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Description
This book is issued from a 30 year experience on the presentation of variational methods to successive generations of students and researchers in Engineering. It gives a comprehensive, pedagogical and engineer-oriented presentation of the foundations of variational methods and of their use in numerical problems of Engineering. Particular applications to linear and nonlinear systems of equations, differential equations, optimization and control are...
Description
We commonly define the Pythagorean theorem using the formula a2 + b2 = c2. But Pythagoras himself would have been confused by that. Explore how this famous theorem can be explained using common geometric shapes (no fancy algebra required), and how it’s a critical foundation for the rest of geometry.
Author
Formats
Description
"What's new in this edition? We have added new content and also tried to make improvements to the existing material. There are five new historical sketches, on: The tangent function and how it made its way into trigonometry. Logarithms, both decimal and natural. Conic sections: ellipses, parabolas, and hyperbolas. Irrational numbers. The derivative. As always, each of these come with Questions and Projects that try to address both the mathematics...
Author
Pub. Date
2015.
Physical Desc
288 pages : illustrations ; 25 cm
Description
"In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen: we learn, for example, how the béchamel in a lasagna can be a lot like the number 5, and why making a good custard proves that math is easy but life is hard."--Publisher description.
Author
Formats
Description
Calculus Essentials For Dummies (9781119591207) was previously published as Calculus Essentials For Dummies (9780470618356). While this version features a new Dummies cover and design, the content is the same as the prior release and should not be considered a new or updated product. Many colleges and universities require students to take at least one math course, and Calculus I is often the chosen option. Calculus Essentials For Dummies provides...
Author
Formats
Description
"The fascinating world of graph theory goes back several centuries and revolves around the study of graphs - mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics - and some of its most famous problems. For example, what is the shortest route for a traveling salesman seeking to visit...
Author
Description
"Where does math come from? From a textbook? From rules? From deduction? From logic? Not really, Eugenia Cheng writes in Is Math Real?: it comes from curiosity, from instinctive human curiosity, "from people not being satisfied with answers and always wanting to understand more." And most importantly, she says, "it comes from questions": not from answering them, but from posing them. Nothing could seem more at odds from the way most of us were taught...
Pub. Date
c2008
Physical Desc
xx, 1034 p. : ill., music ; 27 cm.
Description
This is a one-of-a-kind reference for anyone with a serious interest in mathematics. Presents entries, written especially for this book by some of the world's leading mathematicians, that introduce basic mathematical tools and vocabulary; trace the development of modern mathematics; explain essential terms and concepts; examine core ideas in major areas of mathematics; describe the achievements of scores of famous mathematicians; explore the impact...
Author
Formats
Description
"Magical Mathematics reveals the secrets of amazing, fun-to-perform card tricks--and the profound mathematical ideas behind them--that will astound even the most accomplished magician. Persi Diaconis and Ron Graham provide easy, step-by-step instructions for each trick, explaining how to set up the effect and offering tips on what to say and do while performing it. Each card trick introduces a new mathematical idea, and varying the tricks in turn...
10) The Joy of 9
Pub. Date
2017.
Physical Desc
1 online resource (streaming video file) (32 minutes): digital, .flv file, sound
Description
Adding the digits of a multiple of 9 always gives a multiple of 9. For example: 9 x 4 = 36, and 3 + 6 = 9. Inmodular arithmetic, this property allows checking answers by "casting out nines." A related trick: mentally computing the day of the week for any date in history.
Pub. Date
2017.
Physical Desc
1 online resource (streaming video file) (31 minutes): digital, .flv file, sound
Description
Arguably the most important area of mathematics, algebra introduces the powerful idea of using an abstract variable to represent an unknown quantity. This lecture demonstrates algebra's golden rule: Do unto one side of an equation as you do unto the other.
Pub. Date
2017.
Physical Desc
1 online resource (streaming video file) (32 minutes): digital, .flv file, sound
Description
Algebra can be used to solve geometrical problems, such as finding where two lines cross. The technique is useful in real-life problems, for example, in choosing a telephone plan. Graphs help us better understand everything from lines to equations with negative or fractional exponents.
Pub. Date
2017.
Physical Desc
1 online resource (streaming video file) (31 minutes): digital, .flv file, sound
Description
Exploiting the idea of the derivative, we can approximate just about any function using simple polynomials. This lecture also shows why a formula sometimes known as "God's equation" (involvinge,i, p, 1, and 0) is true, and how to calculate square roots in your head.
Pub. Date
2017.
Physical Desc
1 online resource (streaming video file) (29 minutes): digital, .flv file, sound
Description
Combinatoricsis the study of counting questions such as: How many outfits are possible if you own 8 shirts, 5 pairs of pants, and 10 ties? A trickier question: How many ways are there to arrange 10 books on a shelf? Combinatorics can also be used to analyze numbering systems, such as ZIP Codes or license plates, as well as games of chance.
Pub. Date
2017.
Physical Desc
1 online resource (streaming video file) (33 minutes): digital, .flv file, sound
Description
Calculus is the mathematics of change, and answers questions such as: How fast is a function growing? This lecture introduces the concepts oflimitsandderivatives, which allow the slope of a curve to be measured at any point.
Pub. Date
2017.
Physical Desc
1 online resource (streaming video file) (31 minutes): digital, .flv file, sound
Description
TheFibonacci numbersfollow the simple pattern 1, 1, 2, 3, 5, 8, etc., in which each number is the sum of the two preceding numbers. Fibonacci numbers have many beautiful and unexpected properties, and show up in nature, art, and poetry.
Pub. Date
2017.
Physical Desc
1 online resource (streaming video file) (31 minutes): digital, .flv file, sound
Description
Geometry is based on a handful of definitions and axioms involving points, lines, and angles. These lead to important conclusions about the properties ofpolygons. This lecture uses geometric reasoning to derive the Pythagorean theorem and other interesting results.
Pub. Date
2017.
Physical Desc
1 online resource (streaming video file) (32 minutes): digital, .flv file, sound
Description
This lecture shows how to solvequadratic(second-degree) equations from the technique of completing the square and the quadratic formula. The quadratic formula reveals the connection between Fibonacci numbers and thegolden ratio.
Pub. Date
2017.
Physical Desc
1 online resource (streaming video file) (32 minutes): digital, .flv file, sound
Description
Starting with the analysis of the proposition 0.999999999 ... = 1, this lecture explores what it means to add up an infinite series of numbers. Some infinite series converge on a definite value, while others grow arbitrarily large.
Pub. Date
2017.
Physical Desc
1 online resource (streaming video file) (30 minutes): digital, .flv file, sound
Description
What is the meaning of infinity? Are some infinite sets "more" infinite than others? Could there possibly be an infinite number of levels of infinity? This lecture explores some of the strange ideas associated with mathematical infinity.
