New Tertiary Mathematics
Further Applied Mathematics
- 1st Edition - January 1, 1981
- Imprint: Pergamon
- Authors: C. Plumpton, P. S. W. Macliwaine
- Language: English
- Paperback ISBN:9 7 8 - 1 - 4 8 3 1 - 1 5 3 1 - 3
- eBook ISBN:9 7 8 - 1 - 4 8 3 1 - 4 7 7 3 - 4
New Tertiary Mathematics, Volume 2, Part 2: Further Applied Mathematics deals with various topics of theoretical mechanics and probability, from statics and the dynamics of a rigid… Read more
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Request a sales quoteNew Tertiary Mathematics, Volume 2, Part 2: Further Applied Mathematics deals with various topics of theoretical mechanics and probability, from statics and the dynamics of a rigid body to the dynamics of a particle with one and two degrees of freedom. Many examples of varying difficulty are worked in the text and exercises are added after each major topic is covered. This book is comprised of five chapters and opens with a discussion on statics, with particular reference to the analysis of systems of forces in three dimensions, along with virtual work, stability, and the catenary. Complicated equilibrium problems are considered. The reader is then introduced to the dynamics of a particle in one and two dimensions, as well as the implications of the Galilean transformation and the general theorems of motion for a system of particles. These theorems are applied to simple cases of the motion of a rigid body. The final chapter on probability examines normal and Poisson distributions, Markov chains, and miscellaneous problems. This monograph will be a useful resource for mathematical pupils and students engaged in private study.
Glossary of Symbols and Abbreviations
Chapter 7 Further Statics
7:1 Forces in Three Dimensions
Exercise 7.1
7:2 Conditions of Equilibrium for a Rigid Body Acted Upon by a System of Coplanar Forces
Exercise 7.2
7:3 Hinged Bodies—Equilibrium Problems Involving More than One Body
1. Smooth Hinges
2. Rough Hinges
3. The Action of One Part of a Body on Another
4. Problems of Equilibrium Involving More than One Body
5. The Equilibrium of the Hinge
Exercise 7.3
7:4 The Principle of Virtual Work
The Equilibrium of a Particle
Applications of the Principle of Virtual Work
Exercise 7.4
7:5 Determination of Equilibrium Positions
7:6 Types of Equilibrium—Stability
Exercise 7.6
7:7 A Uniform Flexible Inelastic String Hanging under Gravity
The Tightly Stretched Wire
Exercise 7.7
7:8 A Rope in Contact with a Rough Surface
Exercise 7.8
Miscellaneous Exercise 7
Chapter 8 Further Dynamics of a Particle with One Degree of Freedom
8:1 Damped Harmonic Oscillations
Forced Oscillations
Exercise
8:2 Motion in a Straight Line under Variable Forces
Exercise 8.2(a)
Miscellaneous Problems
Motion under Gravity in a Resisting Medium
Exercise 8.2(b)
8:3 The Rectilinear Motion of Bodies with Variable Mass
Exercise 8.3
Miscellaneous Exercise 8
Chapter 9 Dynamics of a Particle with Two Degrees of Freedom
9:1 Further Differentiation of Vectors—Applications to Kinematics
1. Polar Coordinates
2. Intrinsic Coordinates
Exercise 9.1
9:2 Motion Referred to Cartesian Axes
Exercise 9.2
9:3 Motion of a Particle on a Smooth Curve
Exercise 9.3
9:4 Motion under a Central Force—Polar Coordinates
1. A Central Orbit is a Plane Curve
2. The Angular Momentum Integral
3. The Theorem of Areas
Exercise 9.4
9:5 The Motion of Projectiles
1. The Range on an Inclined Plane
Exercise 9.5(a)
2. The Bounding Parabola
Exercise 9.5(b)
9:6 Oblique Impact of Elastic Bodies
Exercise 9.6
9:7 The Galilean Transformation
1. Frames with Uniform Relative Velocity
2. Frames with Uniform Relative Acceleration
9:8 The Motion of a System of Particles—General Theorems
1. Notation
2. Linear Momentum
3. Kinetic Energy
4. Moment of Momentum
5. The Motion of the Center of Mass
6. Motion About the Center of Mass
7. Motions Generated By Simultaneously Applied Impulses
9:9 The Motion of Connected Particles
Exercise 9.9
9:10 The Two-Dimensional Motion of a Projectile in a Resisting Medium
Exercise 9.10
Miscellaneous Exercise 9
Chapter 10 An Introduction to the Dynamics of a Rigid Body
10:1 Rotation of a Lamina about a Fixed Axis
10:2 Momentum and Energy Equations for Angular Motion of a Lamina
Exercise 10.2
10:3 The Compound Pendulum
Exercise 10.3
10:4 The Force Exerted on the Axis of Rotation
Exercise 10.4
10:5 Impulse and Angular Momentum
Exercise 10.5
10:6 Note on the Relationship Between the Equations of Angular Motion of a Rigid Body and the Equations of Motion of a Particle Moving in a Straight Line
10:7 The Motion of a Lamina in Its Own Plane—Instantaneous Center of Rotation
Exercise 10.7
10:8 The General Motion of a Rigid Lamina in Its Own Plane
10:9 Application to Miscellaneous Problems
Exercise 10.9
Miscellaneous Exercise 10
Chapter 11 Further Probability
11:1 The Binomial and Geometric Probability Distributions
Exercise 11.1
11:2 Continuous Probability Distributions
Exercise 11.2
11:3 The Poisson Distribution
Exercise 11.3
11:4 The Normal Distribution
Exercise 11.4
11:5 Transition Matrices for Markov Chains
11:6 Steady-State Vector and Matrix
11:7 An Equivalence Relation on Transition States
Exercise 11.7
11:8 Further Probability Problems
Exercise 11.8
Miscellaneous Exercise 11
Answers to the Exercises
Index
- Edition: 1
- Published: January 1, 1981
- No. of pages (eBook): 233
- Imprint: Pergamon
- Language: English
- Paperback ISBN: 9781483115313
- eBook ISBN: 9781483147734
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