Best Reference Books – Differential Calculus and Vector Calculus

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We have compiled the list of Top 10 Best Reference Books on Differential Calculus and Vector Calculus subject. These books are used by students of top universities, institutes and colleges. Here is the full list of top 10 best books on Differential Calculus and Vector Calculus along with reviews.

Kindly note that we have put a lot of effort into researching the best books on Differential Calculus and Vector Calculus subject and came out with a recommended list of top 10 best books. The table below contains the Name of these best books, their authors, publishers and an unbiased review of books on "Differential Calculus and Vector Calculus" as well as links to the Amazon website to directly purchase these books. As an Amazon Associate, we earn from qualifying purchases, but this does not impact our reviews, comparisons, and listing of these top books; the table serves as a ready reckoner list of these best books.

1. “Vectors, Tensors and the Basic Equations of Fluid Mechanics (Dover Books on Mathematics)” by Rutherford Aris

“Vectors, Tensors and the Basic Equations of Fluid Mechanics (Dover Books on Mathematics)” Book Review: This book is designed for engineers, physicists. And also for applied mathematicians at advanced undergraduate and graduate levels. It covers Cartesian and general tensors to physical field theories. It includes calculus of partial differentiation and multiple integrations, algebra, and calculus of Cartesian vectors. It also includes subsequent chapters like the kinematics of fluid motion, stress in fluids, equations of motion, and energy in Cartesian coordinates, tensors. Later it focuses on the geometry of surfaces in space, the equations of surface flow, and equations for reacting fluids. It contains a generous number of exercises and diagrams.

2. “Calculus of Variations (Dover Books on Mathematics)” by Isarel M Gelfand and S V Fomin

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“Calculus of Variations (Dover Books on Mathematics)” Book Review: This book is designed for engineers, physicists. And also for applied mathematicians at advanced undergraduate and graduate levels. It includes canonical equations, variational principles of mechanics, and conservation laws. It also includes the theory of fields and sufficient conditions,the application of variational methods. Later it focuses on direct methods in the calculus of variations. It contains a generous number of exercises and diagrams.

3. “The Variational Principles of Mechanics (Dover Books on Physics)” by Cornelius Lanczos

“The Variational Principles of Mechanics (Dover Books on Physics)” Book Review: This book is designed for engineers, physicists. And also for applied mathematicians at advanced undergraduate and graduate levels. It includes theories of Euler and Lagrange, Hamilton, Jacobi. It also includes the Partial Differential Equation of Hamilton-Jacobi, Lie algebras, symplectic geometry. Later it focuses on Poisson manifolds, differential geometry, Geometrical interpretation. The book contains a large number of graphs and diagrams for better understanding. The book contains Worked examples and exercises that appear throughout the text.

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4. “Essential Calculus with Applications (Dover Books on Mathematics)” by Richard A Silverman

“Essential Calculus with Applications (Dover Books on Mathematics)” Book Review: This book is designed for engineers, physicists. And also for applied mathematicians at advanced undergraduate and graduate levels. The required chapters are starting from differential calculus with a discussion of the key concept of function. Then it continues with derivatives and limit, velocity, continuous and differentiable functions. It also includes indefinite integral, local extrema, and concrete optimization problems, integral calculus. Later it focuses on Riemann integral, improper integrals, differential equations, and their applications. The final chapter is devoted to the differential calculus of functions of several variables. The book contains numerous problems and answers.

5. “Differential Forms: A Complement to Vector Calculus” by Weintraub
6. “Tensor Analysis on Manifolds (Dover Books on Mathematics)” by Richard L Bishop

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“Tensor Analysis on Manifolds (Dover Books on Mathematics)” Book Review: This book is designed for engineers, physicists. And also for applied mathematicians at advanced undergraduate and graduate levels. This book covers the general theory of relativity and its adaptability to a wide range of mathematical and physical problems. It includes tensor analysis, an emphasis on notation, and the manipulation of indices. It also includes advanced calculus, notation and explains various topics in set theory and topology. Later, it focuses on function-theoretical and algebraic aspects, manifolds, and integration theory. The book contains Worked examples and exercises that appear throughout the text.

7. “Introduction To Space Dynamics (Dover Books On Aeronautical Engineering)” by William T Thomson

“Introduction To Space Dynamics (Dover Books On Aeronautical Engineering)” Book Review: This book is designed for undergraduate and graduate students of aerospace engineering. The required topics starting from vector algebra and kinematics. Then it includes angular velocity vector tangential and normal components and the general case of space motion. It also includes the transformation of coordinates, with sections of Euler’s angles, and the transformation of angular velocities. Later it focuses on the two-body problem, orbital change due to impulsive thrust, long-range ballistic trajectories, and the effect of the Earth’s oblateness. It also describes gyrodynamics and the dynamics of gyroscopic instruments, covering such topics as the displacement of a rigid body, precession, and nutation of the Earth’s polar axis. Finally, an examination of space vehicle motion, with analyses of general equations in body conditions and their transformation to inertial coordinates is discussed. The book contains clear, comprehensive text, practice problems (with answers to many), numerous charts and diagrams reinforce each lesson.

8. “Mathematics for Physicists (Dover Books on Physics)” by Philippe Dennery and Andre Krzywicki

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“Mathematics for Physicists (Dover Books on Physics)” Book Review: This book is designed for advanced undergraduate and graduate mathematics students. Also for students of physics, and engineering. The required chapters starting from the theory of analytic functions, linear vector spaces, and linear operators. It includes orthogonal expansions (including Fourier series and transforms), the theory of distributions. Later it focuses on ordinary and partial differential equations and special functions: series solutions, Green’s functions, eigenvalue problems, integral representations. The book contains a large number of graphs and diagrams for better understanding. The book contains Worked examples and exercises that appear throughout the text.

9. “Quantum Mechanics in Simple Matrix Forms (Dover Books on Physics)” by Thomas F Jordan

“Quantum Mechanics in Simple Matrix Forms (Dover Books on Physics)” Book Review: This book is designed for advanced undergraduate and graduate mathematics students. Also for students of physics, and engineering. It includes wave mechanics and matrix mechanics. It also includes a simple introduction to quantum mechanics, complex numbers, matrix algebra, and probability. Later it focuses on The Principles of Quantum Mechanics (International Series of Monographs on Physics). The book contains more than 100 problems. It provides an easy way to learn part of the quantum language and to employ this new skill in solving problems.

10. “Fundamentals of Astrodynamics (Dover Books on Aeronautical Engineering)” by R R Bate

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“Fundamentals of Astrodynamics (Dover Books on Aeronautical Engineering)” Book Review: This book is designed for undergraduates majoring in astronautics or aerospace engineering. The book covers the universal variable formulation. It includes the development of the basic two-body and n-body equations of motion; orbit determination is then treated. It also includes the classical orbital elements, coordinate transformations, and differential correction. Later, it also discusses Orbital transfer maneuvers are developed, the Kepler and Gauss problems are treated in detail. In the end, it focuses on the lunar and interplanetary flight, special perturbations, integration schemes and errors, and analytic formulation of several common perturbations. Example problems are used frequently. It contains exercises at the end of each chapter including derivations and quantitative and qualitative problems.

People who are searching for Free downloads of books and free pdf copies of these top 10 books on Differential Calculus and Vector Calculus – we would like to mention that we don’t have free downloadable pdf copies of these good books and one should look for free pdf copies from these Authors only if they have explicitly made it free to download and read them.

We have created a collection of best reference books on "Differential Calculus and Vector Calculus" so that one can readily see the list of top books on "Differential Calculus and Vector Calculus" and buy the books either online or offline.

If any more book needs to be added to the list of best books on Differential Calculus and Vector Calculus subject, please let us know.

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Manish Bhojasia, a technology veteran with 20+ years @ Cisco & Wipro, is Founder and CTO at Sanfoundry. He is Linux Kernel Developer & SAN Architect and is passionate about competency developments in these areas. He lives in Bangalore and delivers focused training sessions to IT professionals in Linux Kernel, Linux Debugging, Linux Device Drivers, Linux Networking, Linux Storage, Advanced C Programming, SAN Storage Technologies, SCSI Internals & Storage Protocols such as iSCSI & Fiber Channel. Stay connected with him @ LinkedIn | Youtube | Instagram | Facebook | Twitter