Study.com's collection of precalculus and calculus courses is designed for high school or college students as well as independent learners who want to learn more about higher math.
We define calculus as the study of rates of continuous change, especially instantaneous change or change over short time intervals. Calculus enables individuals to graph and create models of change. It also helps in making predictions of future change. Mathematical operations are used to study and model rates of change. It also helps determine the consequences of change.
Calculus developed over many centuries. Eudoxus and Archimedes in ancient Greece, as well as mathematicians in ancient China, helped lay the foundations of calculus. By the 15th century, Indian mathematicians were using some calculus-type processes. In more recent times, Johannes Kepler contributed to the understanding of advanced math. Isaac Newton and Gottfried Leibniz then developed modern calculus. Newton focused on the geometric aspects of calculus, while Leibniz concentrated on analysis and created a notational system.
Key terms to understand in calculus math are function, derivative, and integral. Functions show relationships or connections between variables. Each input will result in one output. In calculus, they describe motion. Derivatives demonstrate the rate of change with respect to a variable. Integrals deal with areas. The two primary types of calculus are differential calculus and integral calculus. Basic calculus deals with single variables, while more advanced calculus studies the impact of multiple variables.
Calculus is commonly used in physics, engineering, medicine, economics, and computer science. It is also used in navigation and space travel. It is a common math requirement in many college programs and utilizes all the math skills students have previously developed, including those in algebra, geometry, and trigonometry.
Study.com's precalculus and calculus courses, as well as additional skills practice, provides students with the tools they need to succeed in higher math. Some of these courses and practices are designed to meet common high school academic standards, while others are tailored to expectations for college-level work.
Those who complete the precalculus courses will be able to:
Students will have a firm grasp of these concepts and be able to apply them to their current coursework or be ready to continue their mathematical studies with calculus.
Calculus students will have a firm foundation in both differential and integral calculus. By working through various calculus examples and problems, students will:
The links in this section provide many practice problems geared to meeting specific math standards in both Florida and Texas. Many other states have similar standards, so the practice skills are easily transferable regardless of the student's location. These practice equations and problems allow students to practice key skills or to work on areas in which they may need extra help. Step-by-step guides on how to solve the equations will help students develop a better understanding of how to answer problems. Teachers may also find these practice problems helpful in building their own skills and understanding as well as developing material for their courses.
With the lessons and skills that Study.com offers, students who wish to pursue higher math studies beyond calculus will be well-prepared to do so.
Students and prospective teachers can take advantage of Study.com's calculus test prep courses. Students hoping to earn college credit can study using the CLEP, AP Calculus AB, AP Calculus BC, or AP Calculus AB & BC courses. Prospective teachers planning to teach in Georgia can prepare for the GACE Math Test 1 while those hoping to teach in California can take advantage of the CSET Math Subtest Prep.
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