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...Learning outcomes - After studying this course, you should be able to: find a rational and an irrational number between any two distinct real numbers solve inequalities by rearranging into simpler equivalent forms and solve inequalities involving modulus signs state and use the Triangle Inequality and use the Binomial Theorem and mathematical induction to prove...

...Learning outcomes - After studying this course, you should be able to: explain what is meant by a symmetry of a plane figure find the composite of two symmetries find the inverse of a symmetry determine whether a given set and binary operation form a group by checking group axioms describe the symmetries of some bounded three-dimensional figures...Introduction to group...

...Learning outcomes - After studying this course, you should be able to: understand what functionals are, and have some appreciation of their applications apply the formula that determines stationary paths of a functional to deduce the differential equations for stationary paths in simple cases use the Euler-Lagrange equation or its first integral to find differential...

...Learning outcomes - After studying this course, you should be able to: apply the Internal Direct Product Theorem in simple cases decide whether a given group is cyclic, and given a finite cyclic group, find a generator for a subgroup of a given order express a given finite cyclic group as the direct product of cyclic groups of prime power order and, given two direct...

...Learning outcomes - After studying this course, you should be able to: derive the pathlines and the streamlines in Cartesian and polar form from a velocity field derive the stream function from a velocity field model different flows from a combination of uniform flows, sources, sinks and doublets use the continuity equation to determine whether an inviscid flow is...

...Learning outcomes - After studying this course, you should be able to: use the method of Gauss-Jordan elimination to find the solutions of systems of simultaneous linear equations solve a system of linear equations by row-reducing its augmented form perform the matrix operations of addition, multiplication and transposition and express a system of simultaneous linear...

...Learning outcomes - After studying this course, you should be able to: understand and use basic terms for the description of the motion of particles, vector functions and the fundamental laws of Newtonian mechanics solve mechanics problems in one dimension that involve one or more of the forces of gravity, friction and air resistance understand the concept of terminal...