Essential Maths and Stats for Higher Education, 1st edition

Published by Pearson (November 7, 2012) © 2013

  • David N. Cox Simon Fraser University
  • David Cox
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Essential Maths and Stats provides a comprehensive overview of tertiary level mathematics and statistics and is the only definitive New Zealand text for mathematics and statistics at entry level. It is also an excellent 'extension' text for secondary school students.

Divided into six key sections Numerical Mathematics, Algebra (1 and 2), Trigonometry, Calculus and Statistics the text includes: differential equations, integration techniques, networks, differential equations, vectors, determinants, matrices, linear programming, probability distributions, hypothesis testing, correlation, regression, chi-squared tests and ANOVA.

The text provides full explanations, worked examples and a wide variety of graded exercises (with solutions) and is structured so that readers can dip in and out and refer to relevant sections on a need-to-know basis.

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  • Section 1: Numerical mathematics
  • 1 The basics: integers, decimals, fractions, percentages
  • 2 Order of operations, powers, roots
  • 3 The metric system, area, volume, speed, density, flow
  • 4 Standard form, approximation
  • 5 Rates, ratios, proportion
  • 6 Indices, logarithms, index equations
  • 7 Financial mathematics
  • 8 Spreadsheets
  • Section 2: Algebra 1
  • 9 Basic algebra 1: expansions, solving linear equations and inequations,algebraic fractions
  • 10 Basic algebra 2: factorising, rearranging formulae, simultaneous equations, quadratic equations
  • 11 The quadratic formula, completing the square, nature of roots
  • 12 Graphs 1: straight lines, parabolas, cubics
  • 13 Graphs 2: functions and transformations
  • 14 Graphs 3: hyperbolas, circles, exponential graphs, logarithmic graphs
  • Section 3: Trigonometry
  • 15 Right-angled triangles: Pythagoras, trigonometric ratios, bearings,trigonometry in three dimensions, special triangles
  • 16 Sine and cosine rules, radians, arcs, segments
  • 17 Trig graphs and equations
  • Section 4: Calculus
  • 18 Limits, continuity, gradients, derived functions, first principles, differentiability
  • 19 Differentiation rules, differentiation of composite functions products and quotients, l'Hopital's rule
  • 20 Applications of differentiation: tangents, stationary points,rates of change
  • 21 Differentiation of parametric functions, implicit differentiation
  • 22 Integration of polynomials, definite integration, areas
  • 23 Integration of other functions, integration by substitution
  • 24 Calculus applications: kinematics, solids of revolution
  • 25 Differential equations
  • 26 Integration by parts, partial fractions, integrating factors
  • Section 5: Algebra 2
  • 27 Networks
  • 28 Arithmetic and geometric sequences
  • 29 Infinite series
  • 30 Long division, remainder and factor theorems
  • 31 Vectors, determinants, matrices
  • 32 Linear programming
  • Section 6: Statistics
  • 33 Averages, data display, sampling methods, standard deviation
  • 34 Probability
  • 35 Expectation algebra, linear combination of random variables
  • 36 Factorials, permutations, combinations
  • 37 Binomial theorem, binomial and Poisson distributions
  • 38 Normal distribution, distribution of the sample mean and total, linear combinations
  • 39 Hypothesis testing, confidence intervals, t-distribution
  • 40 Correlation and regression
  • 41 Chi-squared tests, ANOVA
  • Appendices
  • Appendix 1: Proofs
  • Appendix 2: Useful formulae
  • Appendix 3: Statistical tables
  • Answers

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