Fundamentals of university mathematics /
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 bas...
Saved in:
| Main Author: | |
|---|---|
| Other Authors: | , |
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Oxford, Philadelphia, PA :
Woodhead Pub.,
2010.
|
| Edition: | 3rd ed. |
| Series: | Woodhead Publishing in mathematics.
|
| Subjects: | |
| Online Access: | CONNECT CONNECT |
Table of 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.
