Engineering is a diverse field that touches on many different aspects of the modern world. From computer circuits to container ships to heavy machinery, much of what people use on a daily basis is in some way impacted by the work of engineers. It is a discipline that applies mathematical principles to solve practical problems and every area requires a substantial background in mathematics.

### Types of Engineering Degrees

Many universities offer Bachelor of Science degrees in engineering with concentrations in particular areas like mechanical engineering, electrical engineering, aerospace engineering or civil engineering. Sometimes, universities offer degrees specifically in these areas, though the actual coursework does not vary dramatically between the two options. In addition, universities offer master's and doctoral degrees in these engineering disciplines. Regardless of the type of degree, engineering requires students to take a number of core classes in mathematics, which form the basis of all upper-level engineering coursework.

### Calculus

Calculus, the study of the rates of change of functions, is one of the core mathematics areas that is required in an engineering curriculum. Most programs require students to take calculus 1, calculus 2, calculus 3 and advanced calculus. Calculus 1 and 2 focus on derivatives and integrals of functions in one dimension, also known as single-variable calculus. They introduce and cover topics like the basics of taking derivatives, integration, velocity, acceleration and optimization. Calculus 3 and advanced calculus focus on rates of change of functions in two and three dimensions, typically known as multivariable calculus. These courses cover topics such as surface integrals, volume integrals and partial derivatives.

### Physics

Most engineering programs require some courses in physics as prerequisites for upper-level engineering classes. Some programs require students to take a series of courses in general physics, known as physics 1, 2 and 3, while others offer a specific classes in engineering physics. Unlike lower-level physics courses which are based on algebra, these courses are based on calculus and often have calculus 1 and 2 as prerequisites. Physics courses cover topics like mechanics, gravitation, relativity, fluids and waves.

### Engineering and Advanced Math Courses

Some engineering programs require upper-level mathematics classes like ordinary and partial differential equations, numerical methods for engineers, matrix or linear algebra and boundary value problems for partial differential equations. Also, upper-division engineering classes involve the applications of advanced mathematical principles. Courses, like statics and dynamics, involve topics like kinetics of particles, work and energy, and vector analysis of force systems. Other engineering courses require students to study the mathematical modeling of engineering problems, manipulation of matrices and other subjects that require very strong mathematics skills.

#### References

- Dartmouth University Taylor School of Engineering: Bachelor of Engineering
- University of Texas at San Antonio: Bachelor of Science Degree in Mechanical Engineering
- University of Michigan Department of Mechanical Engineering: Bachelor’s Degree
- University of Texas at San Antonio: Engineering Course Descriptions

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