General guideline for a student pursuing engineering but interested in mathematics
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Linear Algebra
- Book by Gilbert strang
- Essence of linear algebra videos - 3Blue1Brown
- Book by Lyod Trefethen and David Bau (for bit different perspective but in more depth that Gilbert strang)
- Book by Hoffman and Kunze
- Book by Sheldon Axler Linear Algebra done right
- video lecture playlist based on book by Sheldon axler
If wish to understand why and how linear solvers and Eigen solvers work in addition to previous books: follow these advanced ones …
- Book by Golub G.H and Van Loan- Matrix Computations
- Iterative methods (2 books) by Yousuf saad
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Book Play with graphs –Amit Agarwal (don't follow rigorously, because of easy availability of interactive plotting tools these days.. but do go through it someday)
Free interactive Plotting tools -
Geogebra, Desmos, or python libraries like- maxim etc.
3.a). Calculus - Basics of all topics in general books by
- Essence of calculus videos -3Blue1Brown
- George Thomas , calculus
- NCERT books 11'th , 12'th ,lectures by Eddie Woo on certain school topics
- Calculus I and II by Dr. Trefor Bazett(I, II )
- Oxford calculus video lectures by Dr. Tom Crawford
- A perspective on derivative by Aleph 0
- Advanced Engineering maths - Erwyn Kreyszig,
- Advanced Engineering maths - Michael D. Greenberg
3.b) Advanced topics, but essential ones as follows
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Multivariate calculus by Dr. Trefor Bazett
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Vector Calculus -
- Divergence, grad, curl and all that. Book by H.M.Schey (along with some related videos by 3Blue1Brown and video lecture on multivariable calculus by Khan Academy )
- Vector calculus lectures by Dr. Trefor Bazett
- Stokes theorem nicely explained by Aleph 0
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Tensors
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Tensors for begineers and Tensor Calculus videos lectures by eigenchris
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Introduction to Tensor Calculus video lectures by MathTheBeautiful
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Video lecture playlist by WHYBmaths
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Video by Aleph 0 on Tensor Product
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Book by Daniel Fleisch (guide for vectors and tensors)
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Book by Harry Lass- vector and tensor analysis
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Book by Rutherford Aris – vectors, tensors and basic Fluid Mech eqns.
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Digression into continuum mechanics using tensor notations (optional)
- Books By Gurtin Morton on continuum mechanics
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Functional analysis
- Book titled A friendly approach to functional analysis by Amol Sasane
- Video lecture playlist by The bright side of mathematics
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Differential equations (DE)—
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Differential Equations basics video lecture playlist by Dr Trefor Bazett and by Flammable Maths
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Assorted topics in ODEs by Faculty of Khan
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Book by Zill and Cullen
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Book by George F. Simmons ,
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Book by William Boyce ,
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Book by Vladimir Arnold
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Video by 3blue1brown on Differential equation, Fourier series and Fourier transform, videos by commutant
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Video on Laplace transforms by Zach Star, Flammable Maths and Eugene Khutoryansky
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PDEs
- PDEs by Faculty of Khan
- Video by 3blue1brown, Khan academy, Steve burton series on solving PDEs, lectures at ICTP , MathTheBeautiful , commutant
- Partial Differential Equations playlist series by Giovanni Bellettini
- Book by Lawrence Evans for advanced topics. Basic ones already covered in previous books) ,
- Book by Stanley Farlow on PDE
- Book by Arnold Sommerfeld on PDE
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Some not so common topics in DEs ,as follows
- Lectures on Basic perturbation theory by Nitin Upadhyaya.
- Lectures on Advanced Differential Equations course by Dr. Nathan Kutz.
- Asymptotic methods and perturbations theory –advanced mathematics methods Book by Carl Bender and Orszag. and related videos here
- Calculus of variations by Faculty of Khan
- Lectures on Perturbation methods for nonlinear PDEs by Dr. Vishal Vasan
- Asymptotics and perturbation methods by Steven Strogatz ,lectures here
- Nonlinear dynamics and chaos by Steven strogatz and his lectures here . Lectures on same topic by V.Balakrishnan
- Digression to mathematical physics topics (optional)
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Arnold –mathematical methods of classical mechanics
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Fasano mariam's – Analytical methods
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Leonard Meirovitch – Methods of analytical dynamics and all his other books.
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Variational methods – books by J.N.Reddy
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Complex variables and complex calculus –
- A video playlist titled Imaginary Numbers are Real by Welch labs
- Video lecture by Herbert gross MIT, followed by this, and this.
- Video lectures full playlist by Prof Petra Bonfert-Taylor
- Video lectures playlist by Nitin Upadhyaya
- Book by Functions of a complex variable- Carrier, crook and Pearson
- Book by Tristhan Needham - Visual complex analysis
- Book by Ablowitz and Fokas - Complex variables
- Video on Complex Differentiation by vcubingx
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Spectral methods by Boyd (some of his free books) here.
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Applied mathematics by MIT (applications to scientific computing). course material available on github here
Other topics and engineering applications of which I don't have much ideas or did not follow much are real analysis, probability, statistical methods, group theory, and measure theory, etc. Please contribute to the list if you recommend any.
Advanced miscellaneous mathematical methods books that cover almost all topics mentioned above and even more, but used generally for reference and problem practice purpose:
- Book by George Arken and Weber –Mathematical methods for physicists
- Book by Riley, Hobson and Bence -Mathematical methods in physics and engineering
- Book by V. Balakrishnan – Mathematical methods for physicists. (video lectures here)
3B1B Summer of Math Exposition playlist
Summary of important maths YouTube channels to subscribe and follow
- 3Blue1Brown, Faculty of Khan , Khan academy, Eddie Woo
- Wolfram, MATLAB
- University channels: MIT opencourseware, Oxford mathematics, ICTS-TIFR, Institute of pure and applied mathematics, and all other nice universities across globe,
- Steve Burton, Brian Douglas, Zach Star
- Dr Trefor Bazett
- Physics videos by Eugene Khutoryansky
- The Bright Side of Mathematics , Numberphile, Mathologer, MathTheBeautiful
- Welch Labs
- Mathematical monk, commutant.
- vcubingx
- Aleph 0
- Flammable Maths
- Tom Rocks Maths
- Julialang