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(For fully worked solutions from the 1st edition click here.)

**INTRODUCTION Arithmetic for Engineers**

- Intro(a) : Whole numbers
- Intro(b) : Indices
- Intro(c ): Numbers
- Intro(d) : Fractions
- Intro(e ): Arithmetic of fractions
- Intro(f) : Decimals
- Intro(g): Powers of 10
- Intro(h): Conversion
- Intro(i): Arithmetical operations
- Intro(j): Percentages
- Intro(k) : Ratios
- Intro (Miscellaneous exercises)

- 1(a) Substitution and transposition
- 1(b) Transposing engineering formulae
- 1(c) Indices
- 1(d) Dimensional Analysis
- 1(e) Expansion of brackets
- 1(f) Factorization
- 1(g) Quadratic equations
- 1(h) Simultaneous equations
- 1 Examination Questions
- 1 (Miscellaneous exercises)

- 2(a) Graphs
- 2(b) Applications of graphs
- 2 (c) Quadratic graphs
- 2(d) Quadratics revisited
- 2(e) Further graphs
- 2(f) Binomial expansion
- 2 Examination Questions
- 2 (Miscellaneous exercises)

- 3(a) Concepts of functions
- 3(b) Inverse Functions
- 3(c) Graphs of functions
- 3(d) Combinations of functions
- 3(e) Limits of functions
- 3(f) Modulus function
- 3 Examination Questions
- 3 (Miscellaneous exercises)

- 4(a) Trigonometric functions
- 4(b) Angles and graphs
- 4(c) Trigonometric equations
- 4(d) Trigonometric rules
- 4(e) Radians
- 4(f) Wave theory
- 4(g) Trigonometric identities
- 4(h) Applications of identities
- 4(I) Conversion
- 4 Examination Questions
- 4 (Miscellaneous exercises)

- 5(a) Indices revisited
- 5(b) The exponential function
- 5(c) The logarithmic function
- 5(d) Applications of logarithms
- 5(e) Hyperbolic functions
- 5 Examination Questions
- 5 (Miscellaneous exercises)

- 6(a) The derivative
- 6(b) Derivatives of functions
- 6(c) Chain rule revisited
- 6(d) Product and quotient rules
- 6(e) Higher derivatives
- 6(f) Parametric differentiation
- 6(g) Implicit and logarithmic differentiation
- 6 Examination Questions
- 6 (Miscellaneous exercises)

- 7(a) Curve sketching
- 7(b) Optimization problems
- 7(c) First derivative test
- 7(d) Applications to kinematics
- 7(e) Tangents and normals
- 7(f) Series expansion
- 7(g) Binomial revisited
- 7(h) Introduction to infinite series
- 7(i) Numerical solution of equations
- 7 Examination Questions
- 7 (Miscellaneous exercises)

- 8(a) Introduction to integration
- 8(b) Rules of integration
- 8(c) Integration by substitution
- 8(d) Applications of integration
- 8(e) Integration by parts
- 8(f) Algebraic fractions
- 8(g) Integration of algebraic fractions
- 8(h) Integration by substitution revisited
- 8(i) Trigonometric techniques for integration
- 8 Examination Questions
- 8 (Miscellaneous exercises)

- 9(a) Trapezium rule
- 9(b) Further numerical integration
- 9(c) Engineering applications
- 9(d) Applications in mechanics
- 9(e) Miscellaneous applications of integration
- 9 Examination Questions
- 9 (Miscellaneous exercises)

- 10(a) Arithmetic of complex numbers
- 10(b) Representation of complex numbers
- 10(c) Multiplication and division in polar form
- 10(d) Powers and roots of complex numbers
- 10(e) Exponential form of complex numbers
- 10 Examination Questions
- 10 (Miscellaneous exercises)

- 11(a) Manipulation of matrices
- 11(b) Applications
- 11(c) 3 x 3 matrices
- 11(d) Gaussian elimination
- 11(e) Linear equations
- 11(f) Eigenvalues and eigenvectors
- 11(g) Diagonalization
- 11 Examination Questions
- 11 (Miscellaneous exercises)

- 12(a) Vector representation
- 12(b) Vectors in Cartesian co-ordinates
- 12(c) Three-dimensional vectors
- 12(d) Scalar products
- 12(e) Vector products
- 12 Examination Questions
- 12 (Miscellaneous exercises)

- 13(a) Solving differential equations
- 13(b) Using integrating factors
- 13(c) Applications to electrical principles
- 13(d) Further engineering applications
- 13(e) Euler’s numerical method
- 13(f) Improved Euler’s method
- 13(g) Fourth order Runge-Kutta
- 13 Examination Questions
- 13 (Miscellaneous exercises)

- 14(a) Homogeneous differential equations
- 14(b) Engineering applications
- 14(c) Non-homogeneous (inhomogeneous) differential equations
- 14(d) Particular solutions
- 14 Examination Questions
- 14 (Miscellaneous exercises)

- 15(a) Partial derivatives
- 15(b) Applications
- 15(c) Optimization
- 15 Examination Questions
- 15 (Miscellaneous exercises)

- 16(a) Data representation
- 16(b) Data summaries
- 16(c) Probability rules
- 16(d) Permutations and combinations
- 16(e) Binomial distribution
- 16(f) Properties of discrete random variables
- 16(g) Applications of continuous random variables
- 16(h) Normal distribution
- 16 Examination Questions
- 16 (Miscellaneous exercises)

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