What Math Concepts Are Needed to Understand College-Level Physics Classes?

The movement of something as simple as a spring requires differential equations to describe.
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Physics describes the world in terms of mathematics. Even if you do not plan to take any physics classes in college past the introductory level, you'll need to understand some mathematical concepts -- those of algebra, geometry and trigonometry -- to keep up with the class. And if you plan on majoring in physics or otherwise continuing your physics education, you'll need a good grasp of higher mathematical concepts as well.

Algebra

Algebra is an absolutely essential building block for the mathematical skills you'll need in a college physics course. It provides an introduction to the ideas of variables and constants, as well as to the ideas of manipulating and solving both linear and quadratic equations. Linear algebra is necessary in particular for solving systems of linear equations and expressing them as matrices or vectors. Algebra is necessary as well for understanding analytic geometry, which studies geometric objects such as planes and spheres with the use of algebraic equations.

Geometry/Trigonometry

Physics is the study of objects and motion through space and time; geometry, which is the branch of mathematics devoted to properties of space and forms, is vital. Physics students should be familiar with concepts of two-dimensional Euclidean geometry, giving them understanding of concepts like congruence, similarity and symmetry, as well as analytic geometry, including vectors in Cartesian, polar and spherical coordinates. Trigonometry, which begins with the study of right triangles and continues through to the study of the trigonometric functions sin, cos and tan, is particularly necessary in finding the components of vectors.

Calculus

Many colleges offer a physics class for non-science majors that does not require calculus. If you do not intend to take further classes in physics, then physics without calculus serves as a good introduction to the basic concepts. However, there are many concepts in physics that cannot be fully understood without understanding the underlying mathematics. Calculus is required for an accurate definition of the concept of “work,” as well as for describing kinematics and many other aspects of dynamics. Even in physics courses for non-majors, students should have a firm grasp of algebra, geometry and trigonometry.

Other Mathematical Concepts

With the introduction of quantum mechanics into physics, the field of probability suddenly became important in a way that it hadn’t been previously. Students planning to take higher-level physics courses will find that they need an understanding of probability to explore quantum physics. In addition, many problems in physics can’t be solved exactly in closed form, and require mathematical methods of approximation, such as power series expansions and saddle point integration.

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