Which Books Offer Detailed Explanations for Engineering Mathematics Topics?

[judas_priest]

A book that goes very much in depth, explaining and reasoning out every topic is the book that I prefer.

The topics I require are:

Unit-I: First order Differential Equations (10)
Formation – Variables seperable – Homogeneous, non Homogeneous, Linear and Bernoulli equations. Exact equations - Applications of first order differential equations – Orthogonal Trajectories, Newton’s law of cooling, law of natural growth and decay.
Unit-II: Higher order Differential Equations (12)
Complete solutions - Rules for finding complementary function - Inverse operator - Rules for finding particular integral - Method of variation of parameters - Cauchy’s and Legendre’s linear equations - Simultaneous linear equations with constant coefficients - Applications of linear differential equations to Oscillatory Electrical circuits L-C, LCR – Circuits - Electromechanical Analogy.
Unit-III: Mean Value Theorems (08)
Rolle’s, Lagrange’s and Cauchy’s mean value theorems. Taylor’s and Maclaurin’s theorems and applications (without proofs).
Unit-IV: Infinite Series (12)
Definitions of convergence, divergence and oscillation of a series - General properties of series - Series of positive terms - Comparison tests - Integral test - D’ Alembert’s Ratio test - Raabe’s test - Cauchy’s root test - Alternating series - Leibnitz’s rule - Power series - Convergence of exponential, Logarithmic and binomial series (without proofs).
Unit-V: Linear Algebra (12)
Rank of a Matrix – Elementary Transformations – Echelon form - Normal form (self study). Consistency of Linear system of equations A X = B and A X = 0. Eigen Values and Eigen Vectors – Properties of eigen values(without proofs) – Cayley – Hamilton theorem (Statement only without proof) – Finding inverse and powers of a square matrix using Cayley– Hamiton theorem – Reduction to diagonal form – Quadratic form - Reduction of Quadratic form into canonical form – Nature of quadratic forms.

Could be 1 book or more.

But like I said I prefer books that go very much in detail like Calculus by G.B Thomas. What a genius of a book!

 

[STEMucator]

A book that goes very much in depth, explaining and reasoning out every topic is the book that I prefer.

The topics I require are:

Unit-I: First order Differential Equations (10)
Formation – Variables seperable – Homogeneous, non Homogeneous, Linear and Bernoulli equations. Exact equations - Applications of first order differential equations – Orthogonal Trajectories, Newton’s law of cooling, law of natural growth and decay.
Unit-II: Higher order Differential Equations (12)
Complete solutions - Rules for finding complementary function - Inverse operator - Rules for finding particular integral - Method of variation of parameters - Cauchy’s and Legendre’s linear equations - Simultaneous linear equations with constant coefficients - Applications of linear differential equations to Oscillatory Electrical circuits L-C, LCR – Circuits - Electromechanical Analogy.
Unit-III: Mean Value Theorems (08)
Rolle’s, Lagrange’s and Cauchy’s mean value theorems. Taylor’s and Maclaurin’s theorems and applications (without proofs).
Unit-IV: Infinite Series (12)
Definitions of convergence, divergence and oscillation of a series - General properties of series - Series of positive terms - Comparison tests - Integral test - D’ Alembert’s Ratio test - Raabe’s test - Cauchy’s root test - Alternating series - Leibnitz’s rule - Power series - Convergence of exponential, Logarithmic and binomial series (without proofs).
Unit-V: Linear Algebra (12)
Rank of a Matrix – Elementary Transformations – Echelon form - Normal form (self study). Consistency of Linear system of equations A X = B and A X = 0. Eigen Values and Eigen Vectors – Properties of eigen values(without proofs) – Cayley – Hamilton theorem (Statement only without proof) – Finding inverse and powers of a square matrix using Cayley– Hamiton theorem – Reduction to diagonal form – Quadratic form - Reduction of Quadratic form into canonical form – Nature of quadratic forms.

Could be 1 book or more.

But like I said I prefer books that go very much in detail like Calculus by G.B Thomas. What a genius of a book!

If you want a moderately rigorous calculus book which will teach limits, derivatives, integrals, series, differential equations and other physical topics, I would recommend Stewart Calculus. I found the 4th edition to be the best personally, but you can get the 7th if you so please. If you look around you can find a PDF quite quickly.

It will give you a very solid foundation of calculus with plenty of practice. Then you can follow it up with an even more rigorous calculus book if you please ( When i say rigorous I mean very proof heavy ) or move right onto multivariate calculus.

There's lots of linear algebra resources out there as well. Once again, depending on how rigorous you want to be you have plenty of choices. If you want a moderately rigorous book to teach you linear algebra, I would recommend A First Course in Linear Algebra from linear ups. They go very in depth and prove almost every theorem thoroughly step by step. Link : http://linear.ups.edu/download.html ( It's free ).

You will learn about systems, matrices, eigens, spaces and much much more. It is a very difficult book, but a great read due to the author making the material interesting. This book will probably be way more than enough for an engineering curriculum.

As for a focus on differential equations as well as physical problems involving laws of cooling and many other things, I would recommend Boyce Elementary Differential Equations 10th edition. It's not TOO proof heavy, but I find the book is very clear about the concepts and calculations. You can probably find a PDF of the 9th version quite quickly which isn't too different.

You will learn to solve ODEs up to the nth order. Laplace transforms and boundary value problems are also included which will be important for you later. Bernoulli among other things is covered as well.

Hope this helps.

 

[judas_priest]

If you want a moderately rigorous calculus book which will teach limits, derivatives, integrals, series, differential equations and other physical topics, I would recommend Stewart Calculus. I found the 4th edition to be the best personally, but you can get the 7th if you so please. If you look around you can find a PDF quite quickly.

It will give you a very solid foundation of calculus with plenty of practice. Then you can follow it up with an even more rigorous calculus book if you please ( When i say rigorous I mean very proof heavy ) or move right onto multivariate calculus.

There's lots of linear algebra resources out there as well. Once again, depending on how rigorous you want to be you have plenty of choices. If you want a moderately rigorous book to teach you linear algebra, I would recommend A First Course in Linear Algebra from linear ups. They go very in depth and prove almost every theorem thoroughly step by step. Link : http://linear.ups.edu/download.html ( It's free ).

You will learn about systems, matrices, eigens, spaces and much much more. It is a very difficult book, but a great read due to the author making the material interesting. This book will probably be way more than enough for an engineering curriculum.

As for a focus on differential equations as well as physical problems involving laws of cooling and many other things, I would recommend Boyce Elementary Differential Equations 10th edition. It's not TOO proof heavy, but I find the book is very clear about the concepts and calculations. You can probably find a PDF of the 9th version quite quickly which isn't too different.

You will learn to solve ODEs up to the nth order. Laplace transforms and boundary value problems are also included which will be important for you later. Bernoulli among other things is covered as well.

Hope this helps.

Hey, thank you for your reply. I think highly rigorous is what I prefer. I'm not saying I'm the best at Calculus, but single variable calculus has been my strongest subject so far, and I've solved questions from pretty good books known for its rigorous approach like TMH, Integral calculs by arihant publications, etc.

These books, although very good, do not teach the concepts as to how and why. They are more technique/tricks based. I prefer books like G.B Thomas which are thorough with concepts, and go to the deepest of the subject.

I will surely check out the books you recommended and get back to you!

I think I'm looking for more of multivariable calculus. I've been doing single variable for last year and a half, and now I'm a fresher to Electronics and Instrumentation engineering. Most of our syllabus for first semester involves multivariable calculus and other stuff that I mentioned in the description of the question.

 

[STEMucator]

Hey, thank you for your reply. I think highly rigorous is what I prefer. I'm not saying I'm the best at Calculus, but single variable calculus has been my strongest subject so far, and I've solved questions from pretty good books known for its rigorous approach like TMH, Integral calculs by arihant publications, etc.

These books, although very good, do not teach the concepts as to how and why. They are more technique/tricks based. I prefer books like G.B Thomas which are thorough with concepts, and go to the deepest of the subject.

I will surely check out the books you recommended and get back to you!

I think I'm looking for more of multivariable calculus. I've been doing single variable for last year and a half, and now I'm a fresher to Electronics and Instrumentation engineering. Most of our syllabus for first semester involves multivariable calculus and other stuff that I mentioned in the description of the question.

These books, although very good, do not teach the concepts as to how and why

I don't know too many rigorous differential equation resources because DEs are used to solve physical problems for the most part. Even so, Boyce also covers existence and uniqueness and some theoretical topics of DEs in his book. You can choose to read through those if you like, but I don't think they will be very useful to you in engineering.

If you want to turn up the heat for calculus, I would recommend you read Advanced Calculus by Taylor 3rd edition. It goes over single variable calculus all over again with a much much more rigorous approach. Then it moves into real numbers and analysis for awhile to give you a much more intuitive understanding of what's going on. Then it will cover extensions of the laws of the mean.

After sending your brain for a loop there ^ it jumps right into a bit of topology and point set theory before it starts multivariate calculus ( Which it also does very very thoroughly ). Limits, derivatives, integrals, sequences and series are all emphasized. Uniform convergence, lots of physical problems and other very interesting topics are covered.

As for the linear algebra, I think you will like the book a lot then :).