Find your way to Riemann sums through a simple motion problem.
In a sense, differential calculus is local: it focuses on aspects of a function near a given point, like its rate of change there. Integral calculus complements this by taking a more complete view of a function throughout part or all of its domain.
This course provides complete coverage of the two essential pillars of integral calculus: integrals and infinite series. By the end, you'll know their core principles and how to apply them to problems in geometry, probability, and physics.
The core of integral calculus.
The essential toolkit, from the fundamental theorem to substitutions.
Make the connection between limits, Riemann sums, and definite integrals.
Solidify your complete comprehension of the close connection between derivatives and integrals.
Begin to unravel basic integrals with antiderivatives.
Reverse the chain rule to compute challenging integrals.
Dabble with transcendental integrals.
A medley of integration techniques that no professional can do without.
Combine derivative rules to reshape a definite integral into something simpler.
Learn to break rational integrals down into simpler parts.
Simplify tricky trig integrals with Euler's formula.
Uncover powerful integrals through trigonometry.
Look at how integrals are really done in practice.
Use integrals to solve crucial problems in math and science.
Dive into some real-world applications of integrals.
Construct volume integrals for a variety of 3D objects using disks, washers, and shells.
Apply integrals to geometry and explore the paradoxical shape of Gabriel's Horn.
Go beyond geometry and put integrals to work in physics problems.
Apply partial fractions to important real-world problems.
Bring all integral methods to bear on a crucial physics problem.
The fundamental concepts of sums without end.
Learn about infinite series through a legendary footrace.
Master the language of sums both finite and infinite.
Expose familiar functions as infinite sums in disguise.
Convergence tests for infinite sums and their applications.
What does it mean for a sum to converge?
Exploit the geometric sum to create brand new convergence tests.
Connect infinite sums to integrals through geometry.
Explore the strange properties of sums that don't converge absolutely.
Expand the menagerie of convergence tests and create a new fundamental number in the process.
Practice with infinite sums at the heart of many real-world applications.
Step into the world of infinite sums of sines and cosines.