I love calculus, it's such an amazing collection of fascinating, elegant (and useful!) concepts that give you a transformative insight on mathematics in general. A great teacher will make this work and a lower skilled teacher can absolutely kill almost all learning. The number one problem is calculus is 100% dependent on the teacher. People actually think calculus is a hyper abstract algebra when in fact it is putting math into real world solutions. Make math into something where people can truly understand abstract and concrete. Pre-Calculus (needs to be repackaged with the idea of the one consistent in our world is change) should be taught before Algebra and Geometry. a train leaves Chicago at 25 MPH and another train leaves Flint, MI at 35 MPH when will the trains meet? That answer is an estimation of an unattainable constancy but people believe it is logical conclusion. We also teach movement and change as a word problem i.e. 1/3 of a pizza is real and 0.333333 is a fake number. We have a population that can barely do 4th grade arithmetic and it is socially okay.Ĭhildren and people believe that decimal points are accurate and that fractions are abstract when the exact opposite is true. I would have never been able to vocalize what he said in the short half page of text. The prologue is 100% dead on and what I have always thought in terms of the easy part of calculus needs to be taught early. Time spent learning Calculus is worthwhile and if nothing else, understand the fundamental theorem. Finally, if you want a whirlwind tour, Calculus for Dummies by Mark Ryan is great. Work through the problems as they do in the book, you will come away w/ what you need. Otherwise, I think it's hard to go wrong w/ the Stewart books. The Kline book is a MUCH larger read, but is what I would recommend if you want a reasonably priced Calculus book that's easy to grok. The updated version with Martin Gardner does have blurbs where necessary to point it out. Some of the lexicon has changed and there are topics covered in a modern Calculus textbook that aren't covered in the original book (that I personally think are worthwhile spending time on). "Calculus Made Easy" is a good book though I do think there are better ones these days. My dad taught the subject in a high school and community college I suppose I have a soft spot for it. I have an embarrassing amount of Calculus books. These functions and their properties are the sole subject matter of this chapter." What matters most in the subject is not making computations about triangles, but grasping the trigonometric functions as indispensable tools in science, engineering and higher mathematics. ![]() The truth is that the primary importance of trigonometry lies in a completely different direction - in the mathematical description of vibrations, rotations, and periodic phenomena of all kinds, including light, sound, alternating currents and the orbits of the planets around the sun. ![]() Even though very few people become surveyors or navigators, the students who study these books are expected to undertake many lengthy calculations about the heights of flagpoles, the widths of rivers and the positions of ships at sea. "Most trigonometry textbooks have been written by people who appear to believe that the importance of the subject lies in its applications to surveying and navigation. For example here's how he opens his chapter on Trig: ![]() He really boils it down to the essentials. I did the same in my mid-40's.Ī great book for brushing up/re-learning pre-calc is "Precalculus Mathematics in a Nutshell" by George F. Ĭalculus Revisited: Multivariable Calculus | MIT OpenCourseWare. Ĭomplex Variables, Differential Equations, and Linear Algebra. Deriving almost all the basic calculus results that were drilled into me from the basic concept of a limit, deltas and epsilons was really refreshing.Ĭompared to more recent OCW calculus videos, I found this to be better in terms of respecting the learner's intellect, presenting the whole proof rigorously and teaching the student to think a certain way.Ĭalculus Revisited: Single Variable Calculus | MIT OpenCourseWare. It also taught me that math is about reasoning logically and rigorously and we shouldn't always rely on intuition (at least while doing math). There is an unusual mix of rigor and focus on building understanding - where everything comes from. His style of lecturing is clear, he states why things are defined the way they are and derives everything from first principles. It is taught by a lecturer named Herbert Gross. So we write, as the equation of the curve drawn in Fig.MIT recorded a set of Calculus video courses back in 1970s that they have since made publicly available. The great secret has already been revealed that this mysterious symbol ∫.
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