Fully worked solutions

The fully worked solutions for all the exercises in Engineering Mathematics through Applications are available to download onto your PC. Simply right click the links and 'save as' to your harddrive.

(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 Engineering Formulae

• 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 Visualising Engineering Formulae

• 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 Functions in Engineering

• 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 Trigonometry and Waveforms

• 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 Logarithmic, Exponential and Hyperbolic Functions

• 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 Differentiation

• 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 Engineering Applications of Differentiation

• 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 Integration

• 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 Engineering Applications of Integration

• 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 Complex Numbers

• 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 Matrices

• 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 Vectors

• 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 First Order Differential Equations

• 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 Second Order Linear Differential Equations

• 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 Partial Differentiation

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

16 Probability and Statistics

• 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)