Calculus : a complete introduction
Abbott, Paul (Mathematics teacher)2019
eBook
Abstract: Calculus: A Complete Introduction is the most comprehensive yet easy-to-use introduction to using calculus. Written by a leading expert, this book will help you if you are studying for an important exam or essay, or if you simply want to improve your knowledge.
Main title:
Calculus : a complete introduction / P. Abbott & Hugh Neill.
Author:
Edition:
[New edition][Enhanced Credo edition]
Imprint:
Boston, Massachusetts : Credo Reference, 2019.©1992London [England] : John Murray Learning, 2018.
Collation:
1 online resource (25 entries) : 87 images ; digital files.
Series title:
Notes:
First published 1992.Description based on title page of print version.
System details:
Mode of access: World Wide Web.
Linking notes:
Print version: xi, 351 pages : illustrations
Contents:
Introduction -- Functions: 1.1. What is calculus? 1.2. Functions; 1.3. Equations of functions; 1.4. General notation for functions; 1.5. Notation for increases in functions; 1.6. Graphs of functions; 1.7. Using calculators or computers for plotting functions; 1.8. Inverse functions; 1.9. Implicit functions; 1.10. Functions of more than one variable -- Variations in functions; limits: 2.1. Variations in functions; 2.2. Limits; 2.3. Limit of a function of the form; 2.4. A trigonometric limit; 2.5. A geometric illustration of a limit; 2.6. Theorems on limits -- Gradient: 3.1. Gradient of the line joining two points; 3.2. Equation of a straight line; 3.3. Approximating to gradients of curves; 3.4. Towards a definition of gradient; 3.5. Definition of the gradient of a curve; 3.6. Negative gradient -- Rate of change: 4.1. The average change of a function over an interval; 4.2. The average rate of change of a non-linear function; 4.3. Motion of a body with non-constant velocity; 4.4. Graphical interpretation; 4.5. A definition of rate of change -- Differentiation: 5.1. Algebraic approach to the rate of change of a function; 5.2. The derived function; 5.3. Notation for the derivative; 5.4. Differentials; 5.5. Sign of the derivative; 5.6. Some examples of differentiation -- Some rules for differentiation: 6.1. Differentiating a sum; 6.2. Differentiating a product; 6.3. Differentiating a quotient; 6.4. Function of a function; 6.5. Differentiating implicit functions; 6.6. Successive differentiation; 6.7. Alternative notation for derivatives; 6.8. Graphs of derivatives -- Maxima, minima and points of inflexion: 7.1. Sign of the derivative; 7.2. Stationary values; 7.3. Turning points; 7.4. Maximum and minimum values; 7.5. Which are maxima and which are minima?; 7.6. A graphical illustration; 7.7. Some worked examples; 7.8. Points of inflexion -- Differentiating the trigonometric functions: 8.1. Using radians; 8.2. Differentiating sin x; 8.3. Differentiating cos x; 8.4. Differentiating tan x; 8.5. Differentiating sec x, cosec x, cot x; 8.6. Summary of results; 8.7. Differentiating trigonometric functions; 8.8. Successive derivatives; 8.9. Graphs of the trigonometric functions; 8.10. Inverse trigonometric functions; 8.11. Differentiating sin-1 x and cos-1 x; 8.12. Differentiating tan-1 x and cot-1 x; 8.13. Differentiating sec-1 x and cosec-1 x; 8.14. Summary of results -- Exponential and logarithmic functions: 9.1. Compound Interest Law of growth; 9.2. The value of ; 9.3. The Compound Interest Law; 9.4. Differentiating ex; 9.5. The exponential curve; 9.6. Natural logarithms; 9.7. Differentiating ln x; 9.8. Differentiating general exponential functions; 9.9. Summary of formulae; 9.10. Worked examples -- Hyperbolic functions: 10.1. Definitions of hyperbolic functions; 10.2. Formulae connected with hyperbolic functions; 10.3. Summary; 10.4. Derivatives of the hyperbolic functions; 10.5. Graphs of the hyperbolic functions; 10.6. Differentiating the inverse hyperbolic functions; 10.7. Logarithm equivalents of the inverse hyperbolic functions; 10.8. Summary of inverse functions -- Integration; standard integrals: 11.1. Meaning of integration; 11.2. The constant of integration; 11.3. The symbol for integration; 11.4. Integrating a constant factor; 11.5. Integrating xn; 11.6. Integrating a sum; 11.7. Integrating 1/x; 11.8. A useful rule for integration; 11.9. Integrals of standard forms; 11.10. Additional standard integrals -- Methods of integration: 12.1. Introduction; 12.2. Trigonometric functions; 12.3. Integration by substitution; 12.4. Some trigonometrical substitutions; 12.5. The substitution t = tan x; 12.6. Worked examples; 12.7. Algebraic substitutions; 12.8. Integration by parts -- Integration of algebraic fractions: 13.1. Rational fractions; 13.2. Denominators of the form ax2 + bx + c; 13.3. Denominator: a perfect square; 13.4. Denominator: a difference of squares; 13.5. Denominator: a sum of squares; 13.6. Denominators of higher degree; 13.7. Denominators with square roots -- Area and definite integrals: 14.1. Areas by integration; 14.2. Definite integrals; 14.3. Characteristics of a definite integral; 14.4. Some properties of definite integrals; 14.5. Infinite limits and infinite integrals; 14.6. Infinite limits; 14.7. Functions with infinite values -- The integral as a sum; areas: 15.1. Approximation to area by division into small elements; 15.2. The definite integral as the limit of a sum; 15.3. Examples of areas; 15.4. Sign of an area; 15.5. Polar coordinates; 15.6. Plotting curves from their equations in polar coordinates; 15.7. Areas in polar coordinates; 15.8. Mean value -- Approximate integration: 16.1. The need for approximate integration; 16.2. The trapezoidal rule; 16.3. Simpson's rule for area -- Volumes of revolution: 17.1. Solids of revolution; 17.2. Volume of a cone; 17.3. General formula for volumes of solids of revolution; 17.4. Volume of a sphere; 17.5. Examples -- Lengths of curves: 18.1. Lengths of arcs of curves; 18.2. Length in polar coordinates -- Taylor's and Maclaurin's series: 19.1. Infinite series; 19.2. Convergent and divergent series; 19.3. Taylor's expansion; 19.4. Maclaurin's series; 19.5. Expansion by the differentiation and integration of known series -- Differential equations: 20.1. Introduction and definitions; 20.2. Type I: one variable absent; 20.3. Type II: variables separable; 20.4. Type III: linear equations; 20.5. Type IV: linear differential equations with constant coefficients; 20.6. Type V: homogeneous equations -- Applications of differential equations: 21.1. Introduction; 21.2. Problems involving rates; 21.3. Problems involving elements -- Answers.
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Access restricted to authorized users and institutions.
ISBN:
9781787854024 (electronic version)9781473678446 (paperback)1473678447 (paperback)9781473678453 (ebook)
Dewey class:
515
LC class:
QA303.2
Language:
English
BRN:
501634
Electronic access:
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