Civil engineering is a profession that applies mathematical and physical science principles to design and develop structures and methods to utilize materials and forces of nature for the benefit of humanity. Civil engineers create buildings, industrial plants and transportation infrastructure. Today, civil engineering is often combined with environmental engineering as cities and countries place more focus on sustainable building and protecting infrastructure from damage caused by natural disasters.
Calculus is the study of the rate of change in functions. Most civil engineering programs require calculus 1 and calculus 2, while some also require students take calculus 3. Calculus 1 is a prerequisite for most civil engineering courses and so it is generally taken in the first semester, with calculus 2 taken the next. Both classes deal with single-variable calculus, or derivatives and integrals of functions in one dimension. These classes also cover topics like velocity, acceleration and optimization. Calculus 3, which may be required in a civil engineering program, deals with functions in two and three dimensions, and includes topics like surface and volume integrals, and partial derivatives.
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Most civil engineering programs require courses in linear algebra and differential equations. These courses are prerequisites for upper-division civil engineering courses. Linear algebra, or matrix algebra, involves the study of solutions to systems of equations, determinants and vector spaces, including function spaces, linear transformations and quadratic forms. Students typically take this courses after completing calculus 2. Differential equations, taken after calculus 3, is a more advanced mathematics course required by some civil engineering programs. It includes topics like first-order differential equations, undetermined coefficients and systems of linear differential equations, with a focus on applications to science and engineering.
Measuring and analyzing risk is a key skill in engineering, and most civil engineering programs require students take courses in probability and statistics to develop the skills and knowledge to quantify risk and safety in their designs. Courses in statistics cover topics like frequency interpretation of probability, probability theory, discrete probability and combinatorics, distribution and density functions, and sampling theory. These courses also introduce the use of computer software to perform statistical analysis on the kind of large data sets that are involved in engineering problems.
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Civil engineering coursework involves the application of mathematical principles and skills to real world problems. Classes such as structural analysis examine structures like trusses, beams and frames, and concepts like virtual work, energy methods and influence lines. Mechanics of solids includes topics like internal forces and deformation in solids, stresses and deflections in beams, and column theory and analysis. Courses in fluid mechanics involve study of the properties of fluids, fluid dynamics and dynamic similitude to analyze the flow of compressible and incompressible fluids in closed conduits. All of these classes apply the principles and skills learned in the prerequisite mathematics courses.