Students and teachers juggle algebra vs. calculus to solve different math problems. On one hand, algebra helps learners determine the value of unknowns in an equation, whereas calculus is integral to calculating the rate of change of two unknowns in equations. Our Math Assignment Help experts have prepared this in-depth screening of the two concepts for students who’ve been looking for the difference between algebra and calculus. They also help students with their math projects and exams.
Algebra vs. Calculus. Definition of Algebra?
Algebraic equations calculate unknown variables using expressions and operations. These equations are manipulated through division, multiplication, addition, and subtraction to find the true value of the variables. In many equations, unknown variables are represented by x, y, and z. The four types of algebra include:
Elementary algebra uses basic arithmetic operations like addition, subtraction, and multiplication to find the value of unknown variables. It is mainly taught in high school and covers basic concepts such as equation evaluation, exponents, positive rational roots, and variables. Examples of popular variables in elementary algebra include a, b, x, and y.
Advanced or intermediate-level algebra uses complex mathematical operations to determine the value of unknown variables. Besides the basic operations of adding and subtracting, students learn to calculate equations with advanced manipulations such as matrices, logarithmic functions, system of equations, trigonometry, exponential, linear, and quadratic functions.
Linear algebra examines linear combinations and equations used in pure and applied mathematics. The concepts under this branch of algebra apply to studying airplane flights, matrices, lines, and linear functions of vector spaces. Most linear algebra equations also apply in software and computer programming, mapping, and gaming.
The abstract branch of algebra studies algebraic systems independent of the basic algebra equations and manipulations. It deals with concepts around algebraic structures such as modules, vector spaces, lattices, fields, and rings. The topics under abstract algebra can be applied in fields such as software coding and aeronautical engineering.
Algebra vs. Calculus: Definition of Calculus?
Calculus is the study of the rates of change between variables. While algebra determines the value of variables, calculus calculates the rate of change of a specific function between variables. There are two types of calculus. They include:
Differential calculus is a branch of calculus that calculates the rate of instantaneous change of a specific function. The rate of instantaneous change of a function is called a derivative, and the process of finding it is known as differentiation. This rate of change of a function in differential calculus is often denoted by the letter “f.”
Integral calculus is the opposite of differential calculus. It calculates integrals, which are basically minor components of a function. The two types of integrals are:
- Definite – A definite integral is a number in a function where the upper and lower limits are constants. Definite integrals determine the area below a curve at a specific interval.
- Indefinite – Indefinite integrals are a series of functions with “f” derivatives. They calculate the antiderivative function over a specific interval.
The main difference between definite and indefinite integrals is that definite has the lower and upper constants while indefinite doesn’t.
Algebra vs. Calculus: The Differences
There are four major differences between algebra and calculus. Here’s a breakdown of the four algebra vs. calculus fundamental differences.
- Algebra focuses on solving equations using different operations such as division, multiplication, addition, and subtraction to determine unknown variables. On the other hand, calculus deals with calculating the rate of change of a function between variables and the area under a curve of a function.
- Algebra can dissolve into advanced, abstract, linear, and elementary algebra, whereas calculus has two main sub-divisions: differential and integral calculus.
- The knowledge from calculus helps solve complex life problems, while algebra provides the operational tools for simple day-to-day problems, such as calculating weight and circumference.
- Algebra is easier to comprehend and forms the basis of understanding calculus while understanding calculus without learning algebra can be difficult.
Algebra vs. Calculus: The Final Verdict
Algebra vs. calculus are branches of math with few similarities and numerous differences. Calculus is 400 years old, while algebra dates back to 4,000 years ago. Despite these differences, both equations apply in solving real-life issues. For example, algebra can help determine how to subdivide snacks among friends during a party, while calculus can determine the rate of disease spread in an area, like during COVID-19.