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38480 results in Cambridge Textbooks

Page 105 of 1924

Fluid Mechanics
  • Lectures on Theoretical Physics
  • Volume 4
  • David Tong
  • Published online:
    26 June 2025
    Print publication:
    19 June 2025
  • Take anything in the universe, put it in a box, and heat it up. Regardless of what you start with, the motion of the substance will be described by the equations of fluid mechanics. This remarkable universality is the reason why fluid mechanics is important. The key equation of fluid mechanics is the Navier-Stokes equation. This textbook starts with the basics of fluid flows, building to the Navier-Stokes equation while explaining the physics behind the various terms and exploring the astonishingly rich landscape of solutions. The book then progresses to more advanced topics, including waves, fluid instabilities, and turbulence, before concluding by turning inwards and describing the atomic constituents of fluids. It introduces ideas of kinetic theory, including the Boltzmann equation, to explain why the collective motion of 1023 atoms is, under the right circumstances, always governed by the laws of fluid mechanics.

  • 19 - Optimality Conditions in Convex Programming

  • from Part IV - Convex Programming, Lagrange Duality, Saddle Points
  • Fatma Kılınç-Karzan, Carnegie Mellon University, Pennsylvania, Arkadi Nemirovski, Georgia Institute of Technology
  • Book:
    Essential Mathematics for Convex Optimization
    Published online:
    22 October 2025
    Print publication:
    26 June 2025, pp 264-276

  • Summary

    In this chapter we present convex programming optimality conditions in both sadde point form and Karush--Kuhn--Tucker form for mathematical programming, and also optimality conditions for cone-constrained convex programs and for conic problems. We conclude the chapter by revisiting linear programming duality as a special case of conic duality and reproducing the classical results on the dual of a linearly constrained convex quadratic minimization problem.

  • 2 - Quantum Mechanics for Quantum Computers

  • Asma Al-Qasimi, University of Rochester, New York, Daniel F. V. James, University of Toronto
  • Book:
    Quantum Information
    Published online:
    17 October 2025
    Print publication:
    26 June 2025, pp 18-50

  • Summary

    Using linear algebra, the mathematical techniques needed for describing and manipulating qubits are laid out in detail, including quantum circuits. Moreover, the chapter also explains the state evolution of an isolated quantum system, as is predicted by the Schrödinger equation, as well as non-unitary irreversible operations such as measurement. More details of classical and quantum randomness and their mathematical representation is discussed, leading to the density matrix. representation of a quantum state.

  • 4 - Quantum Algorithms

  • Asma Al-Qasimi, University of Rochester, New York, Daniel F. V. James, University of Toronto
  • Book:
    Quantum Information
    Published online:
    17 October 2025
    Print publication:
    26 June 2025, pp 78-100

  • Summary

    This is the chapter that gets down to applying concepts from the previous chapters about qubits to construct a quantum computer. It teaches how numbers can be stored in quantum computers and how their functions can be evaluated. It also demonstrates the computational speed-up that quantum computers offer over their classical counterparts through the study of Deutsch, Deutsch-Jozsa, and Bernstein-Vazirani algorithms. Finally, it gives a practical demonstration of speed-up in search algorithms provided by Grover’s search algorithm.

Page 105 of 1924