Fundamentals of University MathematicsProvides, 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
Preface | 9 |
Matrices and Linear Equations | 11 |
4 | 19 |
7 | 33 |
Functions and Inverse Functions | 40 |
Polynomials and Rational Functions | 63 |
Trigonometry | 101 |
1 | 116 |
Products of Vectors | 316 |
IntegrationFundamentals | 345 |
Logarithms and Exponentials | 370 |
IntegrationMethods and Applications | 400 |
Ordinary Differential Equations | 430 |
Sequences and Series | 452 |
Numerical Methods | 481 |
A Answers to Exercises | 503 |
Common terms and phrases
angle asymptotes bijection chain rule Chapter coefficients complex numbers consider converges Corollary cos² Deduce defined by f(x Definition denoted Determine differentiable dy dx entry equation Example exists factor factorisation Find function ƒ ƒ and g ƒ is continuous gives graph Hence improper integral integral intermediate value theorem interval inverse L'Hôpital's rule Lemma Let f Let ƒ lim f(x Maclaurin series matrix maximal domain mean value theorem metres minimum turning point Mmxn F non-zero notation Note nth roots number system parameters perpendicular plane point of inflection polynomial properties Prove punctured neighbourhood quadratic quotient rule rational function real function real function defined real numbers respectively sec² Section Show shown in Figure sin² sinh Solution Let strictly increasing table of signs tangent value theorem vector x-axis x²+1 zero