• Preface

  Acknowledgement

   

  Chapter 1 MATLAB Preliminaries

                  1.1 Introduction to MATLAB

                                  1.1.1 Features and Uses of MATLAB

                                  1.1.2 Installation

                  1.2 Starting MATLAB

                                  1.2.1 Logging On

                                  1.2.2 Invoking MATLAB

                                  1.2.3 Quitting MATLAB

                  1.3 MATLAB WINDOWS

                                  1.3.1 MATLAB Command Window

                  1.4 Elementary Mathematics Built-in Functions

                                  1.4.1 Trigonometric Functions

                                  1.4.2 Inverse Trigonometric Functions

                                  1.4.3 Hyperbolic Functions

                                  1.4.4 Inverse Hyperbolic Functions

                                  1.4.5 Logarithmic and Exponential Functions

                                  1.4.6 Absolute Value Functions

                  1.5 MATLAB Help

                                  1.5.1 The Semicolon

                                  1.5.2 Typing %

                                  1.5.3 clc Command

                                  1.5.4 clear Command

                                  1.5.5 The Colon

                                  1.5.6 The Three Dots

                  1.6 Making Correction

                  1.7 Online Resources

                  1.8 MATLAB as a Scientific Calculator

                                  1.8.1 Creating MATLAB Variables

                                  1.8.2 Variable Names

                                  1.8.3 Predefined Variables

                  1.9 Saving and Loading

                                  1.9.1 diary()

                  1.10 M-FILE – Script Files

   

  Chapter 2 Matrix Algebra and Matlab

                  2.1 Introduction

                                  2.1.1 Generating Matrices in MATLAB

                                  2.1.2 Dimension of a Matrix [Size of a Matrix]

                  2.2 Special Matrices

                                  2.2.1 Null Matrix or Zero Matrix

                                  2.2.2 Diagonal Matrix

                                  2.2.3 Identity Matrix or Unit Matrix

                                  2.2.4 Upper Triangular Matrix

                                  2.2.5 Lower Triangular Matrix

                                  2.2.6 Symmetric Matrix

                  2.3 Matrix Operations

                                  2.3.1 Transpose of a Matrix

                                  2.3.2 Addition and Subtraction of Matrices

                                  2.3.3 Scalar Multiplication

                  2.4 Matrix Multiplication

                                  2.4.1 Matrix Multiplication Using MATLAB

                                  2.4.2 Properties of Matrix Multiplication

                                  2.4.3 Power of a Matrix

                  2.5 Inverse of a 2×2 Matrix

                                  2.5.1 Finding the Inverse of 2×2 Matrix

                                  2.5.2 Properties of Inverse Matrix

                                  2.5.3 2 × 2 Determinant (2nd Order)

                                  2.5.4 3×3 Determinant (3rd Order)

                                  2.5.5 Singular Matrix

                                  2.5.6 Non-Singular Matrix

                                  2.5.7 Adjoint of a Matrix

                  2.6 Inverse of the 3×3 Matrix

                                  2.6.1 Inverse of the 3×3 Matrix by Adjoint Method [or] Cofactor Expansion Method

                                  2.6.2 Inverse of the 3 × 3 Matrix Using an Algorithm [Gauss – Jordan Reduction]

                  2.7 Matrix Inversion Method and System of Linear Equations

                                  2.7.1 Matrix Inversion Method to Solve a Linear System

                                  2.7.2 Solving a Linear System Using Matrix Inversion Method

                  2.8 Gauss’ Method or Gaussian Elimination Method

                                  2.8.1 Gaussian Elimination by MATLAB

                  2.9 Cramer’s Rule and System of Linear Equations of n Unknowns

                                  2.9.1 Solving Two Variable System with Unique Solutions by Cramer’s Rule

                                  2.9.2 Solving Three Variable System with Unique Solutions by Cramer’s Rule

                                  2.9.3 Cramer’s Rule by MATLAB

   

  Chapter 3 Complex Numbers and Matlab

                  3.1 Introduction

                                  3.1.1 MATLAB for Complex Numbers

                                  3.1.2 Understanding Quadratic Equation

                                  3.1.3 Definition

                                  3.1.4 Real and Imaginary Parts of Complex Numbers in Engineering

                  3.2 The Fundamental Algebraic Operations

                                  3.2.1 Addition of Complex Numbers

                                  3.2.2 Subtraction of Complex Numbers

                                  3.2.3 Multiplication of Complex Numbers

                                  3.2.4 Complex Conjugate

                                  3.2.5 Division of Complex Numbers

                  3.3 Absolute Value (Modulus) and Argument (Amplitude) of a Complex Number

                                  3.3.1 Properties of the Absolute Value of the Complex Number

                  3.4 Polar Form of a Complex Number

                                  3.4.1 Conversion of Rectangular Form into Polar Form

                                  3.4.2 Graphical Polar Representation in MATLAB

                                  3.4.3 Conversion of Polar Form into Rectangular Form

                                  3.4.4 Product of Two Polar Forms

                                  3.4.5 Quotient of Two Polar Forms

                  3.5 Exponential Form of a Complex Number – Euler’ Formula

                                  3.5.1 Conversion of Rectangular Form into Exponential Form

                                  3.5.2 Conversion of Exponential Form into Rectangular Form

                                  3.5.3 Product and Quotient of Two Exponential Form

                  3.6 Power of a Complex Number – De Moivre’s Theorem

                  3.7 Power of j

                  3.8 Equation with Complex Numbers

   

   

  Chapter 4 Differential Calculus and Matlab

                  4.1 Introduction

                                  4.1.1 Rules of Differentiation of Single Variable Function

                  4.2 Derivatives of Polynomial Functions [Algebraic Functions]

                                  4.2.1 Sum and Difference Rule

                                  4.2.2 Product Rule

                                  4.2.3 Quotient Rule

                                  4.2.4 Chain Rule

                  4.3 Derivative of Six Basic Trigonometric Functions

                                  4.3.1 Derivative of Inverse Trigonometric Functions

                  4.4 Derivative of Six Hyperbolic Trigonometric Functions

                                  4.4.1 Derivative of Six Inverse Hyperbolic Trigonometric Functions

                  4.5 Derivative of Exponential Functions

                  4.6 Derivative of Natural Logarithmic Functions

                  4.7 Logarithmic Differentiation

                  4.8 Implicit Differentiation

                                  4.8.1 Plotting Implicit Functions in MATLAB

                                  4.8.2 Parametric Differentiation

                                  4.8.3 Plotting Symbolic Expressions

                  4.9 Higher-Order Derivatives

                                  4.9.1 Higher-Order Implicit Differentiation

                                  4.9.2 Higher-Order Parametric Differentiation

                                  4.9.3 Applications of Derivatives

                                  4.9.4 Optimization in Engineering

   

   

  Chapter 5 Multivariable Calculus and Matlab

                  5.1 Introduction

                                  5.1.1 Function of Two Variables

                                  5.1.2 Rules of Partial Derivatives

                  5.2 Partial Derivative of a Function of Two Variables

                  5.3 Partial Derivative of Trigonometric Functions

                                  5.3.1 Partial Derivative of Inverse Trigonometric Functions

                                  5.3.2 Partial Derivative of Natural Logarithmic Functions

                                  5.3.3 Partial Derivative of Exponential Functions

                                  5.3.4 Graphing in Three-Dimensional Space - The Function of Two Variables Using MATLAB

                  5.4 Function of Three Variables

                                  5.4.1 Partial Derivatives of a Function of Three Variables

                                  5.4.2 Partial Derivatives as a Slope

                  5.5 Higher-Order Partial Derivatives

                                  5.5.1 Second-Order Partial Derivatives

                                  5.5.2 Second-Order Partial Derivatives and Evaluation

                                  5.5.3 Extreme Values and Saddle Point of a Function of Two Variables

                  5.6 Small Increment, Total Differential and Rate of Change

                                  5.6.1 Small Increment

                                  5.6.2 Total Differential for Approximation

                                  5.6.3 Rate of Change

                  5.7 Partial Differentiation of Implicit Functions

   

  Chapter 6 Integral Calculus and Matlab

                  6.1 Introduction

                  6.2 Indefinite Integral

                                  6.2.1 Basic Theorem on Integration

                                  6.2.2 Integrals of Trigonometric Functions

                                  6.2.3 Using a Combination of Standard Integrals for Antiderivatives

                  6.3 Standard Integrals of Hyperbolic Trigonometric Functions

                  6.4 Definite Integral

                                  6.4.1 Fundamental Theorem of Calculus

                                  6.4.2 Property of Definite Integral

                  6.5 Applications of Integration

                                  6.5.1 Calculus of Area of any Shape and Definite Integral

                                  6.5.2 Area Above the x-axis

                                  6.5.3 Area Below the x-axis

                  6.6 Area Between a Curve and a Line [or] Area Between the Curves without Graph

                                  6.6.1 Definition

                                  6.6.2 Average Value [Mean Value] of a Function

                                  6.6.3 Root Mean Square [R.M.S] of a Function

                  6.7 Integration Techniques

                                  6.7.1 Integration by Substitution

                                  6.7.2 Integration by Parts

                                  6.7.3 Bernoulli’s formula for Integration by Parts

                                  6.7.4 Integration by Partial Fraction Decomposition

                  6.8 Multiple Integral

                                  6.8.1 Double Integral

                                  6.8.2 Triple Integral

   

  Chapter 7 Vector Algebra and Matlab

                  7.1 Introduction

                  7.2 Definition of Scalars and Vectors

                                  7.2.1 Typical Notation of Vectors

                                  7.2.2 Types of Vectors

                                  7.2.3 Vector Operations and Properties

                                &

M. M. Mohamed Ubaidullah brings over three decades of teaching experience along with four years of industry exposure. He is currently serving as an educator at the Asia Pacific University of Technology and Innovation, Malaysia. He has taught a wide range of Mathematics and Engineering modules and has been awarded the Vice Chancellor’s Commendation for Teaching Excellence on three occasions. He is also a Member of the International Linear Algebra Society (ILAS). He has authored two textbooks, including Mathematics for Technology 2 (IBS Buku Sdn Bhd, 2013) and Linear Algebra (Vijay Nicole Pvt Ltd, 2022). In addition, he has published research articles in refereed journals.