For the theory part, I referred to standard textbooks and did not use any coaching notes. The textbooks have adequate solved questions for practice as well. For test series simulation, I joined IMS (2020) and Pariksha Ganga (2022). I will also share my topic-wise short notes, Learning Diary and test series copies on Telegram channel. Paper-I
Topic
Source
Strategy
Important Areas
Linear Algebra
Schaum’s Outlines Linear Algebra 4/e
a.Made short notes of each sub-topic
b.Very important to keep revising the short notes
c.Solve a variety of Qs from test series to get a hang of it
a.Orthogonal and
Unitary Matrices
b.Row Echelon Form
c.Change of Basis
d.Diagonalization
Calculus
Mathematical Analysis by SC Malik and Savita
Arora
a.Has very extensive set of Qs to practice
b.Nicely written book with explanations
c.Use Internet videos to help in surface and volume integrals
a.Euler’s theorem for
homogenous functions
b.Taylor Series expansion
c.Beta and Gamma function
3D
Krishna Series Book (2D & 3D)
a.Need to memorise method of solving various types of locus Qs
b.Keep short notes handy
c.Once you get the feel of solving Qs, different shapes will feel repititive
a.Finding asymptotes
b.Radical plane
c.Director sphere
d.Enveloping cone
e.Normal to a conicoid
f.Reduction to std
form algorithm
ODE
MD Raisinghania
a.Solve diverse Qs from the book; the book is an ocean, do not get lost in it, avoid solving same type of Qs it will give you fake confidence
b.Also look for old UPSC PYQs in the book, solve all of them
c.I also learnt : In choice-based questions in the exam (Q6,7,8), opt for ODE only after solving entirely in rough because looks may be deceptive!
a.Reduction of order of ODE
b.Reduction to normal form
c.Laplace transform
Statics and
Dynamics
Krishna Series
a.Physics topics can be very easy if you can visualise the
Qs
b.Less need to memorise here, it is mostly conceptual
c.Solve recent PYQs as they are getting trickier
Vector
Krishna Series
a.Has some overlap with Calculus
b.Mostly logical
c.Memorise the S-F formulae with proof
d.Green’s Theorem and Stokes Theorem Qs can be tricky, need a lot of coneptual clarity regarding surface of integration, etc
a.Here my idea was to master the easier concepts from 10M point of view
b.It is an iterative process : read the theory try to solve the Q – look at the solution repeat
c.Do not waste a lot of preparation time on this; can prioritise other topics but must have enough grasp over easy to moderate questions; keep referring notes to memorise definitions of ring, field, ideals, etc
Real Analysis
Mathematical Analysis by SC Malik and Savita Arora
a.Has very good Q bank
b.Multiple revisions to familiarise with proof methods
a.Memorise all the convergence tests
b.Keep revising the questions and how to solve them
a.Different tests for convergence and where to apply them
Complex Analysis
Krishna Series
a.Simple topic but needs a lot of conceptual clarity
b.Can get lost in the book; keep referring PYQs and Syllabus to filter relevant content
a.Polar form of
Cauchy-Reimann equation
b.Cauchy’s
Integral Formula
c.Residue
Theorem
LPP
Krishna Series book
a.Practice and memorise methods of solving
a.Simplex, Dual
Primal and 2Phase Method
(simplified in my
Learning Diary)
PDE
MD Raisinghania
a.Solve diverse Qs to get a hang of it
b.BVP problems need to be understood properly; develop your short method of solving in exam, since there is also time
and space constraint
a.Practice is the key
a.Origin of PDE
b.Charpit’s
Method
c.Cauchy’s
Method
d.Boundary Value
Problem
Numerical
Analysis and
Computer
Programming
Higher Engineering Mathematics by Dr BS Grewal, 42nd edition
