Substitution reactions may seem like a difficult concept to understand. However, as long as you follow these guidelines, you will be successful. When you first see a substitution reaction, you should answer these questions.

Read MoreWhen solving a system of equations in matrix form, it is often useful to find the inverse of a matrix. This can be accomplished by several methods, one of which involves using the adjoint (also known as the adjugate) and the determinant.

Read MoreWrite a function called **identical_indexes** that takes two lists and returns a list containing the indexes into both lists where the values are identical. If there are no such values, the function should return an empty list. Be careful to not have an index out of bounds error.

Thevenin and Norton Equivalent circuits are most often used to simplify a circuit. They are useful when you are interested about the behavior of an element connected to a rather complicated system through terminals a and b (this scenario is addressed in part c of the question).

Read MoreHave you ever taken manual control of your breathing and had the hardest time trying to get your body to breathe on it’s own again? Did you do it right now? If you did, you’re in luck because we’re going to be going over breathing mechanics and manually controlling your breathing is going to be super helpful in setting up the foundation for understanding this phenomenon.

Read MoreMatrices are a way of grouping numbers, and are organized into rows and columns. Matrices are often used as a way of representing several equations in an easier to organize format, however to solve these systems of equations we must be able to perform matrix operations such as multiplication.

Read MoreAssume V_s(t) is equal to 3u(t). Find v(t) as a function of time and find the capacitances of the two capacitors. Assume all initial conditions are 0.

Read MoreEssentially, trees are an **abstraction** that allow for hierarchical organization of “things”. These “things” can be anything, but when we’re learning trees they are often numbers (or letters). An abstract data type just means that it is a way of organizing data that we may use later, without care for how the abstraction is actually implemented (for example with lists, or with a class).

The quadratic formula is a useful method of factoring second order polynomials. It is commonly used when solving for quantities such as eigenvalues in ordinary differential equations.

Read MoreIn order to use a linear graph to find the equations which describe a system, it first must be processed into a normal tree (also known as a system graph tree). The normal tree can be used to determine the order of a system, and to write a system of equations that describe the system.

Read MoreFirst thing to address is what is D.C. Steady State. Basically, all that means is that the circuit has been active/running for a long time. For power dissipating elements like resistors, this doesn’t mean much, but for energy storing elements such as inductors and capacitors it changes how they behave.

Read MoreIn order to categorize a system it is important to identify its governing set of equations. While this can be completed according to kinematic/mass acceleration diagrams, it is also possible to formulate these equations according to linear graph theory. This is particularly useful for non-mechanical domains, and for systems.

Read MoreOne of the methods used to find the transfer function of a system is to use linear graphs. This graph can then be processed into a normal tree and can be used to determine the elemental and state equations needed to simplify the problem.

Read MoreRecursion occurs when a function calls **itself**. Recursion is useful when dealing with problems that have recursive properties. Consider a function **factorial(n)** that returns the factorial of **n**. This function can be defined recursively because **factorial(5) = 5 * factorial(4) = 5 * 4 * factorial(3) **and so on.

Floating point numbers are used to represent real numbers in computers. Because real numbers can have many digits, we use scientific notation to represent them in binary.

Read MoreStack is a data structure that follows the property of **F**irst **I**n **L**ast **O**ut (**FILO**). So the first element inserted into a stack will be the last element deleted from the stack. You can think of a stack as a stack of dishes. The first dish that goes into the stack will be the last one to be used.

A lot of people seem to freak out when they see an *i* in math or *j* in electrical engineering. So hopefully this will help. The first thing we want to go over is what *i* and *j* even are.

The problem is: Given **N** pairs of parentheses, write a function to generate all combinations of well-formed parentheses. The naive solution is to generate all combinations of **N** pairs of parentheses, then checking if each one is valid.

Now, if you change **main.c**, **factorial.c**, or **factorial.h**, you would need to re-compile those files manually. This is a cumbersome process, especially when the number of files is big. The solution is to automate the compilation process by using Makefile.

At first glance, there seems to be a lot going on in a two-phase diagram. There are temperatures, percentages, different elements, and symbols you’re not used to seeing. But once you understand what you’re looking for, everything makes sense.

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