This book develops elementary classical mechanics in a setting that is appropriate for beginning university mathematics students without requiring a background in physics. It is an ideal first look at the subject for those who will go on to study more advanced aspects of the subject, such as Lagrangian, Hamiltonian, and quantum mechanics. These more advanced developments of mechanics are at the forefront of research in modern mathematics. Certainly, topics such as symplectic geometry, Lagrangian intersection theory, spectral theory, pseudodifferential operators, etc. do not require a background in classical mechanics, but studies in these areas are greatly enriched by a knowledge of their roots and how some of their motivational issues arose.
Contents:
- Preface
- List of Figures
- List of Tables
- Prelude: What is Mechanics and What Framework Will We Use to Understand it?
- Kinematics — Scalars, Vectors, and Vector Algebra
- Kinematics — Vectors and Coordinates
- Kinematics — Space Curves, their Description and Derivatives, Circular Motion, and Line Integrals
- Examples of the Computation of Line Integrals and Newton's Axioms
- Dynamics — Motion of a Particle in One Dimension
- Dynamics — Projectiles, Constrained Motion, Friction
- Dynamics — Work and Power
- Dynamics — Conservation of Energy and Momentum
- Dynamics — The Phase Plane for One-Dimensional Motion
- Dynamics — The Simple Pendulum. Torque and Angular Momentum
- Motion in a Central Force Field
- Bibliography
- Index
Readership: Undergraduate students in physics, mathematics and engineering.
Key Features:
- Comprises material for a one term course in classical mechanics for first-year undergraduates
- Provides students exposure to classical mechanics before more advanced courses in classical, quantum and statistical mechanics in their later undergraduate years
- An extensive set of problems with a solutions manual giving complete solutions to each problem
