Guide to Mathematical Methods 2nd Edition by John Gilbert, Camilla Jordan David Towers ISBN 978-0333794449 0333794443
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Product details:
ISBN 10: 0333794443
ISBN 13: 978-0333794449
Author: John Gilbert, Camilla Jordan David Towers
A second edition of this text for science and engineering undergraduates which introduces the mathematical techniques and tools needed to solve the mathematical problems they will face on the first year of their course. Updated and revised by Camilla Jordan, the book now has additional examples and ‘Aims and Objectives’ sections. As with other titles in the Mathematical Guides series, this book is designed to enable students to acquire confidence and provides a solid foundation for further study.
Table of contents:
1 Preliminaries
1.1 Basic algebraic skills
1.2 Powers and indices
1.3 Algebraic fractions and rationalising
1.4 Factorising
1.5 Completing the square
1.6 Miscellaneous exercises
1.7 Answers to exercises
2 Functions
2.1 Sets and intervals
2.2 Functions
2.3 Polynomials
2.4 Rational functions
2.5 Trigonometric functions
2.6 Composite and inverse functions
2.7 Wave functions
2.8 Computer workshop
2.9 Miscellaneous exercises
2.10 Answers to exercises
3 Differentiation
3.1 Limits and continuity
3.2 What is differentiation?
3.3 Derivatives of combinations of functions
3.4 Derivatives of trigonometric functions
3.5 Miscellaneous exercises
3.6 Answers to exercises.
4 Further functions
4.1 Higher derivatives and Leibnitz’ rule
4.2 Power series and Taylor’s Theorem
4.3 The exponential function
4.4 Logarithms and powers
4.5 Hyperbolic functions
4.6 The family of standard functions
4.7 Computer workshop
4.8 Miscellaneous exercises
4.9 Answers to exercises
5 Applications of differentiation
5.1 Local maxima and minima
5.2 Sketching curves
5.3 Rates of change
5.4 Miscellaneous exercises
5.5 Answers to exercises
6 Integration
6.1 Area and definite integrals
6.2 Velocity and displacement, force and work
6.3 The Fundamental Theorem of Calculus
6.4 Standard integrals and properties of integrals.
6.5 Integration by substitution
6.6 Integrals involving the substitution z = g(u)
6.7 Integration by parts
6.8 Miscellaneous exercises
6.9 Answers to exercises
7 Further integration
7.1 Partial fractions
7.2 Systematic integration of rational functions
7.3 Rational trigonometric functions
7.4 Improper integrals
7.5 Miscellaneous exercises
7.6 Answers to exercises
8 Linear equations and matrices
8.1 Systems of linear equations
8.2 Matrices and Gaussian elimination.
8.3 Determinants.
8.4 Matrix algebra
8.5 Square matrices
8.6 Gaussian elimination revisited
8.7 Miscellaneous exercises
8.8 Answers to exercises
9 Vectors
9.1 Vectors
9.2 The algebra of vectors
9.3 Unit vectors and direction cosines
9.4 Scalar products
9.5 Vector products
9.6 Triple products.
9.7 Lines and planes
9.8 Vector equations of curves in space
9.9 Differentiation of vector functions
9.10 Arc length
9.11 Miscellaneous exercises
9.12 Answers to exercises
10 Functions of two variables
10.1 Introduction
10.2 The family of standard functions
10.3 Graphical representation
10.4 Function of three or more variables
10.5 Partial derivatives
10.6 Chain rules
10.7 Directional derivatives
10.8 Higher partial derivatives
10.9 Maxima and minima
10.10 Miscellaneous exercises
10.11 Answers to exercises
11 Line integrals
11.1 Vector fields
11.2 Line integrals.
11.3 Properties of line integrals
11.4 Conservative fields.
11.5 Miscellaneous exercises
11.6 Answers to exercises
12 Double integrals
12.1 Double integrals
12.2 Change of variables
12.3 Green’s Theorem
12.4 Miscellaneous exercises
12.5 Answers to exercises
13 Complex numbers
13.1 Introduction
13.2 The algebra of complex numbers
13.3 Solutions of equations
13.4 Equalities and inequalities
13.5 Polar form of complex numbers
13.6 Describing sets of complex numbers
13.7 Complex functions
13.8 The exponential function
13.9 Finding n’th roots
13.10 Trigonometric identities
13.11 Miscellaneous exercises
13.12 Answers to exercises
14 Differential equations
14.1 Introduction
14.2 Differential equations with separable variables
14.3 Differential equations where y = uz is a useful substitution
14.4 Exact differential equations
14.5 Linear differential equations
14.6 Solving first-order linear differential equations another way
14.7 Solution of second-order differential equations
14.8 Complementary functions
14.9 General solution of non-homogeneous equation
14.10 Initial and boundary conditions
14.11 Variation of parameters
14.12 Miscellaneous exercises
14.13 Answers to exercises
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Tags: John Gilbert, Camilla Jordan David Towers, Guide to Mathematical Methods