Mathematics for Engineers

Ritu Shrivastava, PhD, is an assistant professor in the Mathematics Department at Bahrain Polytechnic, India with over 20 years of teaching experience. She has published ten articles in national and international journals and conferences of repute. Her teaching interests include applied mathematics, calculus, algebra, coordinate geometry, trigonometry, and probability. Ramakant Bhardwaj, PhD, is professor in the Mathematics Department at the Amity Institute of Applied Sciences, Kolkata, India with over 17 years of teaching experience. He has over 200 publications in national and international journals of repute. His research interest include nonlinear analysis, mathematical modeling, phase transition study, and computer oriented mathematics. Satyendra Narayan, PhD, is a professor in the Applied Science and Technology Department at Sheridan College, Canada with over 25 years of research experience. He has published over 30 articles and worked on a projects with a number of institutions, including the United Nations Development Programme. His research interests include applied computing, geosciences, and electrical monitoring of subsurface processes.

• Preface xi1 Fractions, Decimals, and Percentages 11.1 Introduction 11.2 Fractions 21.2.1 Definition of Fractions 21.2.2 Types of Fractions 21.2.3 Simplest Form or Fraction in Lowest Term 61.2.4 Comparing Fractions 71.2.5 Algebra of Fractions 81.3 Decimals and Percentages 251.4 Check Your Knowledge (MCQ) 311.5 Activity/Experiment 342 Ratio and Proportion 372.1 Introduction 372.2 Ratios 382.2.1 Definition 382.2.2 Simplifying Ratio 382.2.3 Equivalent Ratio 382.2.4 Methods for Finding a Ratio 392.2.5 Methods to Calculate Increasing and Decreasing in Each Ratio 402.3 Rate 452.3.1 Unit Rates 462.4 Proportions 462.4.1 Direct Proportion 472.4.2 Inverse Proportion 492.5 Activity/Experiment—Ratio 552.6 Activity/Experiment—Proportions 573 Two-Dimensional Geometry 593.1 Introduction 593.2 Geometry 603.2.1 One-Dimensional Geometry 603.2.2 Two-Dimensional Geometry 603.3 Area and Perimeter of 2D Shapes 603.3.1 Perimeter 613.3.2 Area of Two-Dimensional Geometry 693.3.3 Finding the Area of Shapes by Counting the Square 693.4 Curved Plane Figures 823.4.1 Circles 823.4.2 Semi-Circles 843.4.3 Quarter Circles (QUADRANT) 843.5 Perimeter and Area of Irregular Polygons and Composite Shapes 883.6 Check Your Knowledge (MCQ) 1163.7 Activity/Experiment 1184 Three-Dimensional Geometry 1214.1 Introduction 1214.2 Nets of Three-Dimensional Shapes 1224.3 Surface Area and Volume of Three-Dimensional Shapes 1244.3.1 A Cube 1304.3.2 A Cuboid 1334.3.3 Cylinder 1414.3.4 Cone 1454.3.5 Sphere 1504.3.6 Hemisphere 1514.3.7 Prism 1534.3.8 Pyramid 1554.4 Compounded Shapes 1564.5 Check Your Knowledge (MCQ) 1654.6 PBL/Experiment 1695 Algebra and Graphs 1715.1 Introduction 1715.1.1 Early History of Algebra 1725.1.2 Modern History of Algebra 1725.1.3 Algebra 1725.1.4 Algebra: What Is It? 1735.1.5 Why Should We Study Algebra? 1735.2 Algebraic Expressions 1735.2.1 How are Expressions Formed? 1735.2.2 Arithmetic Operators 1745.3 Transposition of Formulae 1775.4 Algebraic Fractions 1815.4.1 How Can We Calculate Two Algebraic Fractions? 1815.5 Simple Linear Equation 1875.5.1 Formation of Algebraic Equation 1875.5.2 How to Solve Linear Algebraic Equations? 1885.6 Quadratic Equations 1935.6.1 Solving Quadratic Equation 1935.7 Simultaneous Equations 2005.8 Graphs of Algebraic Functions 2295.8.1 Graph of Linear Equations 2295.8.2 Quadratic Equations Graphs 2345.8.3 Simultaneous Equations 2405.9 Exponential Functions 2425.10 Check Your Knowledge (MCQ) 2455.11 Activity/Experiment 2476 Exponent and Logarithm 2496.1 Introduction 2496.2 Indices 2506.2.1 Definition: Indices—[Concept: Repeated Multiplication] 2506.2.2 Rules of Indices 2516.3 Logarithms 2566.3.1 Definition 2566.3.2 Types of Logarithms [Depending on Base] 2576.3.3 Rules of Logarithm 2586.3.4 Characteristics and Mantissa of Logarithms 2596.3.5 Properties of Logarithms 2606.4 Check Your Knowledge (MCQ) 2637 Trigonometry 2677.1 Introduction 2687.2 Pythagoras Theorem 2687.3 Trigonometric Ratio 2727.4 Trigonometry Table 2747.4.1 Angles 2757.5 The Angle of Elevation and Angle of Depression 2847.5.1 Definition 2847.6 Trigonometric Equation 2887.6.1 Definition 2887.6.2 Oriented Angle 2887.6.3 Identities 2897.6.4 Quadrants 2917.7 Radian Measure 2977.7.1 Converting Between Radians and Degrees 2997.7.2 Area of Sector 3017.8 The Sine and Cosine Rules 3077.8.1 The Sine Rule 3077.8.2 The Cosine Rule 3087.8.3 Ambiguous Case 3097.9 Steps to Use Calculator for Trigonometry 3197.10 Check Your Knowledge (MCQ) 3218 Differential Calculus 3258.1 Introduction 3258.2 Functions 3278.2.1 Types of Functions 3278.3 Limit and Continuity 3288.3.1 Definition 3288.3.2 One-Sided Limits 3298.3.3 Continuity 3298.4 Derivatives 3308.4.1 Definition 3308.4.2 List of Formulae 3308.5 Differentiation Rules 3318.6 Derivatives of Logarithmic and Exponential Function 3448.6.1 Laws of Exponents 3448.6.2 Rules of Logarithm 3448.6.3 Rules for Finding the Derivative of Log and Exp 3448.7 Derivatives of Trigonometric Function 3518.8 Application of Derivatives 3578.9 Maxima and Minima 3588.10 Check Your Knowledge (MCQ) 3688.11 Activity/Experiment 3699 Integral Calculus 3719.1 Introduction 3719.2 Integration Rules 3729.3 Integration by Parts 3829.4 Integration by Partial Fraction 3869.5 Definite Integral 3879.6 Check Your Knowledge (MCQ) 43010 Probability 43510.1 Introduction 43510.2 Fundamental Principle of Counting 43810.3 Permutations and Combinations 44110.3.1 Permutation 44210.3.2 Combinations 44410.4 Simple Probability 44610.4.1 Probability of an Event 44810.4.2 Equally Likely Events 44810.5 Conditional Probability 45010.6 Probability Sample Space Diagram 45410.7 Probability Tree Diagram 45610.8 Probability Using Venn Diagram 45810.8 Check Your Knowledge (MCQ) 46610.9 PBL/Experiment (Experimental Probability Vs. Theoretical Probability) 469Answers 471About the Authors 539Index 541