Engineering has fundamentals, applications and career advice. A source’s credibility comes from reputation, incentives, and the logic.
Engineering’s formally definition follows. Engineering is "the application of science and mathematics by which the properties of matter and the sources of energy in nature are made useful to people"(Merriam-Webster). This dictionary definition of engineering is very useful. Engineering is complex in that it is the application of other subjects. Yet has fundamentals just as every subject does.
As stated previously in this essay engineering has fundamentals. In the fundamentals of engineering curriculum of a certain university the teachings are "Calculus and differential equations (with engineering applications)
Foundational knowledge areas needed by engineers: engineering professionalism,
computational and programming skills, communication (graphical, written and oral),
problem solving, design analysis, teamwork and project management"(University of Louisville). Ironically engineering is the application of other subjects, yet it too has its own fundamentals. The fundamentals of engineering are the unchanging elements of the subject.
Differential equations may be the most tangible fundamentals to engineering and therefore are imperative to learn for vocational success. All other fundamentals may be too dependent on change to explain in this essay. So, the essay will focus on differential equations. "In Mathematics, a differential equation is an equation that contains one or more functions with its derivatives. The derivatives of the function define the rate of change of a function at a point. It is mainly used in fields such as physics, engineering, biology and so on. The primary purpose of the differential equation is the study of solutions that satisfy the equations and the properties of the solutions"(BYJU'S). The source is probably credible because it less customers otherwise. The answer also is logical. In conclusion, a differential equation has been defined for this essay.
Taking a derivative is important to engineering so the rules will be included in this essay. "Frequently Asked Questions on Differentiation Formulas
What are the formulas of differentiation? The formulas of differentiation that helps in solving various differential equations include Derivatives of basic functions Derivatives of Logarithmic and Exponential functions Derivatives of Trigonometric functions Derivatives of Inverse trigonometric functions
Differentiation rules What are the basic rules of differentiation? The basic rules of differentiation are: Power Rule: (d/dx) (xn ) = nx{n-1}
Sum Rule: (d/dx) (f ± g) = f’ ± g’
Product Rule: (d/dx) (fg)= fg’ + gf’
Quotient Rule: (d/dx) (f/g) = [(gf’ – fg’)/g2]
What are the derivatives of trigonometric functions? The derivatives of six trigonometric functions are:
(d/dx) sin x = cos x
(d/dx) cos x = -sin x
(d/dx) tan x = sec2 x
(d/dx) cosec x = -cosec x cot x
(d/dx) sec x = sec x tan x
(d/dx) cot x = -cosec2 x
What is d/dx?
The general representation of the derivative is d/dx. This denotes the differentiation with respect to the variable x. What is a UV formula? (d/dx)(uv) = v(du/dx) + u(dv/dx)
This formula is used to find the derivative of the product of two functions"(BYJU'S). Away to determine the veracity of the source is following the money.
Differential equations also have types and can manifest beyond only words. "We can place all differential equations into two types: ordinary differential equations and partial differential equations. A partial differential equation is a differential equation that involves partial derivatives. An ordinary differential equation is a differential equation that does not involve partial derivatives"(Green 2021). Furthermore, there are the manifestations of differential equations. "((d^2)y)/(dx^2)+(dy)/(dx)=(3x)sin(y)(2.2.1)
is an ordinary differential equation since it does not contain partial derivatives. While (∂y)/(∂t)+x(∂y)/(∂x)=(x+t)/(x−t)(2.2.2) is a partial differential equation, since y is a function of the two variables x and t and partial derivatives are present"(Green 2021). As such solving differential equations can be done either manually or using software. "A differential equation is an equation involving a function and its derivatives. It can be referred toas an ordinary differential equation (ODE) or a partial differential equation (PDE) depending on whether or not partial derivatives are involved. Wolfram Alpha can solve many problems under this important branch of mathematics, including solving ODEs, finding an ODE a function satisfies and solving an ODE using a slew of numerical methods"(Wolfram Alpha)
Wolfram Alpha's software is most likely useful for solving differential equations because the business could lose customers. Noting those at market risk is a feasible way to follow the money and discover the veracity of information. Wolfram Alpha is most likely a useful source of differential equation solving software.
Vocabulary is important in mathematics as it determines what is what and the term derivative should be defined for this essay. "The essence of calculus is the derivative. The derivative is the instantaneous rate of change of a function with respect to one of its variables. This is equivalent to finding the slope of the tangent line to the function at a point"(MIT 1999). That is what a derivative is.
The definition of a derivative covers ordinary ones. Partial ones are different. "The reason for a new type of derivative is that when the input of a function is made up of multiple variables, we want to see how the function changes as we let just one of those variables change while holding all the others constant"(Khan Academy). Khan Academy is describing a partial derivative. Partial derivatives are necessary information for the fundamentals of engineering. Partial derivatives must be learned to do engineering.
Once the fundamentals have been explored the applications are next. "In broad terms, engineering can be divided into four main categories – chemical, civil, electrical and mechanical engineering. Each of these types requires different skills and engineering education"(Cote 2022). The next information in this essay shall be the types of engineering. engineering deserves a definition. Chemical engineering is "engineering dealing with the industrial application of chemistry"(Merriam-Webster). As such the skills necessary for chemical engineering differ from those of other types of the vocation. A knowledge of chemistry would be helpful to this kind of engineering. Knowledge of differential equations would be necessary for chemical engineering.
Civil is another kind of engineering. A civil engineer is "an engineer whose training or occupation is in the design and construction especially of public works (such as roads or harbors)"(Merriam-Webster). Civil engineering is for the public. Differential equations would still be useful for this kind of engineering. Electrical engineering deserves a definition for this essay. Electrical engineering is "a type of engineering that deals with the uses of electricity"(Merriam-Webster). An electrical engineer deals with electricity. Differential equations are still part of electrical engineering.
The last branch of engineering explored in this essay will be mechanical. Mechanical engineering is "a branch of engineering concerned primarily with the industrial application of mechanics and with the production of tools, machinery, and their products"(Merriam-Webster). This branch of engineering also would include differential equations. In conclusion, differential equations are the leading fundamental to engineering and are just equations involving derivatives. The partial differential equations are the ones where the derivative is only taken as part of the equation. The applications of engineering are chemical, civil, electrical and mechanical.
Works Cited
“Engineering.” Merriam-Webster.com Dictionary, Merriam-Webster,https://www.merriam-webster.com/dictionary/engineering. Accessed 14 Sep. 2022.University of Louisville . "ENGINEERING FUNDAMENTALS ." engineering.louisville.edu.engineering.louisville.edu/academics/areasofstudy/engineering-fundamentals/. Accessed14 Sep. 2022.BYJU'S. "Differential Equations ." byjus.com. byjus.com/maths/differential-equation/. Accessed15 Sep. 2022.BYJU'S . "Differentiation Formulas ." byjus.com. byjus.com/maths/differentiation-formulas/.Accessed 16 Sep. 2022.Green, Larry . "2.2: Classification of Differential Equations ." math.libretexts.org. 5 Sep. 2021.math.libretexts.org/Bookshelves/Analysis/Supplemental_Modules_(Analysis)/Ordinary_Differential_Equations/2%3A_First_Order_Differential_Equations/2.2%3A_Classification_of_Differential_Equations. Accessed 15 Sep. 2022.WolframAlpha. "Differential Equations ." wolframalpha.com.www.wolframalpha.com/examples/mathematics/differential-equations. Accessed 16 Sep.2022.
(8) (PDF) Fundamentals and Applications of Engineering Thesis. Available from: https://www.researchgate.net/publication/372503312_Fundamentals_and_Applications_of_Engineering_Thesis [accessed Aug 11 2024].
MIT. "The Definition of Differentiation ." web.mit.edu. 14 Oct. 1999.web.mit.edu/wwmath/calculus/differentiation/definition.html#:~:text=The%20essence%20of%20calculus%20is,the%20function%20at%20a%20point. Accessed 16 Sep. 2022.Khan Academy . "Introduction to partial derivatives ." khanacademy.org.www.khanacademy.org/math/multivariable-calculus/multivariable-derivatives/partial-derivative-and-gradient-articles/a/introduction-to-partial-derivatives. Accessed 16 Sep. 2022.SNHU , and Joe Cote . "Types of Engineering: Salary Potential, Outlook and Using Your Degree." snhu.edu. 10 Aug. 2022.www.snhu.edu/about-us/newsroom/stem/types-of-engineering#:~:text=In%20broad%20terms%2C%20engineering%20can,different%20skills%20and%20engineering%20education. Accessed 15 Sep. 2022. “Chemical engineering.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/chemical%20engineering. Accessed 15Sep. 2022. “Civil engineer.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/civil%20engineer. Accessed 15 Sep. 2022. “Electrical engineering.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/electrical%20engineering. Accessed 15Sep. 2022. “Mechanical engineering.” Merriam-Webster.com Dictionary, Merriam-Webster, https://www.merriam-webster.com/dictionary/mechanical%20engineering. Accessed 15Sep. 2022.
(8) (PDF) Fundamentals and Applications of Engineering Thesis. Available from: https://www.researchgate.net/publication/372503312_Fundamentals_and_Applications_of_Engineering_Thesis [accessed Aug 11 2024].