Calculus C Are Largely Defined By Derivatives Of Vector...

The major topics explored in Calculus C are largely defined by derivatives of vector-valued and parametrically defined functions, integration by partial fractions, improper integrals, series convergence (Taylor and Maclaurin), L’Hopitals Rule, and numerous applications. All of the following topics require a solid foundation in not only Calculus A but also Calculus B. Vector-valued functions include mathematical functions of one or more variables whose range is defined as a set of both multidimensional vectors and infinite dimensional vectors. Much of this was expanded on by Newton and Descartes during the Enlightenment in Europe. Newton largely defined calculus in his book Principia Mathematica whereas Descartes was the founder of analytic†¦show more content†¦The derivative of a three-dimensional vector function can be differentiated by using standard differentiating rules, taught in a standard Calculus A course, as it breaks up the components in the Cartesian coordinate system. Integration by partial fractions, or in other words commonly known as the partial derivative of a vector function, is defined with a commonly used variable a, with respect to the frequently used scalar variable q. A sub I is the scalar component of a in the direction of e sub i. Sometimes, it is also called the direction cosine of a and e sub i, but it is also frequently known in most math classes as the dot product. The vectors e1,e2,e3 form what is known as an orthonormal basis that is commonly fixed in the reference frame in which the derivative of the partial is being taken. This was also further expanded on by Newton in the 17th century in his famous book Principia Mathematica and he often used the notation from Gottfried Leibniz, another 17th century mathematician. Defined by Isaac Newton and Descartes, in calculus C, another frequently taught topic is what is known as an improper integral. It is defined as the limit of a definite integral as an endpoint of the interval or intervals of integration approach either a specified definite real number or infinity or even in some cases negative infinity. In other cases both endpoints approach limits. Such an integral is often written symbolically just like a standard definite integral,