Determine a function y = f(x) such that {eq}y" = \dfrac{1}{10}y {/eq} and {eq}f(0) = -3 {/eq}.

Differential equations are equations where rates of change occur with respect to variables. Learn how to solve systems of linear differential equations by elimination, using a step-by-step example to reduce the system to one equation.

The Newton-Raphson method is a method used to find solutions for nonlinear systems of equations. Learn what the Newton-Raphson method is, how it is set up, review the calculus and linear algebra involved, and see how the information is packaged. Finally, explore how to solve a problem using this method with a step-by-step example.

Learn how to take the integral of CSC(x) with the help of an example. Understand how to verify if the calculated antiderivative of CSC is the accurate solution.

Learn what are the initial value and rate of change of a function. See how to find the initial value and rate of change of a function, such as a linear function.

Learn what a derivative of a function is, the notational definition of a derivative formula, what higher-order derivatives are, and see worked-out examples.

Learn about when a function is concave down. Discover graphs and examples of functions which are concave down and generate tables of values to see their numbers.

Discover the disk method in calculus. Find the volume of a disk, and use the disk method to find the volume of objects by dividing them into small cylinders.

The Taylor Series can be used to evaluate a function using an infinite series of terms. Explore how the steps of the Taylor Series are used to find and evaluate derivatives through an example using the Maclaurin series, a specific type of Taylor series, to solve for sin(x).

The integrating factor method is useful in solving non-exact, linear, first-order, partial differential equations. Learn the technique of the integrating factors method and its application to the Fundamental Theorem of Calculus.

In mathematics, uniqueness proofs show that a number or other item is the only answer. Learn more by exploring the definition, method, and examples of uniqueness proofs and theorems.

Despite similar roots, customers, consumers, and consumerism have differences in meaning. Distinguish between them, learn their definitions, and explore consumerism through the lens of consumer advocacy groups and consumer regulation.

Read the Taylor series definition and learn about a special case of the Taylor series known as the Maclaurin series. See Taylor series examples and learn how to use the Taylor series formula.

Explore closed sets and learn the definition of a closed set and understand its different applications. Discover the various properties of closed sets with examples.

Points can be plotted in a three-dimensional system by aligning them according to the X, Y, and Z axes. See how this appears through examples of coordinates, and how to locate points in three-dimensional space.

Learn the work done formula and understand the application of work integral in the work done formula with examples problems using calculus.

Learn how to find the shortest distance between two planes. A surface that extends into infinity in every direction is a plane, and if two planes are not parallel they will eventually intersect, making the distance between them zero.