Engineering Mathematics Exam Prep : Problems and Solutions.

Format:

Book

Author/Creator:

Saha, A.

Contributor:

Dutta, D.

Kar, S.

Majumder, P.

Paul, A.

Series:

MLI Exam Prep Series

Language:

English

Subjects (All):

Engineering mathematics--Problems, exercises, etc.

Engineering mathematics.

Physical Description:

1 online resource (655 pages)

Edition:

1st ed.

Place of Publication:

Bloomfield : Mercury Learning & Information, 2023.

Summary:

This book provides over 1200 review questions, explanations, and answers for all types of engineering mathematics exams and review. It covers all the aspects of engineering topics from linear algebra and calculus to differential equations, complex analysis, statistics, graph theory, and more.

Contents:

Cover

Half-Title

Title

Copyright

Contents

Chapter 1: Linear Algebra

1.1 Matrices and Their Types

1.1.1 Definition of a Matrix

1.1.2 Types of Matrices

1.2 Algebra of Matrices

1.2.1 Negative, Sum, and Differences of Matrices

1.2.2 Multiplication of a Matrix by a Scalar

1.2.3 Transpose of a Matrix

1.2.4 Multiplication of Matrices (Product of Matrices)

1.3 Determinant of a Square Matrix

1.3.1 Definition of Determinant

1.3.2 Properties of a Determinant

1.3.3 Minors and Cofactors

1.4 Adjoint and Inverse of a Matrix

1.4.1 Adjoint of a Matrix

1.4.2 Inverse of a Matrix

1.5 Various Types of Real Square Matrices

1.5.1 Symmetric Matrix

1.5.2 Skew-Symmetric Matrix

1.5.3 Orthogonal Matrix

1.5.4 Idempotent Matrix

1.5.5 Involutary Matrix

1.5.6 Nilpotent Matrix

1.6 Complex Matrices and Their Types

1.6.1 Complex Conjugate of a Matrix

1.6.2 Transposed Conjugate of a Matrix

1.6.3 Unitary Matrix

1.6.4 Hermitian Matrix

1.6.5 Skew-Hermitian Matrix

1.7 Rank of a Matrix

1.7.1 Elementary Transformations

1.7.2 Equivalent Matrices

1.7.3 Rank of a Matrix

1.7.4 Determination of the Rank of a Matrix

1.8 System of Linear Equations and Their Solutions

1.8.1 Introduction

1.8.2 Methods for Solving Non-Homogeneous System of Linear Equations

1.8.2.1 Cramer's Rule

1.8.2.2 Matrix Method

1.8.2.3 Rank Method

1.8.3 Homogeneous System of Linear Equations

1.9 Eigenvalues and Eigenvectors

1.9.1 Characteristic Roots (Eigenvalues) of a Matrix

1.9.2. Trace of a Matrix

1.9.3. Eigenvectors or Characteristic Vectors

1.10 Vectors

1.10.1 Introduction

1.10.2 Linear Dependence and Linear Independence

1.10.3 Inner Product and Norm of Vectors

1.10.4 Orthogonal and Orthonormal Vectors

1.10.5 Basis and Dimension

Fully Solved MCQs (Level-I).

Answer Key

Explanation

Fully Solved MCQs (Level-II)

Answer Key

Previous Years Solved Papers (2000-2018)

Questions for Practice

Hints

Chapter 2: Calculus

2.1 Functions and Limits

2.1.1 Definition of a Function

2.1.2 Some Special Functions

2.1.3 Introduction to Limits

2.1.4 Definition of Limit

2.1.5 Fundamental Theorems on Limits

2.1.6 Fundamental Formulas on Limits

2.1.7 The Sandwich Theorem

2.1.8 Infinite Limits

2.1.9 Limits at Infinity

2.1.10 Infinite Limits at Infinity

2.2 Continuity and Differentiability

2.2.1 Continuity

2.2.2 Discontinuity

2.2.3 Derivative

2.2.4 Computation of Derivatives

2.3 Indeterminate Forms

2.3.1 Introduction

2.3.2 The L'Hospital Rule

2.4 Mean Value Theorems

2.4.1 Rolle's Theorem

2.4.2 Lagrange's Mean Value Theorem

2.4.3 Cauchy's Mean Value Theorem

2.5 Increasing and Decreasing Functions

2.6 Maxima and Minima of Functions of a Single Variable

2.6.1 First Derivative Test

2.6.2 Second Derivative Test

2.6.3 Higher Order Derivative Test

2.7 Infinite series and Expansion of Functions

2.7.1 Infinite Series

2.7.2 Test for Convergence of Infinite Series

2.7.3 Taylor's Theorem With Lagrange's Form of Remainder

2.7.4 The Taylor Series

2.7.5 Maclaurin's Series

2.8 Indefinite and Definite Integrals

2.8.2 Fundamental Formulas of Indefinite Integral

2.8.3 Advanced Formulas of Indefinite Integrals

2.8.4 Definite Integral

2.8.5 Properties of Definite Integral

2.8.6 Definite Integral as a Limit of Sum

2.8.7 Differentiation Under the Sign of Integration

2.9 Improper Integrals, Beta, and Gamma Functions

2.9.1 Improper Integral

2.9.2 Evaluation of Improper Integrals

2.9.3 Beta Function

2.9.4 Gamma Function.

2.10 Functions of Several Variables and Partial Derivatives

2.10.1 Functions of Two Variables

2.10.2 Limit of Functions of Two Variables

2.10.3 Continuity of Functions of Two Variables

2.10.4 Partial Derivatives

2.10.5 Homogeneous Function

2.10.6 Euler's Theorem

2.10.7 Total Differential and Total Derivative

2.10.8 Jacobian

2.11 Maxima and Minima of Functions of two Variables

2.11.1 Introduction

2.11.2 Working Rule to Find the Maximum and Minimum Values of f(x, y)

2.11.3 Lagrange's Method for Undetermined Multipliers

2.12 Change of Order of Integration

2.13 Double and Triple Integrals

2.13.1 Double Integrals

2.13.2 Triple Integrals

2.14 Arc Length of a Curve

2.15 Volumes of Solids of Revolution

2.15.1 Working Formulas

2.16 Surface Areas of Solids of Revolution

Fully Solved MCQs (Level-I)

Chapter 3: Vectors

3.1 Basic Concepts

3.1.1 Scalars and Vectors

3.1.2 Position Vector

3.1.3 Equal Vectors

3.1.4 Negative of a Vector

3.1.5 Unit Vectors

3.1.6 Sum and Difference of Two Vectors

3.1.7 Triangle Law of Addition

3.1.8 Product of a Vector with a Scalar

3.1.9 Collinear Vectors

3.1.10 Coplanar Vectors

3.1.11 Section Formula

3.2 Product of Vectors

3.2.1 Scalar Product (Dot Product)

3.2.2 Vector Product (Cross Product)

3.2.3 Scalar Triple Product

3.2.4 Vector Triple Product

3.3 Vector Differentiation and Integration

3.3.1 Derivative of a Vector Function

3.3.2 General Rules for Vector Differentiation

3.3.3 Velocity and Acceleration

3.3.4 Vector Integration

3.4 Gradient, Divergence and Curl

3.4.1 Del Operator.

3.4.2 Gradient of a Scalar Point Function

3.4.3 Divergence of a Vector Point Function

3.4.4 Curl of a Vector Point Function

3.4.5 Vector Identities

3.4.6 Directional Derivative

3.5 Line, Surface, and Volume Integrals

3.5.1 Line Integral

3.5.2 Surface Integral

3.5.3 Volume Integral

3.6 Green's, Stokes', and Gauss Divergence Theorem

3.6.1 Greens Theorem (in a Plane)

3.6.2 Stokes' Theorem

3.6.3 Gauss Divergence Theorem

Fully Solved MCQs

Chapter 4: Ordinary Differential Equations

4.1 Basic Concepts

4.1.1 Definition of a Differential Equation

4.1.2 Classification of Differential Equations

4.1.3 Order of a Differential Equation

4.1.4 Degree of a Differential Equation

4.1.5 Formation of a Differential Equation

4.1.6 Solution of a Differential Equation

4.2 Linearly Dependent and Linearly Independent Solutions

4.2.1 Wronskian

4.2.2 Linearly Dependent Solutions

4.2.3 Linearly Independent Solutions

4.3 Differential Equations of 1st Order and 1st Degree

4.3.1 General Form

4.3.2 Solution by Separation of Variables

4.3.3 Homogeneous Differential Equation

4.3.4 Exact Differential Equations

4.3.5 Linear Differential Equations

4.4 Linear Differential Equations of 2nd Order

4.4.1 General Form

4.4.2 Complementary Function (C.F)

4.4.3 Particular Integral (P.I)

4.4.4 Complete (General) Solution

4.4.5 Homogeneous Linear Differential Equations of Order Two

Explanations

Previous Years Questions (2000-18)

Questions For Practice

Chapter 5: Partial Differential Equations.

5.1 Basic Concepts

5.1.1 Introduction

5.1.2 Order and Degree

5.1.3 Linear and No-Linear Partial Differential Equations

5.1.4 Formation of Partial Differential Equations

5.2 Classification of 2nd Order Partial Differential Equation

5.3 Heat, Wave, and Laplace Equations

5.3.1 Solution by Separation of Variables

5.3.2 One-Dimensional Heat (Diffusion) Equation and Its Solution

5.3.3 One-Dimensional Wave Equation and Its Solution

5.3.4 The Laplace Equation and Its Solution

Answer key

Chapter 6: Laplace Transforms

6.1 Basics of Laplace Transforms

6.1.1 Definition of the Laplace Transform

6.1.2 Linear Property of the Laplace Transform

6.1.3 Fundamental Formulas of the Laplace Transform

6.1.4 First Shifting Theorem

6.1.5 Some Advanced Formulas of the Laplace Transform

6.1.6 Change of Scale Property

6.2 Laplace Transform on Derivatives

6.3 Laplace Transform on Integrals

6.4 Laplace Transform on Periodic Functions

6.5 Evaluation of Integrals Using Laplace Transforms

6.6 Initial and Final Value Theorems

6.6.1 Initial Value Theorem

6.6.2 Final Value Theorem

6.7 Fundamentals of Inverse Laplace Transform

6.7.1 Definition of Inverse Laplace Transform

6.7.2 Useful Formulas on Inverse Laplace Transforms

6.8 Important Theorems on Inverse Laplace Transforms

6.9 Unit Step Function and Unit Impulse Function

6.9.1 Unit Step Function

6.9.2 Second Shifting Theorem

6.9.3 Unit Impulse Function

6.10 Solving Ordinary Differential Equations

Answers key

Explanation.

Previous Years Questions (2000-2018).

Notes:

Description based on publisher supplied metadata and other sources.

ISBN:

9781683929086

168392908X

9781683929093

1683929098

OCLC:

1396062752