Author | Murray, Francis J. author |
---|---|
Title | Applied Mathematics [electronic resource] : An Intellectual Orientation / by Francis J. Murray |
Imprint | Boston, MA : Springer US : Imprint: Springer, 1978 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-3312-8 |
Descript | XIV, 225 p. online resource |
1. Introduction -- 1.1. Vocational Aspects -- 1.2. Intellectual Attitudes -- 1.3. Opportunities in Applied Mathematics -- 1.4. Course Objectives -- Exercises -- 2. Simulations -- 2.1. Organized Efforts -- 2.2. Staging -- 2.3. Simulations -- 2.4. Influence Block Diagram and Math Model -- 2.5. Temporal Patterns -- 2.6. Operational Flight Trainer -- 2.7. Block Diagrams -- 2.8. Equipment -- 2.9. The Time Pattern of the Simulation -- 2.10. Programming -- 2.11. Management Considerations -- 2.12. Validity -- Exercises -- References -- 3. Understanding and Mathematics -- 3.1. Experience and Understanding -- 3.2. Unit Experience -- 3.3. The Exact Sciences -- 3.4. Scientific Understanding -- 3.5. Logic and Arithmetic -- 3.6. Algebra -- 3.7. Axiomatic Developments -- 3.8. Analysis -- 3.9. Modern Formal Logic -- 3.10. Pure and Applied Mathematics -- 3.11. Vocational Aspects -- Exercises -- References -- 4. Ancient Mathematics -- 4.1. Ancient Arithmetic -- 4.2. Egyptian Mathematics -- 4.3. Babylonian Mathematics -- 4.4. Greece -- 4.5. Euclidโs Elements -- 4.6. Magnitudes -- 4.7. Geometry and Philosophy -- 4.8. The Conic Sections -- 4.9. Parabolic Areas -- Exercises -- References -- 5. Transition and Developments -- 5.1. Algebra -- 5.2. Non-Euclidean Geometry -- 5.3. Geometric Developments -- 5.4. Geometry and Group Theory -- 5.5. Arithmetic -- 5.6. The Celestial Sphere -- 5.7. The Motion of the Sun -- 5.8. Synodic Periods -- 5.9. Babylonian Tables -- 5.10. Geometric Formulations -- 5.11. Astronomical Experience in Terms of Accuracy -- 5.12. Optical Instruments and Developments -- Exercises -- References -- 6. Natural Philosophy -- 6.1. Analysis -- 6.2. The Calculus -- 6.3. The Transformation of Mathematics -- 6.4. The Method of Fluxions -- 6.5. The Behavior of Substance in the Eulerian Formulation -- 6.6. The Generalized Stokesโ Theorem -- 6.7. The Calculus of Variations -- 6.8. Dynamics -- 6.9. Manifolds -- 6.10. The Weyl Connection -- 6.11. The Riemannian Metric -- Exercises -- References -- 7. Energy -- 7.1. The Motion of Bodies -- 7.2. The Stress Tensor -- 7.3. Deformation and Stress -- 7.4. An Elastic Collision -- 7.5. Thermodynamic States and Reversibility -- 7.6. Thermodynamic Functions -- 7.7. The Carnot Cycle and Entropy -- 7.8. The Relation with Applied Mathematics -- Exercises -- References -- 8. Probability -- 8.1. The Development of Probability -- 8.2. Applications -- 8.3. Probability and Mechanics -- 8.4. Relation to Thermodynamics -- 8.5. The Fine Structure of Matter -- 8.6. Analysis -- Exercises -- References -- 9. The Parado -- 9.1. Intellectual Ramifications -- 9.2. The Paradox -- 9.3. Final Comment -- Exercises -- References