MATH08014 2019 Vector Calculus and Geometry

Calculate dot product of vectors and apply this to find the angle between vectors, project one vector onto another and derive the cosine rule

Calculate cross products of vectors and apply this to find the area of a parallelogram, angular velocities and the volume of a parallelpiped

Understand and determine the linear independence of vectors (with geometric interpretation) and find vector equations of lines and planes

Understand and find linear transformations and isometries as matrix operations: rotation, reflection, translation, eigenvalues and eigenvectors

Manipulate and understand vector fields and partial derivatives including their physical meaning

Calculate the vector operators gradient, divergence and curl as well as some applications of them

Calculate the radial and tangential components of rotating systems, derivatives of vector fields and applications

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Vector addition, subtraction and scalar multiplication

Dot product of vectors and applications (angle between vectors, projection of one vector onto another, the cosine rule)

Cross product of vectors and applications (area of a parallelogram, angular velocity in three dimensions)

Scalar triple product and applications (volume of a parallelepiped)

Vector equations of lines and planes

Linear independence of vectors (with geometric interpretation)

Radial and tangential components of rotating systems

Derivatives of vector fields and applications (including Coriolis force)

Introduction to vector fields

Partial derivatives and introduction to the vector operators gradient, divergence and curl, and their physical meaning

Linear transformations and isometries as matrix operations: rotation, reflection, translation, eigenvalues and eigenvectors