Welcome to the Companion Website for Engineering Mathematics Through Applications Engineering by Kuldeep Singh

Contents

INTRODUCTION Arithmetic for Engineers 

• Whole numbers 
• Indices 
• Numbers 
• Fractions 
• Arithmetic of fractions 
• Decimals 
• Powers of 10 Conversion 
• Arithmetical operations 
• Percentages 
• Ratios  

1 Engineering Formulae 

• Substitution and transposition 
• Transposing engineering formulae 
• Indices 
• Dimensional analysis
• Expansion of brackets 
• Factorization 
• Quadratic equations 
• Simultaneous equations 

2 Visualising Engineering Formulae 

• Graphs 
• Applications of graphs 
• Quadratic graphs 
• Quadratics revisited 
• Further graphs 
• Binomial expansion 

3 Functions in Engineering 

• Concepts of functions 
• Inverse Functions
• Graphs of functions 
• Combinations of functions 
• Limits of functions 
• Modulus function 

4 Trigonometry and Waveforms 

• Trigonometric functions 
• Angles and graphs 
• Trigonometric equations 
• Trigonometric rules 
• Radians 
• Wave theory 
• Trigonometric identities 
• Applications of identities 
• Conversion 

5 Logarithmic, Exponential and Hyperbolic Functions 

• Indices revisited 
• The exponential function 
• The logarithmic function 
• Applications of logarithms 
• Hyperbolic functions 

6 Differentiation 

• The derivative 
• Derivatives of functions 
• Chain rule revisited 
• Product and quotient rules 
• Higher derivatives 
• Parametric differentiation 
• Implicit and logarithmic differentiation 

7 Engineering Applications of Differentiation 

• Curve sketching 
• Optimization problems 
• First derivative test 
• Applications to kinematics 
• Tangents and normals 
• Series expansion 
• Binomial revisited 
• Numerical solution of equations 

8 Integration 

• Integrals 
• Integration by substitution 
• Definite integrals 
• Integration by parts 
• Algebraic fractions 
• Integration of algebraic fractions 
• Integration by substitution revisited 
• Trigonometric techniques for integration 

9 Engineering Applications of Integration 

• Trapezium rule 
• Further numerical integration 
• Engineering applications 
• Applications in mechanics 
• Miscellaneous applications of integration 

10 Complex Numbers 

• Arithmetic of complex numbers 
• Representation of complex numbers 
• Multiplication and division in polar form 
• Powers and roots of complex numbers 
• Exponential form of complex numbers  

11 Matrices 

• Manipulation of matrices 
• Applications 
• 3 x 3 matrices 
• Gaussian elimination 
• Linear equations 
• Eigenvalues and eigenvectors 
• Applications in heat transfer 

12 Vectors 

• Vector representation 
• Vectors in Cartesian co-ordinates 
• Three-dimensional vectors 
• Scalar products 
• Vector products 

13 First Order Differential Equations 

• Solving differential equations 
• Using integrating factors 
• Applications to electrical principles 
• Further engineering applications 
• Euler’s numerical method 
• Improved Euler’s method 
• Fourth order Runge-Kutta  

14 Second Order Linear Differential Equations 

• Homogeneous differential equations 
• Engineering applications 
• Non-homogeneous (inhomogeneous) differential equations 
• Particular solutions 

15 Partial Differentiation 

• Partial derivatives 
• Applications 
• Optimization  

16 Probability and Statistics 

• Data representation 
• Data summaries 
• Probability rules 
• Permutations and combinations 
• Binomial distribution 
• Properties of discrete random variables 
• Applications of continuous random variables 
• Normal distribution  

Solutions 

Appendix I: Standard Normal Distribution Table

Index