Higher Mathematics for Students of Chemistry and Physics: With Special Reference to Practical Work, by J. W. Mellor ...

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Longmans, Green, 1902 - 543 Seiten
 

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Inhalt

Notation
14
Functions
15
Differentiation
17
Is Differentiation a Method of Approximation only?
19
The Differentiation of Algebraic Functions
22
The Gas Equations of Boyle and van der Waals
30
The Differentiation of Trignometrical Functions
31
The Differentiation of Inverse Trignometrical Functions The Differentiation of Angles
33
Logarithms and their Differentiation
34
The Differential Coefficient of Exponential Functions
38
The Compound Interest Law in Nature
39
Successive Differentiation
47
Leibnitz Theorem
49
Partial Differentiation
50
Eulers Theorem on Homogeneous Functions
56
Successive Partial Differentiation
57
Integrating Factors
58
Illustrations from Thermodynamics
59
COORDINATE OR ANALYTICAL GEOMETRY SECTION PAOK 27 Cartesian Coordinates
63
Graphical Representation
65
Practical Illustrations of Graphical Representation
66
General Equations of the Straight Line
68
Differential Coefficient of a Point moving on a Straight Line
71
Straight Lines Satisfying Conditions
72
Changing the Coordinate Axes
74
The Circle and its Equation
75
The Parabola and its Equation
76
The Ellipse and its Equation
78
The Hyperbola and its Equation
80
A Study of Curves
82
The Parabola resumed
85
The Ellipse resumed
86
The Hyperbola resumed
87
The Rectangular or Equilateral Hyperbola
88
Illustrations of Hyperbolic Curves
89
Polar Coordinates
93
Logarithmic or Equiangular Spiral
95
Trilinear Coordinates and Triangular Diagrams
97
Orders of Curves
99
Coordinate Geometry in Three Dimensions Geometry in Space
101
Orders of Surfaces
110
Periodic or Harmonic Motion III
115
FUNCTIONS WITH SINGULAR PROPERTIES 52 Continuous and Discontinuous Functions
118
Discontinuity accompanied by Breaks
119
The Existence of Hydrates in Solution
120
Discontinuity accompanied by Change of Direction
124
Maximum and Minimum Values of a Function
129
How to find Maximum and Minimum Values of a Function
130
Points of Inflection
132
How to find whether a Curve is Concave or Convex with respect to thexAxis
133
How to find Points of Inflection
134
Multiple Points
135
Cusps
136
Conjugate or Isolated Point
137
Summary
139
Envelopes
142
Six Problems in Maxima and Minima
144
THE INTEGRAL CALCULUS SECTION PAGE 69 Integration
150
Table of Standard Integrals
157
The Simpler Methods of Integration
158
How to find a Value for the Integration Constant
162
Integration by the Substitution of a New Variable
164
Integration by Parts
168
Integration by Successive Reduction
169
Reduction Formulae for reference
170
Integration by Resolution into Partial Fractions
171
Areas Enclosed by Curves To Evaluate Definite Integrals
177
Graphic Representation of Work
182
Integration between Limits Definite Integrals
183
To find the Length of any Curve
186
Elliptic Integrals
188
The Gamma Function
190
Numerical Table of the Gamma Function
191
To find the Area of a Surface of Revolution
192
To find the Volume of a Solid of Revolution
193
Successive Integration Multiple Integrals
194
The Velocity of Chemical Reactions
197
Chemical EquilibriumIncomplete or Reversible Reactions
203
Fractional Precipitation
207
The Isothermal Expansion of Gases
208
The Adiabatic Expansion of Gases
211
The Influence of Temperature on Chemical and Physical Changes vant Hoffs Formula
214
INFINITE SERIES AND THEIR USES 94 What is an Infinite Series?
218
Sorets Diffusion Experiments
220
Approximate Calculation by Means of Infinite Series
222
Maclaurins Theorem
226
Useful Deductions from Maclaurins Theorem
228
Approximate Integration
263
Integration by Infinite Series
267
HYPERBOLIC FUNCTIONS SUCTION lAOK 109 Eulers Exponential Values of the Sine and Cosine
271
The Derivation of Hyperbolic Functions
272
The Graphic Representation of the Hyperbolic Functions
274
Transformation and Conversion Formulae
276
Inverse Hyperbolic Functions
277
Demoivres Theorem
280
HOW TO SOLVE DIFFERENTIAL EQUATIONS
282
The Solution of a Differential Equation by the separation of the Variables
283
What is a Differential Equation?
286
Exact Differential Equations of the First Order
289
How to find Integrating Factors
292
The First Law of Thermodynamics
295
Linear Differential Equations of the First Order
296
Differential Equations of the First Order and of the First or Higher Degree Solution by Differentiation
298
Clairauts Equation
300
Singular Solutions
301
Trajectories
304
The Linear Equation of the nth Order
305
The Linear Equation with Constant Coefficients
307
How to find Particular Integrals
310
The Linear Equation with Variable Coefficients
315
The Exact Linear Differential Equation
317
The Integration of Equations with Missing Terms
319
Equations of Motion chiefly Oscillatory Motion 822
322
The Velocity of Simultaneous and Dependent Chemical Reactions 830
330
Simultaneous Differential Equations
336
Partial Differential Equations
339
What is the Solution of a Partial Differential Equation?
341
The Solution of Partial Differential Equations of the First Order
344
Partial Differential Equations of the nth Order
346
Linear Partial Equations with Constant Coefficients
347
The Particular Integral of Linear Partial Equations
351
The Linear Partial Equation with Variable Coefficients 854
354
The Integration of Differential Equations in Series
355
Harmonic Analysis
357
SECTION PAOB
360
Extension of Fouriers Series
366
Fouriers Linear Diffusion Law
374
USEFUL RESULTS FROM ALGEBRA
385
How to Separate Equal Roots from an Equation
391
van der Waals Equation of State
398
The Expansion of Determinants
405
The Differentiation of Determinants
411
PROBABILITY AND THE THEORY OF ERRORS SECTION PAGE 172 Probability
416
Application to the Kinetic Theory of Gases
421
Errors of Observation
426
The Law of Errors
428
The Probability Integral 481
431
The Best Representative Value for a Set of Observations
433
The Probable Error 486
436
Mean and Average Errors
439
Numerical Values of the Probability Integrals
445
Maxwells Law of Distribution of Molecular Velocities
448
Constant Errors
451
Proportional Errors
453
Observations of Different Degrees of Accuracy
462
Observations Limited by Conditions
469
Gauss Method of Solving a Set of Linear Observation Equations
471
When to Reject Suspected Observations
475
CHAPTER NIL COLLECTION OF FORMULAE FOR REFERENCE 188 Law of Indices and Logarithms
479
Approximate Calculations in Scientific Work
483
Variation
487
Permutations and Combinations
489
Mensuration Formulae
490
Bayers Strain Theory of Carbon Ring Compounds
492
Plane Trignometry
493
Spherical Trignometry
502
Summary of Relations among the Hyperbolic Functions
504
REFERENCE TABLES TABLE I Standard Integrals 158
507
Standard Integrals Hyperbolic Functions 278
509
Numerical Values of the Hyperbolic Sines
510
Numerical Values of the Hyperbolic Cosines
511
Numerical Values of the Factor
512
Numerical Values of the Factor 0 8453
513
Numerical Values of the Probability Integral j I e Mix
514
Numerical Values of the Probability Integral f Jr erdj
515
Application of Chauvenets Criterion
516
Square Roots of Numbers from 01 to 9 9
517
Cube Roots of Numbers from 1 to 100
518
Numerical Values of ez from x 0 to x 10
519
Logarithms of Numbers to the Base
520
Miscellaneous Examples
523
Index
527
n vn 1
16

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