- Артикул:00-01113225
- Автор: Pease E.M.J., Wadsworth G.P.
- Обложка: Твердая обложка
- Издательство: International Textbook Company (все книги издательства)
- Город: Scranton, Pennsylvania
- Страниц: 493
- Год: 1946
- Вес: 1382 г
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Репринтное издание
Издание на английском языке
This book is designed to introduce students to the mathematical foundations of engineering disciplines. It presents both theoretical and applied problems, divided into conventional and engineering applications, which allows the material to be adapted to different teaching approaches. Particular attention is paid to developing skills in moving from physical situations to mathematical modeling and back, as well as using methods to simplify complex problems. The book helps to bridge the gap between mathematical theory and its practical application in engineering, emphasizing the understanding and interpretation of models.
Content
Preface
Chapter 1. Trigonometry Defined. Vocabulary Build-Up
Scope of Trigonometry-Some Prerequisites to the Study of Trigonometry.
Chapter 2. Trigonometric Functions. Right Triangles
Definitions and Interrelations of the Trigonometric Functions of an Angle-Numerical Values of the Trigonometric Ratios for the Special Angles 30°, 45°, 60° and Multiples of 90° - General Procedure for Solving a Right Triangle - Method of Obtaining the Trigonometric Ratios - Determination of Any Trigonometric Ratio for Any Angle - Graphical Representation of Principal Trigonometric Ratios
Chapter 3. Illustrative Engineering Applications on Preceding Chapters
Problems From Electrical Engineering-Solutions of Right Triangles in Electrical Engineering-Problems From Applied Mechanics - Problems From Surveying
Chapter 4. Logarithms
Significance of a Logarithm - Characteristic and Mantissa of a Logarithm - Operations That May Be Simplified by Logarithms - Subtraction of a Large Logarithm From a Small Logarithm - Use of Logarithms in Raising a Decimal Value to a Decimal Power - Logarithm Tables-Arrangement and Use of Typical Table of Logarithmic Functions - The Natural System of Logarithms for Which Base =e =2.71828.. - Arrangement and Use of Typical Table of Natural Logarithms-Illustrative Problems Using Common or Briggs Logarithms (Base = 10) – Cologarithms - Illustrative Problems Involving Natural Logarithms - Change of Bases; Relation Between Common and Natural Logarithms
Chapter 5. Stationary Adjacent Scales and Slide Rules
Use of Stationary Adjacent Scales and Slide Rules-Illustrative Examples on Construction and Use of Stationary Adjacent Scales - 1 Use of Slide Rule for Multiplication and Division - Illustrative
Examples on Construction and Use of Sliding Scales in General - Illustrative Examples on Folded and Inverted Scales-Practice in Use of К, T, and S Scales - Additional Illustrative Slide Rule Examples - Construction and Use of a Slide Rule Designed for a Particular Formula
Chapter 6. Trigonometric Relations and Identities
Some Other Interrelations Between the Trigonometric Ratios – Identities - Formulas for sin (x+y) and cos (x+y) - Formulas for tan (x+y) and cot (x+y) - Functions of x-у - Formulas for Double Angle-The "Half-Angle Formulas" - Product to Sum Formulas - Sum to Product Formulas
Chapter 7. Complex Numbers
Imaginary Numbers-Operations With Imaginary Numbers - Complex Numbers; Visualization of Imaginary Numbers - Addition and Subtraction of Complex Numbers; Equality of Complex Numbers - Multiplication and Division of Complex Numbers - Representation of Complex Numbers in Polar Coordinates - Multiplication of Complex Numbers in Polar Form - Division of Complex Numbers in Polar Form - Engineering Illustrative Examples on Multiplication and Division of Complex Numbers - DeMoivre’s Theorem-Infinite Series for sin a and cos a - Complex Numbers and Trigonometric Functions in Terms of e-Hyperbolic Functions
Chapter 8. Oblique Triangles
Definition of Oblique Triangle - Methods of Solving Oblique Triangles-Law of Sines-Law of Cosines-Law of Tangents - Area of Triangles in Terms of Sides by Heron's Formula - Radius of Inscribed Circle in Terms of Sides of Triangle - Formulas for Tangents of Half-Angles in Terms of Sides-Discussion of Type IV-Solution of Triangles of Type IV
Chapter 9. Inverse Functions
Inverse-Function Notation-Multiple - Valuedness of an Inverse Function; Principal Values-Inverse Hyperbolic Functions
Chapter 10. Process of Inversion. Graphs
Inversion With Respect to the Unit Circle - Use of Process of Inversion in Drawing Graphs-A Circle Inverts Into a Circle - Graphic Process of Inversion for Reciprocal of a Complex Number-Engineering Applications of Process of Inversion
Chapter 11. Page Oblique Triangles Solved By Complex Numbers
Derivation of Law of Sines by Complex Numbers - Solution of Triangle of Type I (Given One Side and Two Angles) by Complex Numbers-Complex - Number Investigation of Triangle of Type II (Given Two Sides and Included Angle) - Complex-Number Investigation of Triangle of Type III (Given Three Sides) - Complex-Number Investigation of Triangles of Type IV (Given Two Sides and the Angle Opposite One of Them) - Summary of Investigations of Triangles of the Four Types
Chapter 12. Approximate Number Computations
Exact, Approximate and Round Numbers - Significant Figures - Absolute Error and Relative Error - Rounding off Numbers - Sum of Approximate Numbers-Sum of Approximate Numbers With Limit on Relative Error - Correctness of Round Numbers - S um of Approximate Numbers That Is to Be Correct to a Particular Place - Product of an Exact Factor and an Approximate Factor That Is to Be in Error by not More Than One Unit in a Particular Place - Product of an Exact Factor and an Approximate Factor With a Pre-Stated Limit of Relative Error - Product of Two Approximate Factors That Is to Be in Error by not More Than One Unit in a Particular Place - Additional Discussion-Product of Two Exact Factors With a Pre-Stated Relative Error - Product of Two or More Factors With a Pre-Stated Limit of Relative Error - Relation Among Numbers of Significant Figures in Dividend, Divisor, and Quotient - Approximations in Given Parts of Triangles
Chapter 13. Right Spherical Triangles
Geometric Properties of General Spherical Triangle-Limiting Conditions-Classes of Right Spherical Triangles - Polar Triangle; Quadrantal Triangle - Ten Formulas and Three Theorems for Solving Right Spherical Triangles - Illustrative Problems on Solutions of Right Spherical Triangles - Terrestrial Triangles - Celestial Triangles
Chapter 14. Oblique Spherical Triangles
Law of Sines - Law of Cosines for Sides - Law of Cosines for Angles - Classification of Spherical Triangles-Solution of Class I Triangles by Tangent Half-Angle Method-Solution of Class I Triangles by Haversine Method - Solution of Class II Triangles by Tangent Half-Side Method – S olution of Triangles of Classes III and IV by Napier's Analogies - How to Visualize a Spherical Triangle From Given Values-Solution of Triangles of Classes V and VI by Simultaneous Laws
Chapter 15. Page Navigation
Time and Point of the Horizon at Which the Sun Rises on a Specified Date - Difference Between True Solar Time and Mean Solar Time; Equation of Time - Sidereal Time; Conversion of Greenwich Civil Time to Greenwich Sidereal Time - The "Time Sight" - Checking of Latitude-Graphical Process for Determining Latitude and Longitude - Determination of the Coordinates (Greenwich Hour Angle and Declination) of a Subsolar Point-Dead Reckoning Position (D.R.P.) and Sumner Line-Determination of Observer’s Latitude and Longitude Without Plotting Subcelestial Points
Appendix 1. Recapitulation of Formulas
Appendix 2. Derivations of Ten Formulas For Right Spherical Triangles
Appendix 3. Instructions For Use of Tables
Tables
Table I. Mantissas of Common Logarithms
Table II. Natural Trigonometric Functions
Table III. Logarithmic Trigonometric Functions
Table IV. Natural Logarithms
Table V. Radian Measure
Table VI. Powers, Roots, Reciprocals
Table VII. Powers of "e" and Hyperbolic Functions
Table VIII. Haversines
Index
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