potential functions), line integrals (arc length; work; pathindependent integrals and conservative fields; flux across a curve), iterated integrals (double and triple integrals; polar, cylindrical and spherical coordinates; areas, volumes and mass; Green's Theorem), flux integrals (flow through a surface; flux integrals through a surface defined by a function of two variables, though cylinders, spheres and parametrised surfaces), Gauss' Divergence Theorem and Stokes' Theorem.
Unit details and rules
Unit code  MATH2061 

Academic unit  Mathematics and Statistics Academic Operations 
Credit points  6 
Prohibitions
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MATH2961 or MATH2067 or MATH2021 or MATH2921 or MATH2022 or MATH2922 
Prerequisites
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(MATH1X21 or MATH1011 or MATH1931 or MATH1X01 or MATH1906) and (MATH1014 or MATH1X02) and (MATH1X23 or MATH1933 or MATH1X03 or MATH1907) 
Corequisites
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None 
Assumed knowledge
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None 
Available to study abroad and exchange students  Yes 
Teaching staff
Coordinator  Laurentiu Paunescu, laurentiu.paunescu@sydney.edu.au 

Lecturer(s)  Haotian Wu, haotian.wu@sydney.edu.au 
Laurentiu Paunescu, laurentiu.paunescu@sydney.edu.au 