Engineering mathematics covers a wide range of topics, and there are many textbooks that provide detailed analyses of these topics. Here is a list of some of the key topics in engineering mathematics, along with some textbooks that provide a detailed analysis of these topics:

**Calculus:** Calculus is a branch of mathematics that deals with rates of change and accumulation. It includes differential calculus and integral calculus.

- “Calculus: Early Transcendentals” by James Stewart
- “Calculus” by Michael Spivak
- “Calculus: Single Variable” by Deborah Hughes-Hallett

**Linear Algebra:** Linear algebra is a branch of mathematics that deals with vector spaces and linear transformations. It includes topics such as matrices, determinants, eigenvalues, and eigenvectors.

- “Linear Algebra and Its Applications” by Gilbert Strang
- “Linear Algebra Done Right” by Sheldon Axler
- “Matrix Analysis and Applied Linear Algebra” by Carl D. Meyer

**Differential Equations:** Differential equations are equations that involve derivatives or differentials. They are used to model a wide variety of physical phenomena.

- “Differential Equations and Their Applications” by Martin Braun
- “Elementary Differential Equations” by Earl D. Rainville
- “Partial Differential Equations for Scientists and Engineers” by Stanley J. Farlow

**Complex Analysis:** Complex analysis is a branch of mathematics that deals with functions of a complex variable. It includes topics such as analytic functions, Laurent series, and conformal mapping.

- “Complex Analysis” by Joseph Bak and Donald J. Newman
- “Complex Variables and Applications” by James Ward Brown and Ruel V. Churchill
- “Functions of One Complex Variable” by John B. Conway

**Probability and Statistics:** Probability and statistics are branches of mathematics that deal with the analysis of random phenomena.

- “Probability and Statistics for Engineers and Scientists” by Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, and Keying Ye
- “Introduction to Probability and Statistics for Engineers and Scientists” by Sheldon M. Ross
- “Mathematical Statistics with Applications” by Dennis Wackerly, William Mendenhall, and Richard L. Scheaffer

**Numerical Methods:** Numerical methods are techniques used to solve mathematical problems using numerical approximations.

- “Numerical Methods for Engineers” by Steven C. Chapra and Raymond P. Canale
- “Numerical Analysis” by Richard L. Burden and J. Douglas Faires
- “Numerical Recipes in C: The Art of Scientific Computing” by William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery

If you want to cover the complete syllabus of Mathematics, you want to study Mathematics in detail, then you can read some Engineering Mathematics books given below and read about Engineering Mathematics in a detailed manner.

**Here are 30 of the best books on engineering mathematics with detailed analysis:**

- “Advanced Engineering Mathematics” by Michael Greenberg
- “Mathematical Methods in the Physical Sciences” by Mary L. Boas
- “Applied Mathematics for Engineers and Physicists” by Louis A. Pipes and Lawrence R. Harvill
- “Numerical Methods for Engineers” by Steven C. Chapra and Raymond P. Canale
- “Mathematics for Engineers and Scientists” by Alan Jeffrey
- “Engineering Mathematics” by John Bird
- “Fundamentals of Applied Mathematics” by Peter Inglis
- “Engineering Mathematics: A Foundation for Electronic, Electrical, Communications and Systems Engineers” by Anthony Croft and Robert Davison
- “A First Course in Mathematical Analysis” by J.C. Burkill
- “Mathematical Methods for Physics and Engineering” by K.F. Riley, M.P. Hobson, and S.J. Bence
- “Mathematics for Engineers” by M.A. Denn and R.B. Johnson
- “Advanced Engineering Mathematics” by Peter V. O’Neil
- “Calculus and Analytic Geometry” by George B. Thomas and Ross L. Finney
- “Advanced Calculus” by Angus E. Taylor and W. Robert Mann
- “Introduction to Partial Differential Equations” by Peter J. Olver
- “Partial Differential Equations: An Introduction” by Walter A. Strauss
- “An Introduction to Ordinary Differential Equations” by Earl A. Coddington
- “Differential Equations with Boundary-Value Problems” by Dennis G. Zill and Warren S. Wright
- “Linear Algebra and Its Applications” by Gilbert Strang
- “Matrix Analysis and Applied Linear Algebra” by Carl D. Meyer
- “Numerical Linear Algebra” by Lloyd N. Trefethen and David Bau III
- “Numerical Analysis” by Richard L. Burden and J. Douglas Faires
- “Numerical Methods for Scientific and Engineering Computation” by M.K. Jain, S.R.K. Iyengar, and R.K. Jain
- “Numerical Recipes in C: The Art of Scientific Computing” by William H. Press, Saul A. Teukolsky, William T. Vetterling, and Brian P. Flannery
- “Introduction to Probability and Statistics for Engineers and Scientists” by Sheldon M. Ross
- “Probability and Statistics for Engineers and Scientists” by Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, and Keying Ye
- “Introduction to Optimization” by Edwin K. P. Chong and Stanislaw H. Zak
- “Convex Optimization” by Stephen Boyd and Lieven Vandenberghe
- “Optimization Methods in Finance” by Gerard Cornuejols and Reha Tutuncu
- “Game Theory: An Introduction” by Steven Tadelis

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