# 5.4: How Do Math and Science Connect with Engineering in High School and College?

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- 4533

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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)**Preparatory High School and College Courses**

Many high school and college courses are needed to prepare for an engineering education.

**Precollege Courses**

If a student wants to consider the possibility of pursuing a college degree in engineering, what types of K-12 courses should he/she take? Before even entering high school, students should investigate the admittance requirements of the universities for a student’s high school education. Universities set guidelines of **prerequisite** requirements upon applying. Most require a minimum of four years of high school mathematics, including at least the basic math courses (algebra one and two, geometry, trigonometry, and analytical geometry), and a minimum of four years of science, again covering at least the basic courses (chemistry, biology, and physics). Also, along with these set requirements for course work, most reputable engineering programs require submitting a placement exam (such as ACT or SAT) scores and show no deficiencies in either math or science.

**College Courses**

Once admitted into a college engineering program students will be required to complete a year of college math and physics (about 10 courses). This would include fundamental science courses (Chemistry, Biology, Physics) and basic math courses (Calculus I, II, III and Differential Equations). These are usually the minimum level required for engineers in general, but specific engineering disciplines may require more. Most programs also require about a semester (5 courses) of “engineering science courses” where the understandings of math and science are directed toward broad applied science and math courses. They might include courses such as Circuits, Statics, Dynamics, Fluids, Materials, Thermodynamics, and Statistics. The connections of math and science to engineering in these applied courses are quite obvious, for example, with the chemistry and differential equations used in Engineering Thermodynamics.

**Science and Mathematics Courses Connected to Engineering**

Basic math and science provide the tools of mathematical techniques and science phenomena that engineers use to address design problems related to phenomena of the natural world. They build on similar math and science foundational courses in high school that are introductory with a lower level of math that describe natural phenomena. The college level math and science courses provide a base for advanced math and science courses necessary to address more complex problems in a given engineering discipline. The basic math and science courses have also been utilized for a broad range of practical engineering applications to develop courses that are referred to as engineering science courses such as Thermodynamics, Circuits, and Fluids. For example, the Engineering Science course of Fluids is typically taken by Chemical, Mechanical, Aerospace, and Biomedical Engineering students. That is because the general principles of Fluids apply to fluid flow of air for airplanes as well as flow of gases in internal combustion engines while fluid flow of liquid is used to analyze blood flow in humans as well as flow of chemicals in chemical processing plants. Thus, the connection of basic math and science to engineering is shown directly and unambiguously both as a base for advanced courses as well as being integrated into broadly subscribed Engineering Science courses. Brief descriptions of the basic math and science courses are presented here followed by short descriptions of the most widely subscribed Engineering Science courses.

**Physics.** Physics is the science of matter and the interaction of matter. It describes and predicts phenomena about matter, movement and forces, space and time, and other features of the natural world.

**Chemistry.** Chemistry is the science of the phenomena about composition, structure, and properties of matter, as well as the changes it undergoes during chemical reactions, especially as related to various atoms, molecules, crystals, and other aggregates of matter.

**Biology and Biological Sciences.** Biology is the science of living organisms that describes and predicts phenomena related to the structure, function, growth, origin, evolution, and distribution of living things as well as the interactions they have with each other and with the natural environment.

**Calculus.** Calculus is the mathematics of change which includes the study of limits, derivatives, integrals, and infinite series; many disciplines in engineering address problems that must be solved by differential calculus and integral calculus.

**Differential Equations.** Differential equations are equations with variables that relate the values of the function itself to its derivatives of various orders. Differential equations are used for engineering applications where changing quantities modeled by functions and their rates of change expressed as derivatives are known or postulated giving solutions that are dependent on boundary conditions.

**Engineering Courses Connected to Science and Mathematics**

As discussed previously, the basic math and science courses have been utilized for a broad range of practical engineering applications to develop courses that are referred to as engineering science courses such as Thermodynamics, Circuits, and Fluids. For example, the Engineering Science course of Fluids is typically taken by Chemical, Mechanical, Aerospace, and Biomedical Engineering students. That is because the general principles of Fluids apply to fluid flow of air for airplanes as well as flow of gases in internal combustion engines while fluid flow of liquid is used to analyze blood flow in humans as well as flow of chemicals in chemical processing plants. Thus, the connection of basic math and science to engineering is shown directly and unambiguously both as a base for advanced courses as well as being integrated into broadly subscribed Engineering Science courses. Brief descriptions of the basic math and science courses are presented here followed by short descriptions of the most widely subscribed Engineering Science courses. Similar arguments apply to other engineering science courses that are also broadly subscribed by many disciplines. The courses will be briefly described in this section.

**Dynamics.** The field of dynamics uses the knowledge of classical mechanics that is concerned with effects of forces on motion of objects. Engineers use the concepts in design of any moving parts, such as for engines, machinery and motors. For example, a mechanical engineer would have used Dynamics extensively in the design of the pneumatically powered, multirow seed planter that was invented in 1956.

**Electric Circuits.** The field of circuits applies physics of electrical phenomena to the design, analysis, and simulation of linear electric circuits and measurements of their properties. The principles are used in circuit designs for wide ranging applications such as motors, cell phones, and computers. For example, an electrical engineer would have used Circuits extensively in the design in 1980 of the first circuit board with built-in self-testing technology.

**Fluids.** The subject of fluid mechanics uses physics of fluids to understand and predict the behavior of gases and liquids at rest and in motion which are referred to as fluid statics and fluid dynamics. As described previously, there are a broad set of engineering applications including air flow for airplanes and in internal combustion engines as well as fluid flow of liquid blood in humans as well as flow of chemicals in chemical processing plants. For example, a chemical engineer would have used the subject of Fluids extensively in the design of deep-draft pumping of oil from a depth of 4800 feet in the Gulf of Mexico begun in 2000.

**Materials Science and Engineering.** This subject utilizes the synthesis techniques of chemistry and the characterization tools of physics, such as the atomic force microscope, to control and characterize the properties of the structure and properties of solid materials. The principles of materials science are broadly used by a variety of engineering disciplines including electronics, aerospace, telecommunications, information processing, nuclear power, and energy conversion. Applications vary from structural steels to computer microchips. A materials engineer would have applied the principles of Materials Science extensively in the design of synthetic skin which can act as a framework for live cells that grow into a layer of skin while the framework is absorbed by the body.

**Mechanics of Solids.** This subject uses concepts and knowledge of continuum mechanics emerging from physics and mathematics to understand and predict the behavior of solid matter under external actions, such as external forces, temperature changes, and displacement or strain. The principles are broadly used on a variety of topics for a number of engineering disciplines. It is part of a broader study known as continuum mechanics. Engineers use the principles to determine what happens when a stress is applied to a component. Concepts are useful anytime that a component departs away from the rest shape due to stress. The amount of departure from rest, which is initially elastic or proportional to stress, is safe as long as the material is below its yield strength. For example, an aerospace engineer would have used Mechanics of Solids extensively in the design of the Space Shuttle first launched on April 12, 1981.

**Statics.** This is the engineering application of a branch of physics called Mechanics. It describes bodies which are acted upon by balanced forces and torques so that they remain at rest or in uniform motion. In statics, the bodies being studied are in equilibrium. The equilibrium conditions are very similar in the planar, or two-dimensional, and the three-dimensional rigid body statics. These are that the vector sum of all forces acting upon the body must be zero; and the resultant of all torques about any point must be zero. Thus it is necessary to understand the vector sums of forces and torques. For example, a civil engineer would have used Statics extensively in the design of the Golden Gate Bridge in 1937.

**Engineering Thermodynamics.** This subject uses the concepts of science that deal with transfer of heat and work which are used to solve engineering problems. Engineers use thermodynamics to calculate energies in chemical processing, to calculate the fuel efficiency of engines, and to find ways to make more efficient systems, be they rockets, refineries, or nuclear reactors. For example, a mechanical engineer would have used “thermo” extensively in the design of an “alternative energy vehicle” that uses natural gas.

**Activity—Differing educational focus of different engineering disciplines**

*Choose two or three types of engineers and describe and write down what you think are the typical math and science classes they might take that will provide a focus for their future professional activities.*

**Review Questions**

The following questions will help you assess your understanding of the How Do Math and Science Connect with Engineering in High School and College? section. There may be one, two, three, or even four correct answers to each question. To demonstrate your understanding, you should find all of the correct answers.

- College engineering programs require
- ACT or SAT scores
- letters or recommendation
- four years of high school mathematics
- an essay about engineering

- Engineering students must be able to
- apply math and science to problems
- remember math and science problems
- major in a math or science field
- use math and science as tools

- If you want to become an engineer you should study
- mostly mathematics
- mostly science
- mathematics and science
- some history

- English is as important as mathematic and science because
- engineers must be able to write
- engineers must communicate with the public
- engineers must communicate with coworkers
- engineers must be well rounded

- Engineering requires that you understand
- timelines
- calculus
- geometry
- formulas

- The best indicator of success in an engineering major in college is
- overall grade point average in high school
- taking three years of metal shop in high school
- taking two computer science courses in high school
- successfully completing four years of math courses in high school