In this elementary calculus tutorial we study a number of topics in preparation for studying calculus. These include geometric thinking exercises, calculating distance between two points, calculating the slope of a line, sketching curves, and calculating the average slope.
In this elementary calculus tutorial we start with elementary algebraic simplification, factorization of polynomials, discuss continuity, limits, use the limit definition of the derivative, learn how to calculate very simple derivatives, sketch curves, find the slope of a tangent line, and take the second derivative.
In this elementary calculus tutorial we work through several examples of differentiation. We begin with polynomial long division, then do examples on differentiating using the product rule, quotient rule, and chain rule.
In this elementary calculus tutorial we review simple trigonometry concepts, learn to differentiate trigonometric functions, and use the product rule, the quotient rule and the chain rule together with sin and cos functions.
Understand sin(x) and cos(x) by associating triangles, circles, and sin and cos waves. In this video you will learn the relationship between these, learn to plot them by hand, and we will use Mathematica to animate sin and cos together with the unit circle.
In this elementary calculus tutorial we will learn to differentiate functions involving logarithms or exponential functions. We will use the chain rule, the product rule, and the quotient rule to differentiate these functions. We will rely on a list of 20 rule you must know to succeed in calculus. Many of these 20 rules are log rules and exponent rules.
In this elementary calculus tutorial, we learn how to sketch functions using differentiation and then we find the maxima and minima of functions with some applications. Some Mathematica code is used to display graphics.
In this elementary calculus tutorial, we will learn the basics of calculating an integral, also called an anti-derivative. We will then estimate some definite integrals using the trapezoidal rule and Simpson's rule.
In this elementary calculus tutorial we learn how to integrate by substitution and do integration by parts.
In this elementary calculus tutorial we show how to calculate the mean value of a function in an interval, calculate the area between two curves, and calculate volume of revolution of a function rotated about the x axis. The problem set was created by Dr. Aaron Wiegand of the University of the Sunshine Coast, Australia.
In this elementary calculus tutorial we will learn how to solve simple differential equations and initial value problems. All of the equations in this problem set will be separable first order differential equations. We will also show you how to use Mathematica to solve a differential equation.
In this elementary calculus tutorial we work though several problems on first order linear differential equations, we then solve some second order homogeneous linear equations and finally we solve a first order initial value problem using Euler's method and we compare the solution with the analytic solution by plotting points with Mathematica.
In this elementary calculus tutorial we work through several problems on complex numbers. These include simplifying complex numbers in various forms, converting between the polar form, the exponential form, and the rectangular for of a complex number. This allows us to be able to solve a second order homogeneous differential equation when the roots of the characteristic equation are not real numbers.
If it's your first time learning about complex numbers, and you are wondering whether there is any tangible application, the this video is for you. We illustrate how complex numbers are used to solve a second order differential equation.
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