Basic Training in Mathematics: A Fitness Program for Science Students by R. Shankar
If you are looking for a book that can help you improve your mathematical skills and prepare you for upper-level courses in the physical sciences, you might want to check out Basic Training in Mathematics: A Fitness Program for Science Students by R. Shankar. This book is based on course material used by the author at Yale University and covers various topics in differential calculus, integral calculus, calculus of many variables, infinite series, complex numbers, functions of a complex variable, vector calculus, matrices and determinants, linear vector spaces and differential equations.
The book is designed to address the widening gap between the mathematics required for advanced courses in physics, chemistry and engineering and the knowledge of incoming students. By presenting the material in its simplest form, the book aims to help students gain confidence and competence in solving mathematical problems. The book also provides numerous examples and exercises with answers to test the students' understanding and application of the concepts.
Basic Training in Mathematics: A Fitness Program for Science Students by R. Shankar was published by Springer in 1995 and has received positive reviews from both students and instructors. The book is suitable for undergraduate and graduate students who want to refresh their mathematical background or learn new topics that are essential for their chosen field of study. The book can also serve as a reference for researchers and professionals who need to use mathematics in their work.
If you are interested in buying this book, you can find it on Springer, Google Books, or Archive.org. You can also read more about the author, R. Shankar, who is the John Randolph Huffman Professor of Physics at Yale University, USA.
In this article, we will give you a brief overview of the main topics covered in Basic Training in Mathematics: A Fitness Program for Science Students by R. Shankar and explain why they are important for science students.
Differential Calculus of One Variable
The first chapter of the book introduces the concept of differentiation and its applications in physics and engineering. The author explains how to find the derivative of a function, the rules of differentiation, the chain rule, the product rule, the quotient rule and the power rule. He also discusses how to use derivatives to find the slope of a curve, the rate of change of a quantity, the maximum and minimum values of a function, the linear approximation of a function and the Taylor series expansion of a function. The chapter ends with some examples and exercises on differentiation.
The second chapter of the book introduces the concept of integration and its applications in physics and engineering. The author explains how to find the integral of a function, the rules of integration, the substitution method, the integration by parts method and the partial fractions method. He also discusses how to use integrals to find the area under a curve, the volume of a solid, the work done by a force, the center of mass of a system and the arc length of a curve. The chapter ends with some examples and exercises on integration.
Calculus of Many Variables
The third chapter of the book extends the concepts of differentiation and integration to functions of more than one variable. The author explains how to find the partial derivatives and total derivatives of multivariable functions, how to use them to find the tangent plane and normal line to a surface, how to apply the chain rule and implicit differentiation to multivariable functions and how to use them to solve related rates problems and optimization problems. He also explains how to find the double integrals and triple integrals of multivariable functions, how to use them to find the area and volume of regions in two-dimensional and three-dimensional space, how to change variables in multiple integrals using Jacobians and how to use them to solve problems involving mass density, center of mass and moment of inertia. The chapter ends with some examples and exercises on calculus of many variables.