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Fundamentals of university mathematics
Author
Title
Fundamentals of university mathematics / Colin McGregor, Jonathan Nimmo and Wilson Stothers.
ISBN
0857092243
9780857092243
0857092235
9780857092236
9781904275459
1904275451
9780857092236
0857092235
Edition
3rd ed.
Published
Oxford, Philadelphia, PA : Woodhead Pub., 2010.
Physical Description
1 online resource (xii, 552 pages) : illustrations
Local Notes
Access is available to the Yale community.
Access and use
Access restricted by licensing agreement.
Summary
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. One volume, unified treatment of essential topicsClearly and comprehensively covers material beyond standard textbooksWorked examples, challenges and exercises throughout.
Variant and related titles
O'Reilly Safari. OCLC KB.
Other formats
Print version: McGregor, C.M. (Colin M.). Fundamentals of university mathematics. 3rd ed. Oxford, Philadelphia, PA : Woodhead Pub., 2010
Format
Books / Online
Language
English
Added to Catalog
January 10, 2020
Series
Woodhead Publishing in mathematics
Contents
Cover; Fundamentals of University Mathematics; Copyright; Table of contents; Preface to the Third Edition; Notation; Chapter 1 Preliminaries; 1.1 Number Systems; 1 .2 Intervals; 1 .3 The Plane; 1.4 Modulus; 1 .5 Rational Powers; 1.6 Inequalities; 1.7 Divisibility and Primes; 1.8 Rationals and Irrationals; 1.X Exercises; Chapter 2 Functions and Inverse Functions; 2 .1 Functions and Composition; 2.2 Real Functions; 2.3 Standard Functions; 2.4 Boundedness; 2.5 Inverse Functions; 2.6 Monotonic Functions; 2.X Exercises; Chapter 3 Polynomials and Rational Functions; 3.1 Polynomials.
3.2 Division and Factors3.3 Quadratics; 3.4 Rational Functions; 3.X Exercises; Chapter 4 Induction and the Binomial Theorem; 4.1 The Principle of Induction; 4.2 Picking and Choosing; 4.3 The Binomial Theorem; 4.X Exercises; Chapter 5 Trigonometry; 5.1 Trigonometric Functions; 5.2 Identities; 5.3 General Solutions of Equations; 5.4 The t-formulae; 5.5 Inverse Trigonometric Functions; 5.X Exercises; Chapter 6 Complex Numbers; 6.1 The Complex Plane; 6.2 Polar Form and Complex Exponentials; 6.3 De Moivre's Theorem and Trigonometry; 6.4 Complex Polynomials; 6.5 Roots of Unity.
6.6 Rigid Transformations of the Plane6.X Exercises; Chapter 7 Limits and Continuity; 7.1 Function Limits; 7.2 Properties of Limits; 7.3 Continuity; 7.4 Approaching Infinity; 7.X Exercises; Chapter 8 Differentiation-Fundamentals; 8.1 First Principles; 8.2 Properties of Derivatives; 8.3 Some Standard Derivatives; 8.4 Higher Derivatives; 8.X Exercises; Chapter 9 Differentiation-Applications; 9.1 Critical Points; 9.2 Local and Global Extrema; 9.3 The Mean Value Theorem; 9.4 More on Monotonic Functions; 9.5 Rates of Change; 9.6 L'HÔpital's Rule; 9.X Exercises; Chapter 10 Curve Sketching.
10.1 Types of Curve10.2 Graphs; 10.3 Implicit Curves; 10.4 Parametric Curves; 10.5 Conic Sections; 10.6 Polar Curves; 10.X Exercises; Chapter 11 Matrices and Linear Equations; 11.1 Basic Definitions; 11.2 Operations on Matrices; 11.3 Matrix Multiplication; 11.4 Further Properties of Multiplication; 11.5 Linear Equations; 11.6 Matrix Inverses; 11.7 Finding Matrix Inverses; 11.X Exercises; Chapter 12 Vectors and Three Dimensional Geometry; 12.1 Basic Properties of Vectors; 12.2 Coordinates in Three Dimensions; 12.3 The Component Form of a Vector; 12.4 The Section Formula.
12.5 Lines in Three Dimensional Space12.X Exercises; Chapter 13 Products of Vectors; 13.1 Angles and the Scalar Product; 13.2 Planes and the Vector Product; 13.3 Spheres; 13.4 The Scalar Triple Product; 13.6 Projections; 13.X Exercises; Chapter 14 Integration- Fundamentals; 14.1 Indefinite Integrals; 14.2 Definite Integrals; 14.3 The Fundamental Theorem of Calculus; 14.4 Improper Integrals; 14.X Exercises; Chapter 15 Logarithms and Exponentials; 15.1 The Logarithmic Function; 15.2 The Exponential Function; 15.3 Real Powers; 15.4 Hyperbolic Functions; 15.5 Inverse Hyperbolic Functions.
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