What is the difference between algebra and calculus?
Algebra and Calculus are closely related as much as one has to constantly use algebra while doing calculus. Being familiar with algebra, makes one feel comfortable with calculus. Algebra will let you grasp topics in calculus better and vice versa. But we can also do an analysis of algebra vs calculus. 
Algebra focuses on solving equations whereas calculus is primarily focused on the rate of change of functions.The two main operations of calculus are differentiation (find the rate of change of a function) and integration (find the area under a curve of a function).  Calculus deals with operations on functions and their derivatives whereas algebra deals with operations on variables and numbers