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Classical Mechanics : The Theoretical Minimum
'Beautifully clear explanations of famously "difficult" things ...It almost makes you think you could have been a Newton yourself' John Gribbin Here is the ultimate master class in modern physics.World-class physicist and father of string theory Leonard Susskind and citizen-scientist George Hrabovsky combine forces in a primer that teaches the skills you need to do physics yourself. Combining crystal-clear explanations of the laws of the universe with basic exercises (including essential equations and maths), the authors cover the minimum that readers should master.They introduce the key concepts of modern physics, from classical mechanics to general relativity to quantum theory, and provide a practical toolkit that you won't find in any other popular science book. 'A good and noble book' Sunday Times 'A wonderful and unique resource.For anyone who is determined to learn physics for real, looking beyond conventional popularizations, this is the ideal place to start' Sean Carroll, physicist and author of The Particle at the End of the Universe'Very readable ... provides a clear description of advanced classical physics concepts, and gives readers who want a challenge the opportunity to exercise their brain' Physics World
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Quantum Mechanics: The Theoretical Minimum
'Quantum mechanics for real. This is the good stuff, the most mysterious aspects of how reality works, set out with crystalline clarity.The place to start' Sean Carroll, physicist, California Institute of Technology, author of The Particle at the End of the UniverseThis is the ultimate practical introduction to quantum mechanics.World-renowned physicist Leonard Susskind and data engineer Art Friedman give you the basic skills you need to tackle this famously difficult topic yourself. They provide clear, lively explanations of basic concepts, introduce the key fields of quantum mechanics and include step-by-step exercises.Making a complex subject 'as simple as possible, but no simpler', this is a practical toolkit for amateur scientists that you won't find anywhere else.
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General Relativity : The Theoretical Minimum
The latest volume in The New York Times bestselling physics series explains Einstein's masterpiece: the general theory of relativityHe taught us classical mechanics, quantum mechanics and special relativity.Now, physicist Leonard Susskind, assisted by a new collaborator, André Cabannes, returns to tackle Einstein's general theory of relativity.Starting from the equivalence principle and covering the necessary mathematics of Riemannian spaces and tensor calculus, Susskind and Cabannes explain the link between gravity and geometry.They delve into black holes, establish Einstein field equations and solve them to describe gravity waves.The authors provide vivid explanations that, to borrow a phrase from Einstein himself, are as simple as possible (but no simpler). An approachable yet rigorous introduction to one of the most important topics in physics, General Relativity is a must-read for anyone who wants a deeper knowledge of the universe's real structure.
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What is the minimum point?
The minimum point of a function is the lowest value that the function reaches. It is the point on the graph where the function has the smallest output. In terms of calculus, the minimum point occurs where the derivative of the function is zero and changes from negative to positive, indicating that the function is decreasing and then increasing. This point is also known as the local minimum, as it is the lowest point in a small neighborhood around it.
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What is the minimum minimum minimum task?
The minimum minimum minimum task is the absolute smallest, simplest, and most basic task that can be performed. It is the fundamental building block of any larger task or project. Identifying the minimum minimum minimum task is important for breaking down complex tasks into manageable steps and ensuring that progress can be made incrementally. This approach can help to reduce overwhelm and increase productivity.
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How do you calculate the zero point and the minimum point?
To calculate the zero point of a function, you set the function equal to zero and solve for the variable. This gives you the value(s) of the variable where the function intersects the x-axis. To find the minimum point of a function, you typically take the derivative of the function, set it equal to zero to find critical points, and then use the second derivative test or evaluate the function at these critical points to determine the minimum value.
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What is the sign change criterion for a minimum point, maximum point, or saddle point?
The sign change criterion for a minimum point is that the second derivative is positive, indicating that the function is concave up at that point. For a maximum point, the sign change criterion is that the second derivative is negative, indicating that the function is concave down at that point. A saddle point occurs when the second derivative changes sign, meaning the function is concave up in one direction and concave down in another.
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What is the difference between a maximum point, a minimum point, and a saddle point in mathematics?
In mathematics, a maximum point is a point on a graph where the function reaches its highest value, while a minimum point is a point where the function reaches its lowest value. A saddle point, on the other hand, is a point where the function is neither a maximum nor a minimum, but rather a point of inflection where the function changes concavity. In essence, a maximum and minimum point represent the peaks and valleys of a function, while a saddle point represents a point of change in direction.
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Is the minimum point of the marginal cost the inflection point of the cost function?
No, the minimum point of the marginal cost is not necessarily the inflection point of the cost function. The inflection point of the cost function is where the rate of change of the cost function changes from increasing to decreasing, or vice versa. On the other hand, the minimum point of the marginal cost is where the rate of change of the marginal cost is zero. These two points may coincide in some cases, but it is not a general rule that the minimum point of the marginal cost is always the inflection point of the cost function.
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"Is 0 a minimum?"
No, 0 is not a minimum. In mathematical terms, a minimum refers to the lowest value in a set of numbers or the lowest point on a curve. Since 0 is not a value in a set and does not represent the lowest point on a curve, it cannot be considered a minimum. Instead, 0 is often considered the starting point or baseline for many mathematical concepts.
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How do you calculate derivatives and find the minimum point in mathematics?
To calculate derivatives, you use the rules of differentiation to find the rate of change of a function at a specific point. This involves finding the slope of the tangent line to the function at that point. To find the minimum point of a function, you set the derivative equal to zero and solve for the critical points. Then, you use the second derivative test or the first derivative test to determine if the critical point is a minimum. If the second derivative is positive at the critical point, then it is a minimum.
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