Introductory Algebra and Calculus (Pearson Original Edition eBook), 2nd Edition

Dann Mallet all

Introductory Algebra and Calculus (Pearson Original Edition eBook), 2nd Edition

By Dann Mallet, Graeme Pettet, Charisse Farr
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Dann Mallet all
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This book has been written specifically for a course at Queensland University of Technology that introduces students to single variable calculus, complex numbers, vectors, matrices and some elementary linear algebra following on from studies in these topics either in high school or introductory studies at university.

The book is intentionally quite small. In writing the text it was not our intention to present absolutely everything there is to know about the topics included in the book. This book has been written to introduce the reader, hopefully in an easy to read way, to some of the more useful concepts that will be picked up on in later studies or that will be needed in other fields of study such as science or engineering. We have also tried to keep to a "how-to" style wherever possible. There are many worked examples scattered throughout the text and exercise sets are provided at the end of each section.

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Table of contents
  • Preliminaries
  • 1.1 Algebraic order of operations
  • 1.2 Index laws
  • 1.3 Rationalising fractions
  • 1.4 Quadratic formula
  • 1.5 Sigma notation
  • 1.6 Binomial theorem
  • 1.7 Elementary series
  • 2 Functions
  • 2.1 Introduction
  • 2.2 Trigonometric functions
  • 2.3 Exponential and logarithmic functions
  • 2.4 Hyperbolic functions
  • 3 Complex numbers
  • 3.1 Arithmetic
  • 3.2 Representations
  • 3.3 Solving equations involving complex numbers
  • 4 Differentiation
  • 4.1 The derivative
  • 4.2 Rules for differentiation
  • 4.3 Implicit differentiation
  • 4.4 Logarithmic differentiation
  • 4.5 Applications
  • 4.6 Newton's method
  • 5 Integration
  • 5.1 The integral
  • 5.2 Integration by parts
  • 5.3 Integration by substitution
  • 5.4 Calculating areas using integrals
  • 6 Vectors
  • 6.1 Geometric representation
  • 6.2 Arithmetic and algebra
  • 6.3 Products of vectors
  • 7 Matrices
  • 7.1 About matrices
  • 7.2 Arithmetic and algebra
  • 7.3 Inverse matrices
  • 7.4 Matrix determinants
  • 7.5 Cramer's rule
  • 7.6 Solving linear systems using Gaussian elimination
  • A Answers to selected exercises