Calculus is an advanced mathematics course that focuses on the rates of change of functions. This is a required class in many college programs including mathematics, physics, computer science and engineering. Most universities offer three one-semester courses in calculus, covering both calculus in one dimension, known as single variable calculus, and calculus in two and three dimensions, known as multivariable calculus.
To succeed in the first semester calculus, typically known as calculus 1, students have to have a strong foundation in algebra and pre-calculus. The types of courses that a student should take prior to calculus vary according to whether the student is taking calculus in high school or in college. Typical high school prerequisites are pre-algebra, algebra 1, algebra 2 and pre-calculus. Each course after pre-algebra assumes a working knowledge and thorough understanding of the courses that come after it. College course equivalents cover the same topics in a compressed manner. Typical college prerequisites for calculus are college algebra 1, college algebra 2 and pre-calculus.
College Algebra 1
College algebra 1, also known as elementary algebra, introduces students to different mathematical concepts including integers, exponents, scientific notation, radicals, polynomials and rational expressions. A good understanding of these concepts and their operations serves as a tool for understanding the other major concepts covered in this course: equations and inequalities. After learning what equations and inequalities are, students spend the rest of the time learning how to manipulate and solve different types of equations and inequalities, including linear, quadratic, radical, rational and absolute value.
College Algebra 2
The second part of college algebra, also known as intermediate algebra, focuses on graphing equations introduced in college algebra 1. Students learn how to find and graph the slope of a line, and how to write and graph equations of lines. College algebra 2 also introduces students to some elementary topics in functions. In particular, students learn what a function is, how to do different operations of functions and how to graph certain functions. This introduction lays the foundation for topics covered in pre-calculus. The material covered in the two sections on college algebra vary, and some universities compress both courses into one prerequisite course.
Building upon the knowledge gained in college algebra, the last prerequisite for calculus is pre-calculus. This course introduces students to functions and the graphing of functions. It covers topics such as linear and polynomial functions, inverse functions, exponential functions, logarithmic functions, trigonometric functions and inverses. Other possible topics include vectors, conic sections and polar coordinates. Graphing is an important part of pre-calculus and students in this class learn how to use a graphing calculator. A graphing calculator plays an important role in calculus, and this class introduces students to its various uses in mathematics.
Kate Prudchenko has been a writer and editor for five years, publishing peer-reviewed articles, essays, and book chapters in a variety of publications including Immersive Environments: Future Trends in Education and Contemporary Literary Review India. She has a BA and MS in Mathematics, MA in English/Writing, and is completing a PhD in Education.