DrOfEng

This physics video covers a tutorial on the conservation of momentum applied to elastic and inelastic collisions. Worked examples on elastic and inelastic collisions are provided to reinforce your understanding on the conservation of momentum.

This engineering video covers a tutorial on how to derive the equilibrium equations for a continuous body, continuum or continuous medium. The assumption of a continuous medium is that it fills the entire volume that it occupies, which is what we observe at the macroscopic level. Newton's first law is used to derive the equilibrium equations for a continuous body, which apply to solids and fluids.

This computer science video covers a tutorial on how to traverse 2D arrays using enhanced for loops. 2D arrays can be created and indexed in a similar way to 1D arrays. Effectively, they can be visualised as arrays of arrays. The tutorial also demonstrates how 2D arrays can be traversed in row-major order. An example of a 2D matrix array is demonstrated in Java using the Eclipse IDE.

This chemistry video covers a tutorial on crystalline and amorphous solids. It explains the difference between the structures of crystalline and amorphous solids and provides examples. For example, metals and ceramics have a densely packed crystalline structure whereas glass has an amorphous structure.

This calculus video covers a tutorial on the definition of the extreme value theorem, which is an analytical application of the derivative to determine the minimum and maximum of a continuous function in a closed interval. The extreme value theorem states that if a function is continuous over a closed interval, it has at least one minimum and one maximum.

This physics video covers a tutorial on the conservation of momentum applied to inelastic collisions. Momentum is conserved for a system of particles undergoing inelastic collisions with no external forces acting on the system but kinetic energy is not conserved. In a perfectly inelastic collision both masses are connected and have the same velocity after the collision occurs.

This engineering video covers a tutorial on how to derive the stresses and strains for the torsion of a non-circular shaft. The torsion of a non-circular shaft extends the torsion theory for a circular shaft from the strength of materials approach by introducing a warping function. Warping of the section counteracts the shear stress at the boundary of the shaft, which results in a zero complementary shear stress at the free surface.

This computer science video covers a tutorial on how to traverse 2D arrays using nested for loops. 2D arrays can be created and indexed in a similar way to 1D arrays. Effectively, they can be visualised as arrays of arrays. The tutorial also demonstrates how 2D arrays can be traversed in row-major and column-major order. An example of a 2D matrix array is demonstrated in Java using the Eclipse IDE.

This chemistry video covers a tutorial on large biomolecules and polymers. It explains how the structure of a large biomolecule leads to stable forms, such as the ring formation of glucose, which is more stable in water than dry glucose. Polymers are also covered, which are composed of a chain of repeating units called monomers.

This calculus video covers a tutorial on the mean value theorem for derivatives, which is an analytical application of the derivative to determine the average value of a function in a closed interval. Several examples are covered to demonstrate the mean value theorem.

This physics video covers a tutorial on the conservation of momentum applied to elastic collisions. Both momentum and kinetic energy are conserved for a system of particles undergoing elastic collisions with no external forces acting on the system.

This engineering video covers a tutorial on how to derive and visualise the stress and strain tensors in 3D Cartesian coordinates. Stresses and strains develop internally in a body that is subjected to external loads. Multi-variable calculus is used to derive the axial and shear strains, which are the partial derivatives of the displacements. The shear deformations of an element cut out from a 3D body is sketched in the xy, xz and yz planes for better visualisation of the strain deformations.

This computer science video covers a tutorial 2D arrays. 2D arrays can be created and indexed in a similar way to 1D arrays. Effectively, they can be visualised as arrays of arrays. 2D arrays can be traversed in row-major and column-major order. An example of a 2D matrix array is demonstrated in Java using the Eclipse IDE.

This chemistry video covers a tutorial on metallic solids. It explains how the lattice structure, which can be represented using a sea of electrons model, and includes delocalised valence electrons, can be used to describe the properties of metallic solids, including malleability, ductility and conductivity of both electricity and heat. An example of an interstitial alloy is provided, being steel, to show how the addition of carbon at the interstitial sites can increase the rigidity while decreasing the ductility of the alloy.

This calculus video covers a tutorial on the definition of the mean value theorem for derivatives, which is an analytical application of the derivative to determine the average value of a function in a closed interval. The mean value theorem can give more than one point in a continuous interval where the instantaneous rate of change is equal to the average rate of change.

This physics video covers a tutorial on the conservation of momentum for a system of particles in 2D Cartesian coordinates. It explains when momentum is conserved and when it is not. Generally, momentum is conserved when there is no net external force acting on the system. The conservation of momentum is commonly applied to solve for the velocities of particles involved in in elastic and inelastic collisions. Note that the internal forces in the system cancel each other out by Newton's third law, so momentum is not conserved for a single particle subjected to an impulse.

This engineering video covers a tutorial on how to derive the torsional displacements in Cartesian coordinates for a shaft with a circular section subjected to an applied torque. The displacements are derived using Cartesian coordinates because they can be readily used to derive the stresses and strains for a shaft with a non-circular open section.

This computer science video covers a tutorial on the ethical issues associated with data collection. Java applications (standalone and web) typically store data in a database. ArrayLists and other data structures are used by Java programs to store and read data from databases. Cryptography, hash algorithms and data encapsulation are some of the key methods for protecting data in terms of privacy and preventing data corruption.

This chemistry video covers a tutorial on molecular solids. It explains how the intermolecular interactions, including dipoles and london dispersion forces, and the restricted movement of valence electrons are used to describe the properties of molecular solids, including low melting and sublimation points, and poor conductivity. Several examples of molecular solids are covered including dry ice and ice.

This calculus video demonstrates how to use L'Hopital's rule to evaluate limits. L'Hospital's rule is used to evaluate limits of the indeterminate forms 0/0 and infty/infty. Several worked examples are covered to test your understanding of L'hopital's rule. The basic idea of L'hopital's rule is to take the derivatives of the functions in the numerator and denominator until the limit becomes determinate.

This physics video covers a tutorial on the conservation of momentum for a system of particles. It explains when momentum is conserved and when it is not. Generally, momentum is conserved when there is no net external force acting on the system. The conservation of momentum is commonly applied to solve for the velocities of particles involved in in elastic and inelastic collisions. Note that the internal forces in the system cancel each other out by Newton's third law, so momentum is not conserved for a single particle subjected to an impulse.

This engineering video covers a tutorial on how to derive the torsion formula for a shaft with a thin-walled closed section subjected to an applied torque. This torsion formula applies to thin-walled closed sections because the shear flow is constant and tangent to the boundary, and the shear stress can be assumed constant across the thickness of the wall. The section of the shaft may also have a non-uniform thickness.

This computer science video covers a tutorial on how to analyse the selection sort and insertion sort algorithms. The time complexity of both sorting algorithms is compared using the number of comparisons made during each iteration. The arithmetic series is used to come up with an equation that compares the size of the sorted arraylist with the total number of comparisons made by both sorting algorithms. An introduction to Big O notation is provided to explain why the selection and insertion sort algorithms are both O(n^2).

This chemistry video covers a tutorial on covalent network solids. It explains how the chemical structures of covalent network solids and their restricted bond angles are used to describe their properties including rigidity, hardness, brittleness and poor conductivity. Several examples of covalent network solids are covered including diamond, graphite and silicon carbide, which are arranged in a tetrahedral or multi-layered configuration.

This calculus video cover a tutorial on how to prove L'Hopital's rule for indeterminate limits. L'Hospital's rule is used to evaluate limits of the indeterminate forms 0/0 and infty/infty. An informal proof of L'hopital's rule is given for limits of the indeterminate form infty/infty. The basic idea of L'hopital's rule is to take the derivatives of the functions in the numerator and denominator until the limit becomes determinate.