# What Kind of Math Is Expected of a Civil Engineering Student?

#### 26 SEP 2017

#### COLLEGE

Civil engineers design and supervise the great construction projects of the world, from the “Chunnel” between France and the United Kingdom to the Hoover Dam on the Colorado River to the world's great skyscrapers. The college math required for this profession is rigorous but not in excess of what is asked of typical engineering students.

## 1 Calculus: Multiple Levels

At the college level, civil engineers will typically be required to complete three to four levels of calculus. Calculus is the study of changing unknown variables in relation to a system. It enables engineers to make physics-related calculations. For example, according to Dr. Barney of Drexel University, if a civil engineer were designing a concrete bridge, he would need to know how the strength of the concrete columns would change over time. The engineer could use the equation S=c(1-e^-kt) to find the strength of the concrete as a function of time, where S=strength, t=time, and c and k are constants specific to this particular form of concrete. Because calculus measures change over time, the engineer can determine when the concrete will be at half its strength and what sorts of variables, such as floods or automobile crashes, might further affect its strength. The engineer can then determine at what point the infrastructure should be replaced.

## 2 Differential Equations

Civil engineers will often have to take a course specifically focused on differential equations. Differential equations allow engineers to see how different functions of their designs experience infinitesimal changes in relationship to changing variables in a system. These equations are critical to civil engineering work and allow engineers to see how well components of a structure deflect different forces, how well open channels in a structure will accommodate steady uniform airflow and how well the soils underneath a structure will drain water.

## 3 Linear Algebra

Linear algebra works with the mathematical properties of lines and their transformation properties, including rotations in space, least squares fitting and the ability of three points to pass through a circle. Civil engineers frequently use matrices in linear algebra to analyze the properties of springs and two-dimensional structural frames as well as to model the impact of uniformly distributed loads and concentrated loads on the components of a structure. This often involves computer modeling, which is an inexpensive way to test different approaches to structural design in advance.

## 4 Statistics and Probability

Statistics enables civil engineers to see patterns in large amounts of data about a site on which they are building, as well as the human population that their structure will serve. It also enables engineers to make predictions about future conditions and usage based on this data. Engineers use statistics to determine the typical air flow and climate in an area, as well as the typical water usage of a human population. This makes it possible for them to design a structure that responds to the conditions of their target building site and the needs of their target human population.

- 1 The Math Forum at Drexel – Ask Dr. Math: Civil Engineering and Math
- 2 Wolfram MathWorld: Differential Equation
- 3 Wolfram MathWorld: Derivative
- 4 Wolfram MathWorld: Linear Algebra
- 5 American Statistical Association: What Is Statistics?
- 6 BLS Occupational Outlook Handbook: Civil Engineers
- 7 UW Civil & Environmental Engineering: Bachelor of Science in Civil Engineering (BSCE) Degree Requirements
- 8 Arizona State University: Civil Engineering Flowchart
- 9 Queen's University Belfast: Types of things Civil Engineering students do with mathematics