Engineering Calculus Made Simple (Derivatives)

Name: Engineering Calculus Made Simple (Derivatives)
Rating: 5.0 (2 reviews)

A look at derivatives...the short version

Created byGraham Van Brunt P. Eng., B.Sc.

Last updated 5/2019

English

English [Auto],

What you'll learn

Students will learn mathematical derivatives as they apply to electrical functions
Students will learn about limits.
Students will learn useful Trig Identities.
Students will learn the Squeeze Theorem.

Course content

1 section • 9 lectures • 3h 35m total length

Introduction8:20
Explore the essentials of derivatives through a condensed differential calculus overview, covering instantaneous rates of change, limits, and common derivatives for quadratic, trig, exponential, and logarithmic functions.
Functions24:02
Explore how functions map inputs to outputs using Ohm's law and simple formulas, and plot them on Cartesian coordinates to visualize f(x) and g(x) relationships.
Limits42:16
Explore the concept of limits, continuity, and limit properties with clear graphical and algebraic examples, including left/right limits, removable discontinuities, and limits of composite functions.
The Derivative40:03
Learn how the derivative captures the instantaneous rate of change as the slope of the tangent line, using secant lines and limits, and verify with f(x)=x^2 where f'(x)=2x.
Trig Identities21:58
Examine trig identities from the Pythagorean theorem, proving sine squared theta plus cosine squared theta equals one and deriving sine of x+y and cosine of x+y.
The Squeeze Theorem31:13
Understand the squeeze theorem and its use in derivative proofs, illustrated with three functions and limit arguments, including sin theta over theta and (1 - cos x)/x limits.
The Derivative of Sin(x)8:25
Learn how to derive the derivative of sine using the limit definition and the sine addition identity, yielding d/dx sin x = cos x.
The Derivative of Cos(x)10:10
Explore the derivative of cos x by applying the cosine addition identity and limit definitions, showing d/dx cos x = - sin x.
Other Derivatives28:58
Study common derivatives across polynomials, trig, and exponential functions, applying the power and constant multiple rules, and using sin, cos, e^x, and ln x derivatives.

Requirements

A basic knowledge of mathematics and trigonometry

Description

In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances.

The derivative of a function of a single variable at a chosen input value, when it exists, is the slope of the tangent line to the graph of the function at that point. The tangent line is the best linear approximation of the function near that input value. For this reason, the derivative is often described as the "instantaneous rate of change", the ratio of the instantaneous change in the dependent variable to that of the independent variable.

This course is designed as the basics review of derivatives as they apply to electrical functions. It is designed for the student of electrical engineering who comes across theoretical formulas that reference derivatives. A detailed understanding of derivatives is not required in order to continue the electrical topic and this course will provide the basic amount required. During this course, the student will learn useful trig identities and approach derivatives with the help of limits and theorems such as the squeeze theorem.

Who this course is for:

Electrical Engineers, Technologists, Technicians & Electrical Students