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Full Description
Mathematics for Engineers serves as a comprehensive guide on the basics of mathematics and their applications in engineering for students and seasoned professionals alike.
Mathematics for Engineers is designed to help students develop mathematical proficiencies, which are required in technical courses and careers involving strategic mathematical competence and adaptive reasoning. This volume also acts as a reference for professionals in engineering who need a refresher for their technical math skills. Through this book, students and professionals in the engineering discipline will build a capacity and expand their fundamental mathematical skills for logical thought, reflection, explanation, and justification in the field of applied science. This book is designed for general use for science and engineering students across the globe.
The book effectively compiles important information in one place alongside examples and practice problems with application and practice based questions. Emphasis is placed on the application of mathematics in appropriate context and modeling of real-world situations. By the end of this book, students and professionals in the engineering discipline will be able to present and process their mathematical reasoning and conclusions numerically, graphically, symbolically, and verbally.
Contents
Preface xi
1 Fractions, Decimals, and Percentages 1
1.1 Introduction 1
1.2 Fractions 2
1.3 Decimals and Percentages 23
1.4 Check Your Knowledge (MCQ) 31
1.5 Activity/Experiment 34
2 Ratio and Proportion 37
2.1 Introduction 37
2.2 Ratios 38
2.3 Rate 45
2.4 Proportions 36
2.5 Activity/Experiment--Ratio 55
2.6 Activity/Experiment--Proportions 57
3 Two-Dimensional Geometry 59
3.1 Introduction 59
3.2 Geometry 60
3.3 Area and Perimeter of 2D Shapes 60
3.4 Curved Plane Figures 82
3.5 Perimeter and Area of Irregular Polygons and Composite Shapes 88
3.6 Check Your Knowledge (MCQ) 116
3.7 Activity/Experiment 118
4 Three-Dimensional Geometry 121
4.1 Introduction 121
4.2 Nets of Three-Dimensional Shapes 122
4.3 Surface Area and Volume of Three-Dimensional Shapes 124
4.4 Compounded Shapes 156
4.5 Check Your Knowledge (MCQ) 165
4.6 PBL/Experiment 169
5 Algebra and Graphs 171
5.1 Introduction 171
5.2 Algebraic Expressions 173
5.3 Transposition of Formulae 177
5.4 Algebraic Fractions 181
5.5 Simple Linear Equation 187
5.6 Quadratic Equations 193
5.7 Simultaneous Equations 200
5.8 Graphs of Algebraic Functions 229
5.9 Exponential Functions 242
5.10 Check Your Knowledge (MCQ) 245
5.11 Activity/Experiment 247
6 Exponent and Logarithm 249
6.1 Introduction 249
6.2 Indices 250
6.3 Logarithms 256
6.4 Check Your Knowledge (MCQ) 263
7 Trigonometry 267
7.1 Introduction 268
7.2 Pythagoras Theorem 268
7.3 Trigonometric Ratio 272
7.4 Trigonometry Table 274
7.5 The Angle of Elevation and Angle of Depression 284
7.6 Trigonometric Equation 288
7.7 Radian Measure 297
7.8 The Sine and Cosine Rules 307
7.9 Steps to Use Calculator for Trigonometry 319
8 Differential Calculus 325
8.1 Introduction 325
8.2 Functions 327
8.3 Limit and Continuity 328
8.4 Derivatives 330
8.5 Differentiation Rules 331
8.6 Derivatives of Logarithmic and Exponential Function 344
8.7 Derivatives of Trigonometric Function 351
8.8 Application of Derivatives 357
8.9 Maxima and Minima 358
8.10 Check Your Knowledge (MCQ) 368
8.11 Activity/Experiment 369
9 Integral Calculus 371
9.1 Introduction 371
9.2 Integration Rules 372
9.3 Integration by Parts 382
9.4 Integration by Partial Fraction 386
9.5 Definite Integral 387
9.6 Check Your Knowledge (MCQ) 430
10 Probability 435
10.1 Introduction 435
10.2 Fundamental Principle of Counting 438
10.3 Permutations and Combinations 441
10.4 Simple Probability 446
10.5 Conditional Probability 450
10.6 Probability Sample Space Diagram 454
10.7 Probability Tree Diagram 456
10.8 Probability Using Venn Diagram 458
10.8 Check Your Knowledge (MCQ) 466
10.9 PBL/Experiment (Experimental Probability Vs. Theoretical Probability) 469
Answers 471
About the Authors 539
Index 541
