1. Calculate integrals of multivariable functions
- determine whether a given vector field is conservative and if so, identify its potential
- parametrise curves and surfaces and compute line integrals of scalar and vector fields
2. apply the theorems of Gauss (Divergence), Green and Stokes
- compute the divergence and curl of a vector field and explain their physical meanings
- decide which type of integral is relevant for each application
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This course focuses on the calculation of vector fields. The concepts of rotation, divergence and gradient are introduced, and special attention is given to conservative vector fields. In addition, integrals of vector fields along a line, a surface and 3D volume are treated, using the theorems of Green, Stokes and Gauss (Divergence) to establish relationships between these different types of integrals. This provides more insight into the meaning of integrals of vector fields and important theoretical relationships, but can also often be used to calculate these integrals more easily. The three big theorems of Vector Calculus extend the Fundamental Theorem of Calculus into higher dimensional spaces.
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