Research Catalog

Title

Applications of undergraduate mathematics in engineering, written and edited by Ben Noble.

Author

Noble, Ben

Publication

• [Buffalo?] Mathematical Association of America [1967]
• ©1967

Items in the Library & Off-site

Details

Description

xvii, 364 pages illustrations; 24 cm

Series Statement

Textbooks in applied mathematics

Subject

• Engineering mathematics
• Mathématiques de l'ingénieur
• engineering
• wiskunde
• mathematics
• technologie
• technology
• Applied Mathematics
• Toegepaste wiskunde

Bibliography (note)

• Bibliographical footnotes.

Contents

• 1. Introduction -- 1.1. The purpose of this book -- 1.2. Mathematicians and engineers -- 1.3. Some comments on mathematics in engineering -- 1.4. The method of exposition -- pt. I. Illustrative applications of elementary mathematics -- 2. Optimum-location problems -- 2.1. Optimum location of a power plant -- 2.2. A machine-location problem -- 2.3. Special cases of the straight-movement model -- 2.4. The rectangular-movement case -- 2.5. Level curves -- 2.6. Summary and concluding remarks -- 3. The exploration of functional relationships -- an aspect of optimization -- 3.1. Introduction : an underground-exploration problem -- 3.2. An optimization problem in chemical engineering -- 3.3. Design of optical lenses -- 3.4. Analysis of the general second-degree surface -- 3.5. A straightforward numerical example -- 3.6. A stationary plane ridge in three variables -- 3.7. Some general comments and advice -- 4. Miscellaneous applications of elementary mathematics -- 4.1. Summary -- 4.2. A problem arising in yarn spinning -- 4.3. A yo-yo for de-spinning a satellite -- 4.4. A minimization problem in seismic prospecting -- 4.5. Maximum yield in an ammonia reactor -- 4.6. Masks to pack circles densely -- 4.7. Recovery of a band-limited signal
• Pt. II. Applications of ordinary differential equations -- 5. Differential equations and electrical circuits -- 5.1. The ignition system of an internal-combustion engine -- 5.2. Deductions from the analysis in section 5.1 -- 5.3. A difference-equation example -- 5.4. A linear-algebra treatment of transients in an electrical circuit -- 5.5. A linear-algebra treatment of transients (continued) -- 6. Examples involving nonlinear differential equations -- 6.1. Introduction -- 6.2. Surge tanks in a hydroelectric system -- 6.3. Approximate solution of the equations for the differential surge tank -- 6.4. The stability of a surge tank to small disturbances -- 6.5. Chemical-tank-reactor stability -- 6.6. Chemical-tank-reactor stability (continued) -- 6.7. A nonlinear electrical circuit -- 6.8. Concluding remarks on nonlinear differential equations
• Pt. III. Applications to field problems -- 7. The approximate formulation and solution of field problems -- 7.1. Introduction -- 7.2. The permeation of water vapor through cable sheaths -- 7.3. The flow of fluids in porous media -- 7.4. Closure of a cavity in a salt dome -- 7.5. The cigarette problem -- 8. The mechanism of overthrust faulting in geology -- 8.1. Normal, reverse, and overthrust faults -- 8.2. Mohr's stress circle, with applications -- 8.3. The mechanical paradox of large overthrusts -- 8.4. The beer-can experiment -- 8.5. The effect of internal pressure on fluid-filled porous rocks -- 8.6. Summary and concluding remarks -- 9. Some approximations in heat transfer -- 9.1. Heat conduction -- 9.2. Ingot solidification -- 9.3. Thermal explosions and self-ignition -- 9.4. A class of boundary-layer heat-transfer problems -- 9.5. Film condensation and film boiling -- 9.6. Natural convection, film melting, and comparison with experiment -- 9.7. Concluding remarks
• Pt. IV. Applications of linear algebra -- 10. Some Applications of matrix algebra -- 10.1. Summary -- 10.2. Plane pin-jointed frameworks -- 10.3. The application of automatic computers to framework calculation -- 10.4. Kron's fundamental formula for the mesh analysis of an electrical network -- 10.5. The concavity of resistance functions -- 10.6. The determination of star positions from photographs -- 11. Some applications of linear dependence, elementary row operations, and rank -- 11.1. Mathematical prerequisites -- 11.2. Examples from dimensional analysis -- 11.3. An example from radiative heat transfer -- 11.4. Linear dependence and chemical reactions (stoichiometry) -- 11.5. The reduction of systems of differential equations to canonical form -- 11.6. Reduction of a nonlinear system of differential equations to canonical form -- 12. The structure and analysis of linear chemical reaction systems -- 12.1. The basic problem -- 12.2. Some properties of the matrix of rate constants -- 12.3. A geometrical interpretation for the case of three species -- 12.4. A numerical example (butene isomerization over pure alumina catalyst)
• Pt. V. Applications of probability theory -- 13. Miscellaneous applications of probability theory -- 13.1. Summary -- 13.2. The analysis of speech dynamics -- 13.3. The breakdown voltage of long transmission lines -- 13.4. Minimization of error in telegraphy -- 13.5. A simplified statistical model for missile launching -- 13.6. A problem of tape alignment -- 13.7. Survival of communication facilities during nuclear attack -- 13.8. The minimization of the cost of a digital device (the juke-box problem) -- 13.9. The Monte Carlo method -- 14. A probabilistic model of a conveyor system -- 14.1. An idealized model of a conveyor -- 14.2. The mathematical analysis of the model by probability considerations -- 14.3 An application to an example -- 14.4 The evaluation of competing proposals for improving performance -- 14.5. Evaluation of assumptions -- 14.6. Summary and concluding remarks -- 14.7. A postscript on the storage and retrieval of material -- 15. Waiting-line and traffic problems -- 15.1. Introduction -- 15.2. Completely random arrivals -- 15.3. A traffic problem : safe gaps at school crossings -- 15.4. A waiting-line problem in an aircraft factory -- 15.5. Formulas required for the factory problem -- 15.6. The factory problem (concluded) -- 15.7 Simulation of waiting-line problems by computer -- 16. Random plane networks and needle-shaped crystals -- 16.1. Random plane networks -- 16.2. Theoretical arguments concerning the critical value of E -- 16.3. An experimental determination of the critical value of E -- 16.4. Surface films of needle-shaped crystals -- 16.5. Cell nucleation -- 16.6. Johnson-Mehl nucleation -- Name index -- Subject index.

LCCN

66027577

OCLC

• ocm00568836
• 568836
• SCSB-236449

Owning Institutions

Princeton University Library