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Basic Engineering Mathematics (Fourth Edition) by John Bird

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Basic Engineering Mathematics (Fourth Edition) written by John Bird This is an other great mathematics book cover the following topics.

  • Basic arithmetic
    Arithmetic operations, Highest common factors and lowest common multiples, Order of precedence and brackets

  • Fractions, decimals and percentages

  • Indices, standard form and engineering notation
    Indices, Worked problems on indices, Further worked problems on indices, Standard form, Worked problems on standard form, Further worked problems on standard form, Engineering notation and common prefixes

  • Calculations and evaluation of formulae
    Errors and approximations, Use of calculator, Conversion tables and charts, Evaluation of formulae, Assignment

  • Computer numbering systems
    Binary numbers, Conversion of binary to denary, Conversion of denary to binary, Conversion of denary to binary via octal, Hexadecimal numbers

  • Algebra
    Basic operations, Laws of indices, Brackets and factorization, Fundamental laws and precedence, Direct and inverse proportionality, Assignment

  • Simple equations
    Expressions, equations and identities, Worked problems on simple equations, Further worked problems on simple equations, Practical problems involving simple equations, Further practical problems involving simple equations

  • Transposition of formulae
    Introduction to transposition of formulae, Worked problems on transposition of formulae, Further worked problems on transposition of formulae, Harder worked problems on transposition of formulae, Assignment 4

  • Simultaneous equations
    Introduction to simultaneous equations, Worked problems on simultaneous equations in two unknowns, Further worked problems on simultaneous equations, More difficult worked problems on simultaneous equations, Practical problems involving simultaneous equations

  • Quadratic equations
    Introduction to quadratic equations, Solution of quadratic equations by factorization, Solution of quadratic equations by ‘completing the square, Solution of quadratic equations by formula, Practical problems involving quadratic equations, The solution of linear and quadratic equations simultaneously

  • Inequalities
    Introduction to inequalities, Simple inequalities, Inequalities involving a modulus, Inequalities involving quotients, Inequalities involving square functions, Quadratic inequalities, Assignment 5

  • Straight line graphs
    Introduction to graphs, The straight line graph, Practical problems involving straight line graphs

  • Graphical solution of equations
    Graphical solution of simultaneous equations, Graphical solutions of quadratic equations, Graphical solution of linear and quadratic equations simultaneously, Graphical solution of cubic equations, Assignment 6

  • Logarithms
    Introduction to logarithms, Laws of logarithms, Indicial equations, Graphs of logarithmic functions

  • Exponential functions
    The exponential function, Evaluating exponential functions, The power series for ex, Graphs of exponential functions, Napierian logarithms, Evaluating Napierian logarithms, Laws of growth and decay, Assignment 7

  • Reduction of non-linear laws to linear-form
    Determination of law, Determination of law involving logarithms

  • Graphs with logarithmic scales
    Logarithmic scales, Graphs of the form y = axn, Graphs of the form y = abx, Graphs of the form y = aekx

  • Geometry and triangles
    Angular measurement, Types and properties of angles, Properties of triangles, Congruent triangles, Similar triangles, Construction of triangles, Assignment 8

  • Introduction to trigonometry
    Trigonometry, The theorem of Pythagoras, Trigonometric ratios of acute angles, Solution of right-angled triangles, Angles of elevation and depression, Evaluating trigonometric ratios of any angles

  • Trigonometric waveforms
    Graphs of trigonometric functions, Angles of any magnitude, The production of a sine and cosine wave, Sine and cosine curves, Sinusoidal form A sin(?t ± a), Assignment 9

  • Cartesian and polar co-ordinates
    Introduction, Changing from Cartesian into polar co-ordinates, Changing from polar into Cartesian co-ordinates, Use of R?P and P ?R functions on calculators

  • Areas of plane figures
    Mensuration, Properties of quadrilaterals, Worked problems on areas of plane figures, Further worked problems on areas of plane figures, Areas of similar shapes, Assignment 10

  • The circle
    Introduction, Properties of circles, Arc length and area of a sector, The equation of a circle

  • Volumes of common solids
    Volumes and surface areas of regular solids, Worked problems on volumes and surface areas of regular solids, Further worked problems on volumes and surface areas of regular solids, Volumes and surface areas of frusta of pyramids and cones, Volumes of similar shapes, Assignment 11

  • Irregular areas and volumes and mean values of waveforms
    Areas of irregular figures, Volumes of irregular solids, The mean or average value of a waveform

  • Triangles and some practical applications
    Sine and cosine rules, Area of any triangle, Worked problems on the solution of triangles and their areas, Further worked problems on the solution of triangles and their areas, Practical situations involving trigonometry, Further practical situations involving trigonometry, Assignment 12

  • Vectors
    Introduction, Vector addition, Resolution of vectors, Vector subtraction, Relative velocity

  • Adding of waveforms
    Combination of two periodic functions, Plotting periodic functions, Determining resultant phasors by calculation

  • Number sequences
    Simple sequences, The n’th term of a series, Arithmetic progressions, Worked problems on arithmetic progression, Further worked problems on arithmetic progressions, Geometric progressions, Worked problems on geometric progressions, Further worked problems on geometric progressions, Assignment 13

  • Presentation of statistical data
    Some statistical terminology, Presentation of ungrouped data, Presentation of grouped data

  • Measures of central tendency and dispersion
    Measures of central tendency, Mean, median and mode for discrete data, Mean, median and mode for grouped data, Standard deviation, Quartiles, deciles and percentiles

  • Probability
    Introduction to probability, Laws of probability, Worked problems on probability, Further worked problems on probability, Assignment 14

  • Introduction to differentiation
    Introduction to calculus, Functional notation, The gradient of a curve, Differentiation from first principles, Differentiation of y = ax n by the general rule, Differentiation of sine and cosine functions, Differentiation of eax and ln ax, Summary of standard derivatives, Successive differentiation, Rates of change

  • Introduction to integration
    The process of integration, The general solution of integrals of the form axn, Standard integrals, Definite integrals, Area under a curve

  • List of formulae

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