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Submit a ProposalMathematics for Engineers
One Line 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.
Audience
Undergraduate, graduate, and post-graduate students and educators looking for a comprehensive introduction to the application of mathematics in the engineering field, as well as industry professionals looking for a quick reference
Undergraduate, graduate, and post-graduate students and educators looking for a comprehensive introduction to the application of mathematics in the engineering field, as well as industry professionals looking for a quick reference
Description
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.
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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.
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Author / Editor Details
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.
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.
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.
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.
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Table of Contents
Preface
1. Fractions, Decimals, and Percentages
1.1 Introduction
1.2 Fractions
1.2.1 Definition of Fractions
1.2.2 Types of Fractions
1.2.3 Simplest Form or Fraction in Lowest Term
1.2.4 Comparing Fractions
1.2.5 Algebra of Fractions
1.3 Decimals and Percentages
1.4 Check Your Knowledge (MCQ)
1.5 Activity/Experiment
2. Ratio and Proportion
2.1 Introduction
2.2 Ratios
2.2.1 Definition
2.2.2 Simplifying Ratio
2.2.3 Equivalent Ratio
2.2.4 Methods for Finding a Ratio
2.2.5 Methods to Calculate Increasing and Decreasing in Each Ratio
2.3 Rate
2.3.1 Unit Rates
2.4 Proportions
2.4.1 Direct Proportion
2.4.2 Inverse Proportion
2.5 Activity/Experiment—Ratio
2.6 Activity/Experiment—Proportions
3. Two-Dimensional Geometry
3.1 Introduction
3.2 Geometry
3.2.1 One-Dimensional Geometry
3.2.2 Two-Dimensional Geometry
3.3 Area and Perimeter of 2D Shapes
3.3.1 Perimeter
3.3.2 Area of Two-Dimensional Geometry
3.3.3 Finding the Area of Shapes by Counting the Square
3.4 Curved Plane Figures
3.4.1 Circles
3.4.2 Semi-Circles
3.4.3 Quarter Circles (QUADRANT)
3.5 Perimeter and Area of Irregular Polygons and Composite Shapes
3.6 Check Your Knowledge (MCQ)
3.7 Activity/Experiment
4. Three-Dimensional Geometry
4.1 Introduction
4.2 Nets of Three-Dimensional Shapes
4.3 Surface Area and Volume of Three-Dimensional Shapes
4.3.1 A Cube
4.3.2 A Cuboid
4.3.3 Cylinder
4.3.4 Cone
4.3.5 Sphere
4.3.6 Hemisphere
4.3.7 Prism
4.3.8 Pyramid
4.4 Compounded Shapes
Level 2: Exercise 4.2 Practice Questions
Level 3: Exercise 4.3 Practice Questions
4.5 Check Your Knowledge (MCQ)
4.6 PBL/Experiment
5. Algebra and Graphs
5.1 Introduction
5.1.1 Early History of Algebra
5.1.2 Modern History of Algebra
5.1.3 Algebra
5.1.4 Algebra: What Is It?
5.1.5 Why Should We Study Algebra?
5.2 Algebraic Expressions
5.2.1 How are Expressions Formed?
5.2.2 Arithmetic Operators
5.3 Transposition of Formulae
5.4 Algebraic Fractions
5.4.1 How Can We Calculate Two Algebraic Fractions?
5.5 Simple Linear Equation
5.5.1 Formation of Algebraic Equation
5.5.2 How to Solve Linear Algebraic Equations?
5.6 Quadratic Equations
5.6.1 Solving Quadratic Equation
5.7 Simultaneous Equations
5.8 Graphs of Algebraic Functions
5.8.1 Graph of Linear Equations
5.8.2 Quadratic Equations Graphs
5.8.3 Simultaneous Equations
5.9 Exponential Functions
5.10 Check Your Knowledge (MCQ)
5.11 Activity/Experiment
6. Exponent and Logarithm
6.1 Introduction
6.2 Indices
6.2.1 Definition: Indices—[Concept: Repeated Multiplication]
6.2.2 Rules of Indices
6.3 Logarithms
6.3.1 Definition
6.3.2 Types of Logarithms [Depending on Base]
6.3.3 Rules of Logarithm
6.3.4 Characteristics and Mantissa of Logarithms
6.3.5 Properties of Logarithms
6.4 Check Your Knowledge (MCQ)
7. Trigonometry
7.1 Introduction
7.2 Pythagoras Theorem
7.3 Trigonometric Ratio
7.4 Trigonometry Table
7.4.1 Angles
7.5 The Angle of Elevation and Angle of Depression
7.5.1 Definition
7.6 Trigonometric Equation
7.6.1 Definition
7.6.2 Oriented Angle
7.6.3 Identities
7.6.4 Quadrants
7.7 Radian Measure
7.7.1 Converting Between Radians and Degrees
7.7.2 Area of Sector
7.8 The Sine and Cosine Rules
7.8.1 The Sine Rule
7.8.2 The Cosine Rule
7.8.3 Ambiguous Case
7.9 Steps to Use Calculator for Trigonometry
7.10 Check Your Knowledge (MCQ)
8. Differential Calculus
8.1 Introduction
8.2 Functions
8.2.1 Types of Functions
8.3 Limit and Continuity
8.3.1 Definition
8.3.2 One-Sided Limits
8.3.3 Continuity
8.4 Derivatives
8.4.1 Definition
8.4.2 List of Formulae
8.5 Differentiation Rules
8.6 Derivatives of Logarithmic and Exponential Function
8.6.1 Laws of Exponents
8.6.2 Rules of Logarithm
8.6.3 Rules for Finding the Derivative of Log and Exp
8.7 Derivatives of Trigonometric Function
8.8 Application of Derivatives
8.9 Maxima and Minima
8.10 Check Your Knowledge (MCQ)
8.11 Activity/Experiment
9. Integral Calculus
9.1 Introduction
9.2 Integration Rules
9.3 Integration by Parts
9.4 Integration by Partial Fraction
9.5 Definite Integral
9.6 Check Your Knowledge (MCQ)
10. Probability
10.1 Introduction
10.2 Fundamental Principle of Counting
10.3 Permutations and Combinations
10.3.1 Permutation
10.3.2 Combinations
10.4 Simple Probability
10.4.1 Probability of an Event
10.4.2 Equally Likely Events
10.5 Conditional Probability
10.6 Probability Sample Space Diagram
10.7 Probability Tree Diagram
10.8 Probability Using Venn Diagram
10.8 Check Your Knowledge (MCQ)
10.9 PBL/Experiment (Experimental Probability Vs. Theoretical Probability)
Answers
About the Editors
Index
Back to Top
Preface
1. Fractions, Decimals, and Percentages
1.1 Introduction
1.2 Fractions
1.2.1 Definition of Fractions
1.2.2 Types of Fractions
1.2.3 Simplest Form or Fraction in Lowest Term
1.2.4 Comparing Fractions
1.2.5 Algebra of Fractions
1.3 Decimals and Percentages
1.4 Check Your Knowledge (MCQ)
1.5 Activity/Experiment
2. Ratio and Proportion
2.1 Introduction
2.2 Ratios
2.2.1 Definition
2.2.2 Simplifying Ratio
2.2.3 Equivalent Ratio
2.2.4 Methods for Finding a Ratio
2.2.5 Methods to Calculate Increasing and Decreasing in Each Ratio
2.3 Rate
2.3.1 Unit Rates
2.4 Proportions
2.4.1 Direct Proportion
2.4.2 Inverse Proportion
2.5 Activity/Experiment—Ratio
2.6 Activity/Experiment—Proportions
3. Two-Dimensional Geometry
3.1 Introduction
3.2 Geometry
3.2.1 One-Dimensional Geometry
3.2.2 Two-Dimensional Geometry
3.3 Area and Perimeter of 2D Shapes
3.3.1 Perimeter
3.3.2 Area of Two-Dimensional Geometry
3.3.3 Finding the Area of Shapes by Counting the Square
3.4 Curved Plane Figures
3.4.1 Circles
3.4.2 Semi-Circles
3.4.3 Quarter Circles (QUADRANT)
3.5 Perimeter and Area of Irregular Polygons and Composite Shapes
3.6 Check Your Knowledge (MCQ)
3.7 Activity/Experiment
4. Three-Dimensional Geometry
4.1 Introduction
4.2 Nets of Three-Dimensional Shapes
4.3 Surface Area and Volume of Three-Dimensional Shapes
4.3.1 A Cube
4.3.2 A Cuboid
4.3.3 Cylinder
4.3.4 Cone
4.3.5 Sphere
4.3.6 Hemisphere
4.3.7 Prism
4.3.8 Pyramid
4.4 Compounded Shapes
Level 2: Exercise 4.2 Practice Questions
Level 3: Exercise 4.3 Practice Questions
4.5 Check Your Knowledge (MCQ)
4.6 PBL/Experiment
5. Algebra and Graphs
5.1 Introduction
5.1.1 Early History of Algebra
5.1.2 Modern History of Algebra
5.1.3 Algebra
5.1.4 Algebra: What Is It?
5.1.5 Why Should We Study Algebra?
5.2 Algebraic Expressions
5.2.1 How are Expressions Formed?
5.2.2 Arithmetic Operators
5.3 Transposition of Formulae
5.4 Algebraic Fractions
5.4.1 How Can We Calculate Two Algebraic Fractions?
5.5 Simple Linear Equation
5.5.1 Formation of Algebraic Equation
5.5.2 How to Solve Linear Algebraic Equations?
5.6 Quadratic Equations
5.6.1 Solving Quadratic Equation
5.7 Simultaneous Equations
5.8 Graphs of Algebraic Functions
5.8.1 Graph of Linear Equations
5.8.2 Quadratic Equations Graphs
5.8.3 Simultaneous Equations
5.9 Exponential Functions
5.10 Check Your Knowledge (MCQ)
5.11 Activity/Experiment
6. Exponent and Logarithm
6.1 Introduction
6.2 Indices
6.2.1 Definition: Indices—[Concept: Repeated Multiplication]
6.2.2 Rules of Indices
6.3 Logarithms
6.3.1 Definition
6.3.2 Types of Logarithms [Depending on Base]
6.3.3 Rules of Logarithm
6.3.4 Characteristics and Mantissa of Logarithms
6.3.5 Properties of Logarithms
6.4 Check Your Knowledge (MCQ)
7. Trigonometry
7.1 Introduction
7.2 Pythagoras Theorem
7.3 Trigonometric Ratio
7.4 Trigonometry Table
7.4.1 Angles
7.5 The Angle of Elevation and Angle of Depression
7.5.1 Definition
7.6 Trigonometric Equation
7.6.1 Definition
7.6.2 Oriented Angle
7.6.3 Identities
7.6.4 Quadrants
7.7 Radian Measure
7.7.1 Converting Between Radians and Degrees
7.7.2 Area of Sector
7.8 The Sine and Cosine Rules
7.8.1 The Sine Rule
7.8.2 The Cosine Rule
7.8.3 Ambiguous Case
7.9 Steps to Use Calculator for Trigonometry
7.10 Check Your Knowledge (MCQ)
8. Differential Calculus
8.1 Introduction
8.2 Functions
8.2.1 Types of Functions
8.3 Limit and Continuity
8.3.1 Definition
8.3.2 One-Sided Limits
8.3.3 Continuity
8.4 Derivatives
8.4.1 Definition
8.4.2 List of Formulae
8.5 Differentiation Rules
8.6 Derivatives of Logarithmic and Exponential Function
8.6.1 Laws of Exponents
8.6.2 Rules of Logarithm
8.6.3 Rules for Finding the Derivative of Log and Exp
8.7 Derivatives of Trigonometric Function
8.8 Application of Derivatives
8.9 Maxima and Minima
8.10 Check Your Knowledge (MCQ)
8.11 Activity/Experiment
9. Integral Calculus
9.1 Introduction
9.2 Integration Rules
9.3 Integration by Parts
9.4 Integration by Partial Fraction
9.5 Definite Integral
9.6 Check Your Knowledge (MCQ)
10. Probability
10.1 Introduction
10.2 Fundamental Principle of Counting
10.3 Permutations and Combinations
10.3.1 Permutation
10.3.2 Combinations
10.4 Simple Probability
10.4.1 Probability of an Event
10.4.2 Equally Likely Events
10.5 Conditional Probability
10.6 Probability Sample Space Diagram
10.7 Probability Tree Diagram
10.8 Probability Using Venn Diagram
10.8 Check Your Knowledge (MCQ)
10.9 PBL/Experiment (Experimental Probability Vs. Theoretical Probability)
Answers
About the Editors
Index
Back to Top