Khan Academy. The Calculus Lifesaver: All the Tools You Need to Excel at Calcu. Dismantling the calculus pyramid. A Calculus Analogy: Integrals as Multiplication. Integrals are often described as finding the “area under the curve”. This description is misleading, like saying multiplication is for finding “the area of a rectangle”. Finding area is a useful application, but not the purpose. Integrals help us combine numbers when multiplication can’t. I wish I had a minute with myself in high school calculus: “Psst! You’ll hear a lot of talk about area — area is just one way to visualize multiplication.
When we want to use regular multiplication, but can’t, we bring out the big guns and integrate. That’s my aha moment: integration is a “better multiplication” that works on things that change. Understanding Multiplication Our understanding of multiplication changed over time: With integers (3 × 4), multiplication is repeated additionWith real numbers (3.12 x sqrt(2)), multiplication is scalingWith negative numbers (-2.3 * 4.3), multiplication is flipping and scalingWith complex numbers (3 * 3i), multiplication is rotating and scaling Understanding Area. Calculus Video Lectures + Bonus Basic Math. Hi all. This month I bring to you a bunch of calculus math video courses. As a bonus I have included some on fuzzy logic and really basic math such as trigonometry, algebra and geometry.
Calculus at San Francisco State University (SFSU, professor Dr. Goetz) Course description:The central object of the study in calculus is the concept of a function. Functions are used to describe the real world around us. Course topics:Introduction to limits. The Calculus Lifesaver: All the Tools You Need to Excel at Calculus These are Princeton introductory calculus courses MAT103 and MAT104 by Adrian Banner. Princeton Calculus Video LecturesCourse topics:Functions. MIT's Single Variable Calculus (18.01, professor David Jerison) Course description:The basic objective of Calculus is to relate small-scale (differential) quantities to large-scale (integrated) quantities. Course topics:Derivatives, slope, velocity, rate of change.
MIT's Multivariable Calculus (18.02, professor Denis Auroux) Fuzzy Logic. Calculus in 20 Minutes Part 1. The most enlightening Calculus books. Posted by Antonio Cangiano in Math Education, Suggested Reading on May 13th, 2007 | 60 responses In Walter Rudin’s autobiography The Way I Remember It , he comments on a calculus book defining it as “too good to be widely used” and further states that: Widely used calculus books must be mediocre. — W.
Rudin The temptation to discard that statement as elitist may be strong, but it is worth noticing how there is so much truth to it. Dumbing down mathematics is a dangerous trend which affects students at all levels, from primary school where children are no longer taught how to perform division by following the standard algorithm to a complete emphasis on anti-racist mathematics and calculus courses where delta and epsilon are not mentioned while teaching limits, because they are considered to be “too complicated” or “too confusing” for most students. May be more accurate that we like to think). Calculus by Michael Spivak (Updated in July 2008!)