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Calculus

By David A. Smith

Calculus presents limits, derivatives, and integrals for various types of functions including the common algebraic and transcendental functions. Calculus also involves computing derivatives and differentials of various functions without the aid of a calculator and interpreting certain limits as derivatives. Additionally, computing derivatives by using the definition of the derivative, power rule, product rule, quotient rule, chain rule, implicit differentiation, and logarithmic differentiation would be presented. Solving word problems will be emphasized in calculus by involving the rate of change of a quantity or of related quantities and by solving optimization problems using differentiation and integration in the context of real-life situations including population dynamics, finance, physics, biology, chemistry and sociology. Infinite sequences and series are also covered in detail in calculus including power series and Taylor's formula. In calculus students also learn how to perform calculus in polar coordinates and with vector functions.  

Here is a complete table of contents for the calculus.

After multivariable calculus you will be able to demonstrate techniques of multiple integration and be able to compute iterated integrals over rectangular regions, non-rectangular regions, and in other coordinate systems. You will also be able to apply multiple integrals in problem situations involving area, volume, surface area, center of mass, moments of inertia. Calculus also involves computing line integrals and surface integrals by applying The Fundamental Theorem for line integrals, Green’s theorem, Stoke’s Theorem and the Divergence Theorem.  

Calculus Books