Calculus Help and Problems
This section contains in depth discussions and explanations on key topics that appear throughout Calculus 1 and 2 up through Vector Calculus. The topics are arranged in a natural progression catering typically to late highschool and early college students, covering the foundations of calculus, limits, derivatives, integrals, and vectors.
Calculus is an advanced branch of mathematics, incorporating algebra, geometry, and
trigonometry. Known as the study of change and motion, core calculus concepts include limits,
derivatives, and integrals of functions. In this section, learn about calculus’ history, how it’s the
similar to (and different from!) other branches of math, and how people use calculus in real life.
One of the first topics introduced in any calculus class, limits introduce the component of
infinity to math problems. How do you find the limit of a function? This lesson defines limits and
provides a variety of examples to understand the concept.
The process of finding the derivative of a function at any point is called differentiation, and
differential calculus is the field that studies this process. This overview of differential calculus
introduces different concepts of the derivative and walks you through example problems.
Integral calculus involves the concept of integration. Alongside differentiation, integration is one
of the main operations in calculus. Integration is the process of finding the integral of a function
at any point on a graph. This lesson defines integration and also covers Riemann integration
and the general power rule.
Multivariable calculus, also called vector calculus, deals with functions of two variables in three-
dimensional space. Multivariable calculus extends concepts found in differential and integral
calculus. This group of lessons introduces important concepts such as vectors in two and three-
dimensional space and vector functions.