The Use of Calculus in Engineering (2024)

Calculus, defined as the mathematical study of change, was developed independently by Isaac Newton and Gottfried Wilhelm von Leibniz in the 17th century. Engineering is defined as "the profession in which a knowledge of the mathematical and natural sciences gained by study, experience, and practice is applied with judgment to develop ways to utilize, economically, the materials and forces of nature for the benefit of mankind." Some engineers directly use calculus in their daily practice and some use computer programs based on calculus that simplify engineering design. Two methods of calculus, differentiation and integration, are particularly useful in the practice of engineering, and are generally used for optimization and summation, respectively.

Civil Engineering

Many aspects of civil engineering require calculus. Firstly, derivation of the basic fluid mechanics equations requires calculus. For example, all hydraulic analysis programs, which aid in the design of storm drain and open channel systems, use calculus numerical methods to obtain the results. In hydrology, volume is calculated as the area under the curve of a plot of flow versus time and is accomplished using calculus.

Structural Engineering

In structural engineering, calculus is used to determine the forces in complex configurations of structural elements. Structural analysis relating to seismic design requires calculus. In a soil structure context, calculations of bearing capacity and shear strength of soil are done using calculus, as is the determination of lateral earth pressure and slope stability in complex situations.

Mechanical engineering

Many examples of the use of calculus are found in mechanical engineering, such as computing the surface area of complex objects to determine frictional forces, designing a pump according to flow rate and head, and calculating the power provided by a battery system. Newton's law of cooling is a governing differential equation in HVAC design that requires integration to solve.

Aerospace Engineering

Numerous examples of the use of calculus can be found in aerospace engineering. Thrust over time calculated using the ideal rocket equation is an application of calculus. Analysis of rockets that function in stages also requires calculus, as does gravitational modeling over time and space. Almost all physics models, especially those of astronomy and complex systems, use some form of calculus.

The Use of Calculus in Engineering (2024)

FAQs

Is calculus necessary for engineering? ›

Calculus is a high-level math required for mechanical engineering technology, but it also lays the groundwork for more advanced math courses. Once you have successfully mastered calculus, you will have the fundamental skills to properly grasp a majority of science courses, especially physics.

What is an example of calculus used in engineering? ›

Calculus is used to improve the architecture not only of buildings but also of important infrastructures such as bridges. In Electrical Engineering, Calculus (Integration) is used to determine the exact length of power cable needed to connect two substations, which are miles away from each other.

How important is calculus for you as an engineering student? ›

In many science and technology programs, Calculus is among the first courses taught. It is considered one of the most important early courses in engineering, allowing students to subsequently study and model real problems in ways that can be applied to their professional lives.

Do most engineers use calculus? ›

Many aspects of civil engineering require calculus. Firstly, derivation of the basic fluid mechanics equations requires calculus. For example, all hydraulic analysis programs, which aid in the design of storm drain and open channel systems, use calculus numerical methods to obtain the results.

What math is most used in engineering? ›

Algebra is used by civil engineers on a daily basis. It is a branch of mathematics in which letters and other symbols are used to represent numbers and quantities, and is used to solve equations and find statistics.

What careers actually use calculus? ›

12 jobs that use calculus
  • Animator.
  • Chemical engineer.
  • Environmental engineer.
  • Mathematician.
  • Electrical engineer.
  • Operations research engineer.
  • Aerospace engineer.
  • Software developer.
May 25, 2021

Do engineers struggle with calculus? ›

A lot of people (including many successful engineers) struggle when they first get to Calculus.

What IQ do you need to learn calculus? ›

115-120 is probably required for a solid understanding of the full calculus sequence.

Is calculus The hardest part of engineering? ›

It is not the toughest class, but it is used as a screen. Calculus, especially the second quarter / second semester work on integration, has been widely used in the US as a tool to limit the number of engineering majors. Almost everyone can do differentiation.

Is engineering calculus heavy? ›

Engineering is a calculus-heavy program, regardless of whether it is Mechanical, electrical, or civil engineering focused. The first circuits class you'll take in this program require Calculus 2 as a Pre-req! Other math requirements of the degree are Calc. 3 , differential equations and Linear algebra.

Does NASA use calculus? ›

Astronauts use calculus to determine how the spaceship itself moves. For example, calculus is used to determine the rate of speed required for the spaceship to successfully reach space from the Earth.

Why do civil engineers use calculus? ›

Calculus is the mathematics of change, which makes it a natural fit for a profession like civil engineering that deals with the design and construction of physical infrastructure. Calculus can be used to model and understand complex systems like traffic flow, water distribution, and structural loads.

What are the three applications of calculus? ›

Calculus Applications
  • Finding the Slope of a Curve. Calculus can give us a generalized method of finding the slope of a curve. ...
  • Calculating the Area of Any Shape. ...
  • Calculate Complicated X-intercepts. ...
  • Visualizing Graphs. ...
  • Finding the Average of a Function. ...
  • Calculating Optimal Values.

What are the 3 main topics in calculus? ›

The main concepts of calculus are : Limits. Differential calculus (Differentiation). Integral calculus (Integration).

What is the hardest engineering major? ›

Chemical engineering

What is the most math heavy major? ›

Physics – Physics is regarded as the most math-intensive degree path you can pursue within the sciences. Linear algebra, quantum mechanics, and engineering calculations are just a few of the core courses you'll need to take for this major.

Which engineering branch has toughest maths? ›

Mechanical Engineering deals with a lot of concepts and complex mathematics required to solve immediate real-life problems. This means that you must have these difficult equations and knowledge sets memorized.

Do surgeons use calculus? ›

Calculus and statistics are used in the medical profession in fields ranging from measuring kidney function to analyzing medical images to diagnosing diabetes. Clearly, mathematics is vital to the medical profession.

Why is calculus so stressful? ›

Most of the reasons students have difficulty learning calculus is because they don't study daily after lessons, can't focus in class, have gaps in their math knowledge, and think learning calculus is a waste of time. Here are the steps you can take to make calculus a breeze: Stay curious.

What is the hardest thing to learn in calculus? ›

I'd say the concept of zero, infinity, and the infinitesimal. Often they're thought of like numbers and this leads to calculations which don't make sense where, even if they work numerically, it's not actually correct since the process is wrong.

What engineering requires the least math? ›

Environmental Engineering

It's considered one of the easier engineering majors that you can study though, because it's not as focused on advanced math and physics.

Do software engineers actually use calculus? ›

Yes. If you look at a list of required coursework for a degree in software engineering, you'll typically see Calculus I-III, Differential Equations, Discrete Mathematics, Linear Algebra, and other advanced math classes.

Do electrical engineers actually use calculus? ›

Calculus. As we move beyond resistor circuits and start to include capacitors and inductors, we need calculus to understand how they work. Think of calculus as a corequisite in parallel with electrical engineering. You don't need to have a complete calculus background to get started, but it is helpful before too long.

How many Americans took calculus? ›

It has been estimated that 700,000 students are enrolled in college-level calculus courses in the U. S. in any given year. Of these, 100,000 are in Advanced Placement courses in high schools, 125,000 in two-year colleges, and the rest in four-year colleges or universities [17].

Does Einstein know calculus? ›

Einstein was a strong math student from a very young age. He himself admits: “I never failed in mathematics. Before I was fifteen I had mastered differential and integral calculus.”

What percentage of us knows calculus? ›

If 85% of adults graduate high school, and only 16% of those take take calculus, then 13% of adults in the developed world study calculus.

What is the #1 engineering school in the US? ›

Massachusetts Institute of Technology (MIT) is the top engineering school in America. They have about 3,120 full-time students enrolled.

Do high school engineers need calculus? ›

In order to be well prepared to start an engineering degree, you should take the most challenging courses possible in math and sciences offered at your high school. This usually means having taken calculus by your senior year of high school.

Which engineering has highest salary? ›

Petroleum Engineer tops our list of the highest paying engineering jobs. The primary responsibility of petroleum engineers is to design and develop ways to extract natural resources oil and gas from Earth.

What GPA is required for NASA? ›

Interested applicants must be: U.S. Citizen. Cumulative 3.0 GPA (on a 4.0 scale) 16 years of age at the time of application.

Is calculus used in cars? ›

The rate of change of s at a time t (measured, perhaps, in km/hr) is your velocity v at that time and this is shown on the speedometer in your car. Studying rates of change uses a concept from Calculus I called the derivative.

Did Isaac Newton do calculus? ›

Isaac Newton changed the world when he invented Calculus in 1665. We take this for granted today, but what Newton accomplished at the age of 24 is simply astonishing. Calculus has uses in physics, chemistry, biology, economics, pure mathematics, all branches of engineering, and more.

Is calculus hard in engineering? ›

No not that tough. it is easier than 12th std maths if you practice and if your 12th std concepts are strong. Practice more questions and it will not at all be tough.

Is calculus for engineers essential for first year students? ›

The calculus courses are required of engineering students typically upon entrance to college if they want to graduate with a degree in four years.

What is the hardest thing to engineer? ›

The following are the hardest types of engineering.
  1. Electrical Engineering. ...
  2. Chemical Engineering. ...
  3. Computer Engineering. ...
  4. Aerospace Engineering. ...
  5. Biomedical Engineering. ...
  6. Nuclear Engineering. ...
  7. Robotics Engineering. ...
  8. Quantum Engineering.
Jan 8, 2023

What is the hardest engineer to become? ›

The electrical engineering major is considered one of the most difficult majors in the field, and these are the common reasons students list to explain why it is hard: There is a lot of abstract thinking involved.

Why is engineering the hardest degree? ›

What Is the Hardest Engineering Major? Engineering is a notoriously challenging field. These majors require lots of homework and classes that cover high-level topics like advanced calculus and physics.

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