Advanced Modern Engineering Ma

Advanced Engineering Mathematics is known for its comprehensive coverage.

Engineering Mathematics has helped thousands of students to succeed in their exams. The new edition includes a section at the start of each chapter to explain why the content is important and how it relates to real life. It is also supported by a fully updated companion website with resources for both students and lecturers. It has full solutions to all 1900 further questions contained in the 269 practice exercises.

Advanced Engineering Mathematics is known for its comprehensive coverage, careful and correct mathematics, outstanding exercises, and self contained subject matter parts for maximum flexibility. The new edition continues with the tradition of providing instructors and students with a comprehensive and up-to-date resource for teaching and learning engineering mathematics, that is, applied mathematics for engineers and physicists, mathematicians and computer scientists, as well as members of other disciplines.

Building on the foundations laid in the companion text Modern Engineering Mathematics, this app gives an extensive treatment of some of the advanced areas of mathematics that have applications in various fields of engineering, particularly as tools for computer-based system modelling, analysis and design.

The philosophy of learning by doing helps students develop the ability to use mathematics with understanding to solve engineering problems. A wealth of engineering examples and the integration of MATLAB and MAPLE further support students.

Some of the Table of Contents are:

Hints on Using the Book

Useful Background Information

PART A Ordinary Differential Equations (ODEs)

CHAPTER 1: First-Order ODEs

1.1 Basic Concepts. Modeling

1.2 Geometric Meaning of y′ = f(x, y). Direction Fields, Euler's Method

1.3 Separable ODEs. Modeling

1.4 Exact ODEs. Integrating Factors

1.5 Linear ODEs. Bernoulli Equation. Population Dynamics

1.6 Orthogonal Trajectories. Optional

1.7 Existence and Uniqueness of Solutions for Initial Value Problems

CHAPTER 1 Review Questions and Problems

Summary of Chapter 1

CHAPTER 2: Second-Order Linear ODEs

2.1 Homogeneous Linear ODEs of Second Order

2.2 Homogeneous Linear ODEs with Constant Coefficients

2.3 Differential Operators. Optional

2.4 Modeling of Free Oscillations of a Mass–Spring System

2.5 Euler–Cauchy Equations

2.6 Existence and Uniqueness of Solutions. Wronskian

2.7 Nonhomogeneous ODEs

2.8 Modeling: Forced Oscillations. Resonance

2.9 Modeling: Electric Circuits

2.10 Solution by Variation of Parameters

CHAPTER 2 Review Questions and Problems

Summary of Chapter 2

CHAPTER 3: Higher Order Linear ODEs

3.1 Homogeneous Linear ODEs

3.2 Homogeneous Linear ODEs with Constant Coefficients

3.3 Nonhomogeneous Linear ODEs

CHAPTER 3 Review Questions and Problems

Summary of Chapter 3

CHAPTER 4: Systems of ODEs. Phase Plane. Qualitative Methods

CHAPTER 5: Series Solutions of ODEs. Special Functions

Numerical Solutions of Equations and Interpolation

Laplace Transforms Part 1

Laplace Transforms Part 2

Laplace Transforms Part 3

Difference equations and the Z Transform

Introduction to invariant linear systems

Fourier Series 1

Fourier Series 2

Introduction to the Fourier Transform

Power Series Solutions of Ordinary Differential Equations 1

Power Series Solutions of Ordinary Differential Equations 2

Power Series Solutions of Ordinary Differential Equations 3

Numerical Solutions of Ordinary Differential Equations

Partial Differentiation

Partial Differential Equations

Matrix Algebra

Systems of ordinary differential equations

Numerical Solutions of Partial Differential Equations

Multiple Integration Part 1

Multiple Integration Part 2

Integral Functions

Vector Analysis Part 1

Vector Analysis Part 2

Vector Analysis Part 3

Complex Analysis Part 1

Complex Analysis Part 2

Complex Analysis Part 3

Optimization and Linear Programming.