You may hate it or love it but you can't ignore it , while some have mathematics placed in their list of sworn enemies others think of it as an art and they are the picasso . (I am partially of the second type xd).
The syllabus for the 1st year (1st sem) mainly consists of calculus .
UNIT I
Infinite series: Tests for convergence of series (comparison, ratio, root, integral, Raabe’s, logarithmic), Alternating series, Absolute convergence, Conditional convergence.
UNIT II
Calculus of single variable: Taylor’s & Maclaurin’s expansion, Radius of curvature, applications of definite integral to area, arc length, surface area and volume (in Cartesian, parametric and polar co-ordinates).
UNIT III
Calculus of several variables: Partial differentiation, Euler’s theorem, total differential, Taylor’s theorem, Maxima Minima, Lagrange’s method of multipliers, Application in estimation of error and approximation.
UNIT IV
Multiple Integrals: Double integral (Cartesian and polar coordinates), change of order of integration, triple integrals (Cartesian, cylindrical and spherical co-ordinates), Gamma and Beta functions. Applications of multiple integration in area, volume,centre of mass, and moment of inertia.
UNIT V
Vector Calculus: Continuity and differentiability of vector functions, Scalar and vector point function, Gradient, Directional derivative, divergence, curl and their applications. Line integral, surface integral and volume integral, applications to work done by the force . Applications of Green’s, Stoke’s and Gauss divergence theorems.
So with so much calculus around , one is bound to get scared until he finds the right source to study (this is where we come in ) .
DTU recommends the following :-
1. “Advanced Engineering Mathematics” by Alan Jeffery ; Academic Press
2. “Calculus and Analytic Geometry” by Thomas/Finney; Narosa.
3. “Advanced Engineering Mathematics” by Kreyszig; Wiley.
4. “Advanced Engineering Mathematics” by Taneja ; I K international
5 “Advanced Engineering Mathematics” by Jain/Iyenger; Narosa.
Warning : The first look at the size of these books may cause dizziness , please be courageous .
The books from foreign authors serve their purpose by giving concepts but where they fail is at quality and quantity of problem sets . In the exam where more amount of practice matters , these books are certainly not the complete package .
The Indian authors on the other side try to make their book both good in theory and problems mostly losing out on former and focusing on latter .
You can try 2 (It is a god of concepts , calculus would become crystal clear once you are through) and 3 . (library is filled of both of them) .
4 and 5 are certainly good options to practice and perfect and sometimes learn , but not everytime .
Another book that can be considered is here is this :
"Textbook of Engineering Mathematics" by V.P Jaggi and A.B Mathur
while this book is out of print , you can get it at the library (be fast) . Its a small book , don't go for the larger version . (shhh! - teachers at dtu teach from this book -shhh! )
If you want to become the master of calculus . This is one of the best book you will ever come across . Each and every topic in syllabus is subset of this book .
"Calculus" by Stewart
Books play a major role in understanding mathematics but the biggest role is played by you so be regular at it , Just don't listen to those friends who say they study nothing , they are already ahead of you , gear up and don't stop until you are at the top .
Previous questions papers and their solution can be found in the Tests Section .
Good luck !!
