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

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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:

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

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