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Provides, in a single volume, a unified treatment of first year topics fundamental to university mathematics. Successfully bridges the transitional gap between school and university in a careful, thorough and unusually clear treatment. An essential text for students aiming for an honours degree in mathematics.
Contents: Functions and inverse functions Polynomials and rational functions Induction and the binomial theorem Trigonometry Complex numbers Limits and continuity Differentiation - fundamentals Differentiation applications Curve sketching Matrices and linear equations Vectors and three-dimensional geometry Products of vectors Integration - fundamentals Logarithms and exponentials Integration - methods and applications Ordinary differential equations Sequences and series Numerical methods Appendix A Answers to exercises Appendix B Solutions to problems Appendix C Limits and continuity a rigorous approach Appendix D Properties of trigonometric functions Appendix E Tables of integrals Appendix F Standard Maclaurin series.
Key Features: one volume, unified treatment of essential topics clearly and comprehensively covers material beyond standard textbooks worked examples, challenges and exercises throughout.
Preliminaries
Functions and inverse functions
Polynomials and rational functions
Induction and the binomial theorem
Trigonometry
Complex numbers
Limits and continuity
Differentiation – fundamentals
Differentiation – applications
Curve sketching
Matrices and linear equations
Vectors and three-dimensional geometry
Products of vectors
Integration – fundamentals
Logarithms and exponentials
Integration - methods and applications
Ordinary differential equations
Sequences and series
Numerical methods
Appendicies