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Fundamentals of university mathematics (Third edition)C M McGregor, J J C Nimmo, Glasgow University and W W Stothers, formerly Glasgow University, UK
I found this book to be extremely helpful over a wide range of topics. I must have used this to aid my revision for at least 7 or 8 exams and would probably have struggled without it. Particularly useful sections include those on Complex Numbers, Matrices, Vectors, and Differential Equations. If you can only afford to buy one or two books for your course or study, make sure this is one of them!
Rg Ellam "rob_ellam (review on www.amazon.co.uk)
This book is excellent preparation for 2nd year undergraduate Mathematics courses. It is detailed and step-by-step, so you don't get lost on certain topics. The proofs are complex, but then that's Mathematics for you!
Jon Baldie (review on www.amazon.co.uk)
If you are looking for a first year university text you should carefully look at this, a unifier of mathematical ideas at this level. I found it most valuable.
The Mathematical Gazette (review of a previous edition)
A sound beginning to mathematics degrees, and a reference book for anyone who uses maths regularly. If you seek a first year university text, certainly look at this one. I wish that I [had] had a copy as an undergraduate
Mathematics Today (review of a previous edition)
- one volume, unified treatment of essential topics
- clearly and comprehensively covers material beyond standard textbooks
- worked examples, challenges and exercises throughout
The third edition of this popular and effective textbook provides in one volume a unified treatment of topics essential for first year university students studying for degrees in mathematics. Students of computer science, physics and statistics will also find this book a helpful guide to all the basic mathematics they require. It clearly and comprehensively covers much of the material that other textbooks tend to assume, assisting students in the transition to university-level mathematics.
Expertly revised and updated, the chapters cover topics such as number systems, set and functions, differential calculus, matrices and integral calculus. Worked examples are provided and chapters conclude with exercises to which answers are given. For students seeking further challenges, problems intersperse the text, for which complete solutions are provided. Modifications in this third edition include a more informal approach to sequence limits and an increase in the number of worked examples, exercises and problems.
The third edition of Fundamentals of university mathematics is an essential reference for first year university students in mathematics and related disciplines. It will also be of interest to professionals seeking a useful guide to mathematics at this level and capable pre-university students.
ISBN 0 85709 223 5
ISBN-13: 978 0 85709 223 6
October 2010
568 pages 234 x 156mm paperback
£45.00 / US$75.00 / €55.00
Usually dispatched within 24 hours
About the authors
Colin McGregor is an Honorary Research Fellow in the Department of Mathematics, University of Glasgow, UK, where Jonathan Nimmo is a Reader in Mathematics. Wilson Stothers was also formerly a member of this department.
Titles which may also be of interest:
Mathematics
Mathematics teaching practice
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Contents
Preliminaries
- Number systems
- Intervals
- The plane
- Modulus
- Rational powers
- Inequalities
- Divisibility and primes
- Rationals and irrationals
- Exercises
Functions and inverse functions
- Functions and composition
- Real functions
- Standard functions
- Boundedness
- Inverse functions
- Monotonic functions
- Exercises
Functions and inverse functions
- Functions and composition
- Real functions
- Standard functions
- Boundedness
- Inverse functions
- Monotonic functions
- Exercises
Polynomials and rational functions
- Polynomials
- Division and factors
- Quadratics
- Rational functions
- Exercises
Polynomials and rational functions
- Polynomials
- Division and factors
- Quadratics
- Rational functions
- Exercises
Induction and the binomial theorem
- The principle of induction
- Picking and choosing
- The binomial theorem
- Exercises
Induction and the binomial theorem
- The principle of induction
- Picking and choosing
- The binomial theorem
- Exercises
Trigonometry
- Trigonometric functions
- Identities
- General solutions of equations
- The t-formulae
- Inverse trigonometric tunctions
- Exercises
Trigonometry
- Trigonometric functions
- Identities
- General solutions of equations
- The t-formulae
- Inverse trigonometric tunctions
- Exercises
Complex numbers
- The complex plane
- Polar form and complex exponentials
- De Moivre's theorem and trigonometry
- Complex polynomials
- Roots of unity
- Rigid transformations of the plane
- Exercises
Complex numbers
- The complex plane
- Polar form and complex exponentials
- De Moivre's theorem and trigonometry
- Complex polynomials
- Roots of unity
- Rigid transformations of the plane
- Exercises
Limits and continuity
- Function limits
- Properties of limits
- Continuity
- Approaching infinity
- Exercises
Limits and continuity
- Function limits
- Properties of limits
- Continuity
- Approaching infinity
- Exercises
Differentiation fundamentals
- First principles
- Properties of derivatives
- Some standard derivatives
- Higher derivatives
- Exercises
Differentiation fundamentals
- First principles
- Properties of derivatives
- Some standard derivatives
- Higher derivatives
- Exercises
Differentiation Applications
- Critical points
- Local and global extrema
- The Mean Value theorem
- More on monotonic functions
- Rates of change
- L'H^opital's rule
- Exercises
Differentiation Applications
- Critical points
- Local and global extrema
- The Mean Value theorem
- More on monotonic functions
- Rates of change
- L'H^opital's rule
- Exercises
Curve sketching
- Types of curve
- Graphs
- Implicit curves
- Parametric curves
- Conic sections
- Polar curves
- Exercises
Curve sketching
- Types of curve
- Graphs
- Implicit curves
- Parametric curves
- Conic sections
- Polar curves
- Exercises
Matrices and linear equations
- Basic definitions
- Operations on matrices
- Matrix multiplication
- Further properties of multiplication
- Linear equations
- Matrix inverses
- Finding matrix inverses
- Exercises
Matrices and linear equations
- Basic definitions
- Operations on matrices
- Matrix multiplication
- Further properties of multiplication
- Linear equations
- Matrix inverses
- Finding matrix inverses
- Exercises
Vectors and three dimensional geometry
- Basic properties of vectors
- Coordinates in three dimensions
- The component form of a vector
- The section formula
- Lines in three dimensional space
- Exercises
Vectors and three dimensional geometry
- Basic properties of vectors
- Coordinates in three dimensions
- The component form of a vector
- The section formula
- Lines in three dimensional space
- Exercises
Products of vectors
- Angles and the scalar product
- Planes and the vector product
- Spheres
- The scalar triple product
- The vector triple product
- Projections
- Exercises
Products of vectors
- Angles and the scalar product
- Planes and the vector product
- Spheres
- The scalar triple product
- The vector triple product
- Projections
- Exercises
Integration fundamentals
- Indefnite integrals
- Defnite integrals
- The fundamental theorem of calculus
- Improper integrals
- Exercises
Integration fundamentals
- Indefnite integrals
- Defnite integrals
- The fundamental theorem of calculus
- Improper integrals
- Exercises
Logarithms and exponentials
- The logarithmic function
- The exponential function
- Real powers
- Hyperbolic functions
- Inverse hyperbolic functions
- Exercises
Logarithms and exponentials
- The logarithmic function
- The exponential function
- Real powers
- Hyperbolic functions
- Inverse hyperbolic functions
- Exercises
Integration methods and applications
- Substitution
- Rational integrals
- Trigonometric integrals
- Integration by parts
- Volumes of revolution
- Arc lengths
- Areas of revolution
- Exercises
Integration methods and applications
- Substitution
- Rational integrals
- Trigonometric integrals
- Integration by parts
- Volumes of revolution
- Arc lengths
- Areas of revolution
- Exercises
Ordinary differential equations
- Introduction
- First order separable equations
- First order homogeneous equations
- First order linear equations
- Second order linear equations
- Exercises
Ordinary differential equations
- Introduction
- First order separable equations
- First order homogeneous equations
- First order linear equations
- Second order linear equations
- Exercises
Sequences and serie
- Real sequences
- Sequence limits
- Series
- Power series
- Taylor's theorem
- Exercises
Sequences and serie
- Real sequences
- Sequence limits
- Series
- Power series
- Taylor's theorem
- Exercises
Numerical methods
Errors . . . . . . . . .
- The Bisection method
- Newton's method
- Definite integrals
- Euler's method
- Exercises
Numerical methods
Errors . . . . . . . . .
- The Bisection method
- Newton's method
- Definite integrals
- Euler's method
- Exercises
Appendix A Answers to Exercises