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Recommendations for Introductions to Calculus

On this page you can find some great (and mostly free) resources that introduce you to calculus. My site is in general focussed on the needs of those want to learn about analog electronics. But the resources on this page (with the exception of Kuphaldts work) should be equally useful for everybody who wants an intuitive introduction to calculus because he needs it as a tool. However, if you are looking for rigorous mathematical treatments and proofs (e.g. because you want to study mathematics) you will find them much less useful.

The focus is on introductory calculus, but some of the resources additionally contain material from Calculus II or Calculus III - if I have found a resource that provides a good and intuitive introduction to the foundations of calculus, I have seen no reason to exclude it from this page just because it also covers more advanced topics.

As a prerequisite, knowledge of precalculus would be useful. The basic concepts of calculus (differentiation is determining the slope of a function, and integration is summing something up) are not too hard to understand (if explained carefully). But if you actually want to practice calculus and manipulate equations, you have to know algebra. And it is easy to see graphically how sine and cosine curves are related by differentiation and integration, but first you should fully understand what a sine curve is.

If you are eager to learn about caclulus, but you have the feeling that your knowledge of the necessary prerequisites is a bit rusty, the free course notes Calculus I by Paul Dawkins from Lamar University may be right for you. On the first 80 pages he reviews some typical precalculus topics like functions in general, trigonometric, exponential and logarithmic functions, and graphs. The notes contain very good and clear explanations and lots of examples. If you like Dawkins Calculus I, you may also want to take a look at his Calculus II and Calculus III notes and his Calculus Cheat Sheet.

A very good and easy introduction is the book Calculus by Gilbert Strang, MIT. Before you order the book you should download his free textbook which is very similiar to the book and see if you like it. You can also watch his Highlights of Calculus videos.

If you would like to watch a much longer series of calculus video lectures, take a look at the Single Variable Calculus Video Lectures by David Jerison, MIT (39 lectures, each about 45 minutes).

A very interesting introduction is Calculus by Ben Crowell, Fullerton College. Especially if you want to know the theroretical foundations of calculus. You might also be interested in Crowell's excellent introductions to physics, I put the links to them on the same page.

Advanced calculators will help you with Calculus. But you can also get help online and for free at Wolfram Alpha.

If you are interested in calculus because you need it for learning electronics, you can find some simple applications of caclulus in electronic circuits in Lessons In Electric Circuits (allaboutcircuits) by Tony Kuphaldt. The section Capacitors and Calculus explains how a voltage change across a capacitor will cause a current to flow ( a simple experiment that demonstrates this behavior is described in Rate-Of-Change Indicator ). The section Inductors and Calculus shows how a changing current can induce a voltage. Differentiator and Integrator Circuits discusses how differentiators and integrators can be built with op amps (also see the Integrator experiment, Kuphaldt intentionally uses an Op Amp with a high input bias current to demonstrate the effects that this has on the integrator). This topic is treated in much more detail in Computational Circuits, where Kuphaldt discusses the fundamentals of analog computers. This chapter is very good. Using the example of a car that is moving along the x-axis, Kuphaldt shows how you can use differentiators to determine velocity and acceleration when the postion of the car is known, or, the inverse process, integrate the acceleration to determine the position. Finally, you can test your knowledge in Calculus for Electric Circuits and, if you have questions, you can ask them in the General Electronics Chat of the associated forum.

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