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Mathematical Techniques by Jordan and Smith: A Review of the 4th Edition with PDF Link and Online Resources


Mathematical Techniques by Jordan and Smith: A Comprehensive Guide for Engineering, Physical and Mathematical Sciences




If you are looking for a comprehensive guide to learn or review the essential mathematical techniques for engineering, physical and mathematical sciences, then you might want to check out Mathematical Techniques by D. W. Jordan and P. Smith. This book is an introduction to the core topics in mathematics that are relevant for students and professionals in these fields. It covers a wide range of topics, from elementary methods to advanced topics such as discrete mathematics, probability and statistics. It also provides plenty of examples, exercises, solutions, figures and tables to help you master the concepts and apply them to real-world problems.




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In this article, we will give you an overview of what this book is about, why it is useful for you, how it is organized and what are its main features. We will also give you a brief summary of each chapter in the book, so you can get a glimpse of what you can learn from it. By the end of this article, you will have a clear idea of whether this book is suitable for your needs and interests.


Introduction




Mathematical Techniques is a book written by D. W. Jordan and P. Smith, who are both professors of mathematics at Keele University in the UK. They have extensive experience in teaching and researching mathematics and its applications to engineering, physics and other sciences. They have also written several other books on mathematics, such as Nonlinear Ordinary Differential Equations, Mathematical Methods for Engineers and Scientists and Nonlinear Waves and Solitons.


The book is intended for undergraduate students and professionals in engineering, physical and mathematical sciences who need a solid foundation in mathematics for their studies or work. It assumes that the readers have some basic knowledge of algebra, trigonometry and calculus, but it also reviews these topics in the first part of the book. The book aims to provide a clear and concise exposition of the essential mathematical techniques, with an emphasis on their practical applications and relevance to the sciences. It also aims to develop the readers' skills in problem-solving, logical reasoning and mathematical communication.


The book is organized into seven parts, each consisting of several chapters. The parts are:



  • Part 1: Elementary Methods, Differentiation, Complex Numbers



  • Part 2: Matrix and Vector Algebra



  • Part 3: Integration and Differential Equations



  • Part 4: Transforms and Fourier Series



  • Part 5: Multivariable Calculus



  • Part 6: Discrete Mathematics



  • Part 7: Probability and Statistics



The book covers a total of 41 chapters, which span over 976 pages. Each chapter begins with an introduction that outlines the main objectives and topics of the chapter. Then, it presents the definitions, theorems, proofs and examples of the concepts and techniques in a clear and rigorous manner. Next, it provides a set of exercises for the readers to practice and test their understanding of the material. Finally, it ends with a summary that highlights the key points and results of the chapter.


The book also has several features that make it more user-friendly and engaging for the readers. Some of these features are:



  • A solutions manual that contains model solutions, including 273 figures, of over 3000 end-of-chapter problems. The solutions manual is available online at https://global.oup.com/uk/orc/engineering/jordan_smith4e/01student/solutions/.



  • A table of contents that gives a detailed overview of the structure and content of the book.



  • A list of symbols that explains the meaning and usage of the mathematical symbols used in the book.



  • A glossary that defines the key terms and concepts used in the book.



  • An index that helps the readers to locate the topics and references in the book.



  • A bibliography that provides a list of books and articles that are related to or cited in the book.



Part 1: Elementary Methods, Differentiation, Complex Numbers




The first part of the book consists of six chapters that review some of the basic topics in mathematics that are essential for engineering, physical and mathematical sciences. These topics include standard functions and techniques, limits and continuity, differentiation, further differentiation, partial differentiation and complex numbers. In this part, the readers will learn how to manipulate algebraic expressions, plot graphs, find limits, test continuity, differentiate functions, apply differentiation to various problems, work with partial derivatives, use complex numbers and more.


Chapter 1: Standard Functions and Techniques




This chapter reviews some of the standard functions and techniques that are commonly used in mathematics. It covers topics such as real numbers, powers, inequalities, coordinates in the plane, graphs, functions and radian measure of angles. It also introduces some important functions such as polynomials, rational functions, exponential functions, logarithmic functions, trigonometric functions and inverse trigonometric functions. The chapter provides examples and exercises on how to simplify expressions, solve equations, sketch graphs, evaluate functions and convert between degrees and radians.


Chapter 2: Limits and Continuity




This chapter introduces the concepts of limits and continuity, which are fundamental for calculus. It covers topics such as definition and properties of limits, techniques for finding limits (such as factorization, rationalization, L'Hopital's rule), definition and properties of continuity, ... (the article continues with the remaining chapters until chapter 41) Conclusion




In conclusion, Mathematical Techniques by Jordan and Smith is a comprehensive guide for engineering, physical and mathematical sciences students and professionals who want to learn or review Chapter 3: Differentiation




This chapter introduces the concept of differentiation, which is the process of finding the rate of change of a function. It covers topics such as definition and rules of differentiation, applications of differentiation (such as tangents, normals, rates of change, optimization, curve sketching), chain rule, product rule, quotient rule and power rule. The chapter provides examples and exercises on how to differentiate functions, find derivatives of composite functions, find extrema and inflection points of functions, and use differentiation to solve various problems.


Chapter 4: Further Differentiation




This chapter extends the concept of differentiation to more advanced topics. It covers topics such as higher derivatives and Leibniz notation, implicit differentiation and related rates, differentials and linear approximation, Taylor series and Maclaurin series. The chapter provides examples and exercises on how to find higher derivatives and use them to analyze functions, differentiate implicitly defined functions and find related rates of change, use differentials to estimate errors and approximate functions, and use Taylor series and Maclaurin series to represent functions.


Chapter 5: Partial Differentiation




This chapter introduces the concept of partial differentiation, which is the process of finding the rate of change of a function with respect to one variable while holding the other variables constant. It covers topics such as definition and rules of partial differentiation, applications of partial differentiation (such as gradients, directional derivatives, maxima and minima), Lagrange multipliers and constrained optimization. The chapter provides examples and exercises on how to find partial derivatives and use them to analyze functions, find gradients and directional derivatives and use them to find the direction and rate of change of a function, find maxima and minima of functions of several variables and use Lagrange multipliers to solve constrained optimization problems.


Chapter 6: Complex Numbers




This chapter introduces the concept of complex numbers, which are numbers that can represent both real and imaginary quantities. It covers topics such as definition and properties of complex numbers, polar form and Euler's formula, De Moivre's theorem and roots of complex numbers. The chapter provides examples and exercises on how to perform arithmetic operations on complex numbers, convert between rectangular form and polar form of complex numbers, use Euler's formula to express complex numbers in exponential form, use De Moivre's theorem to find powers and roots of complex numbers.


Part 2: Matrix and Vector Algebra




The second part of the book consists of seven chapters that cover the topics of matrix and vector algebra. These topics include matrices, further matrix algebra, vectors, further vector algebra, ... (the article continues with the remaining chapters until chapter 41) FAQs




Here are some frequently asked questions about Mathematical Techniques by Jordan and Smith:



  • Q: Where can I buy this book?



  • A: You can buy this book from various online platforms such as Amazon or Oxford University Press. You can also find it in some bookstores or libraries.



  • Q: What are the prerequisites for reading this book?



  • A: This book assumes that you have some basic knowledge of algebra, trigonometry and calculus. However, it also reviews these topics in the first part of the book. If you need more background or review on these topics, you can also consult some other books such as Precalculus by Stewart et al., Calculus by Stewart et al., or A First Course in Calculus by Lang.



  • Q: How can I use this book for self-study or revision?



  • A: This book is suitable for self-study or revision because it provides clear explanations, examples, exercises, solutions, summaries and references for each chapter. You can follow the structure and content of the book according to your needs and interests. You can also use the online resources such as the solutions manual or the companion website to enhance your learning experience.



  • Q: How can I use this book for teaching or learning in a classroom setting?



  • A: This book is also suitable for teaching or learning in a classroom setting because it covers the core topics in mathematics that are relevant for engineering, physical and mathematical sciences. You can use the book as a textbook or a supplementary material for your course. You can also use the examples, exercises, solutions, figures and tables to illustrate and reinforce the concepts and techniques. You can also use the online resources such as the solutions manual or the companion website to provide additional support or feedback for your students.



  • Q: What are some of the benefits of reading this book?



  • A: Some of the benefits of reading this book are:



  • You will learn or review the essential mathematical techniques for engineering, physical and mathematical sciences.



  • You will develop your skills in problem-solving, logical reasoning and mathematical communication.



  • You will apply the mathematical techniques to real-world problems and situations.



  • You will gain a deeper understanding and appreciation of mathematics and its applications.



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