Many IAS/IFoS(IFS) aspirants study at home and/or comfortable atmosphere to supplement their class-based learning. However, self study can also be used to master a new skill or learn an entirely new concept – like a language or an instrument. The benefits you can gain from self study are endless and are completely determined by your (aspirant) goals.

There are various self studying methods you can implement at home (whether they’re self study tips to complete solo or with you) that can bring about many educational benefits both in and out of coaching institutes.

**My dear IAS/IFoS(IFS)/UPSC/CSE-Civil Services Exam Maths/Mathematics Optional aspirants USE THE FOLLOWING METHODS TO STUDY AT HOME OR WITH YOUR ROOM.**

**Have a conversation**with your aspirant about what is being learned at their room or home, and what topics your aspirant is interested in. This will encourage aspirants to strive to learn more, so they can keep teaching you what they know. Additionally, the practice of teaching is known as one of the top ways to work towards grasping a concept!**Read books and articles**on a topic of study, or interest. Whether this is in connection with a course, or just at yours’s own leisure, encouraging you to read is a highly effective way to increase understanding of new concepts. Take a trip to the library together, or invest in some classics on a topic to provide the best reading materials which we are providing to self study.**Watch educational videos**to keep aspirants actively engaged in a concept. There are many tutorial videos which we will provide on YouTube that are intended for teaching people new skills, or educational shows aimed at complementing what aspirants learn in Coaching classes. Whether your home learner is trying to learn another language, or figuring out how to conduct a science experiment, they can greatly benefit from the audio and visual walk through.**Educational games**are a mentor and aspirant favourite when it comes to ways to study at home or in your room. There are many apps that you can access through your phone that promote learning in Mathematics/Maths optional for IAS/IFoS(IFS)/UPSC/CSE-Civil Services Exam, GS mains, and prelims CSAT PAPER-1 & CSAT PAPER-2 and a variety of other courses. Or put the phone down and get hold of board games and card games that promote strategy and logic. Encourage you to associate learning with fun.**Work through practice questions**to reinforce skills that are learned at Class room coaching while studying at home or in your room. Help hold yours attention while working through the practice questions by incorporating games, rewards, and challenges. This will help them view the material in a new way, and reinforce what is learned in the classroom coaching.

| Syllabus | Module |

Test-01 | Formulation of differential equations; Equations of first order and first degree, integrating factor; Orthogonal trajectory; Equations of first order but not of first degree, Clairaut’s equation, singular solution. | ODE |

Test-02 | Second and higher order linear equations with constant coefficients, complementary function, particular integral and general solution. Second order linear equations with variable coefficients, Euler-Cauchy equation (Homogeneous linear equations); | |

Test-03 | Determination of complete solution when one solution is known using method of variation of parameters. | |

Test-04 | Laplace and Inverse Laplace transforms and their properties; Laplace transforms of elementary functions. Application to initial value problems for 2nd order linear equations with constant coefficients. | |

Test-05 | Family of surfaces in three dimensions and formulation of partial differential equations; Solution of quasi linear partial differential equations of the first order | PDE |

Test-06 | Cauchy’s method of characteristics; Canonical form, Laplace equation and their solutions; Equation of a vibrating string, heat equation. | |

Test-07 | Linear partial differential equations of the second order with constant coefficients, | |

Test-08 | Cartesian and polar coordinates in three dimensions, Plane, Straight lines & Shortest distance (S.D) between two skew lines | AG |

Test-09 | Sphere | |

Test-10 | Cone & Cylinder | |

Test-11 | paraboloid, ellipsoid, hyperboloid of one and two sheets and their properties. | |

Test-12 | second degree equations in three variables, reduction to canonical forms. | |

Test-13 | Linear programming problems, basic solution, basic feasible solution and optimal solution; Graphical method and simplex method of solutions; Duality. | LPP |

Test-14 | Transportation and assignment problems. | |

Test-15 | Numerical methods: Solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi and Newton-Raphson methods; solution of system of linear equations by Gaussian elimination and Gauss-Jordan (direct), Gauss-Seidel (iterative) methods. Newton’s (forward and backward) interpolation, Lagrange’s interpolation. | NA & CP |

Test-16 | Numerical integration: Trapezoidal rule, Simpson’s rules, Gaussian quadrature formula. Numerical solution of ordinary differential equations: Euler and Runga Kutta-methods. | |

Test-17 | Binary system; Arithmetic and logical operations on numbers; Octal and Hexadecimal systems; Conversion to and from decimal systems; Algebra of binary numbers. Elements of computer systems and concept of memory; Basic logic gates and truth tables, Boolean algebra, normal forms. Representation of unsigned integers, signed integers and reals, double precision reals and long integers. Algorithms and flow charts for solving numerical analysis problems. | |

Test-18 | Groups, subgroups, cyclic groups, cosets, Lagrange’s Theorem | MA |

Test-19 | Normal subgroups, quotient groups, homomorphism of groups, basic isomorphism theorems, permutation groups, Cayley’s theorem. | |

Test-20 | Rings, Integral domains, Fields, sub rings and ideals. | |

Test-21 | Homomorphism of rings; Principal Ideal domains, Euclidean domains and Unique Factorization domains; , Quotient fields. | |

Test-22 | Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension; | |

Test-23 | Linear transformations, rank and nullity, matrix of a linear transformation. | LA |

Test-24 | Algebra of Matrices; Row and column reduction, Echelon form, congruence’s and similarity; Rank of a matrix; Inverse of a matrix; Solution of system of linear equations; Eigen values and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem, Symmetric, skew-symmetric, Hermitian, Skew-Hermitian, orthogonal and unitary matrices and their eigen values. | |

Test-25 | Real number system as an ordered field with least upper bound property; Sequences, limit of a sequence, Cauchy sequence, completeness of real line; Series and its convergence, absolute and conditional convergence of series of real and complex terms, rearrangement of series. | RA |

Test-26 | Continuity and uniform continuity of functions, properties of continuous functions on compact sets. Riemann integral, improper integrals; | |

Test-27 | Fundamental theorems of integral calculus. Uniform convergence, continuity, differentiability and integrability for sequences and series of functions; Partial derivatives of functions of several (two or three) variables, maxima and minima. | |

Test-28 | Real numbers, functions of a real variable, limits, continuity, differentiability, mean value theorem, Taylor’s theorem with remainders, indeterminate forms, maxima and minima, asymptotes; Curve tracing; | CAL |

Test-29 | Functions of two or three variables: limits, continuity, partial derivatives, maxima and minima, Lagrange’s method of multipliers, Jacobian. | |

Test-30 | Riemann’s definition of definite integrals; Indefinite integrals; Infinite and improper integrals; Double and triple integrals (evaluation techniques only); Areas, surface and volumes. | |

Test-31 | Analytic functions, Cauchy-Riemann equations, Cauchy’s theorem, Cauchy’s integral formula, power series representation of an analytic function, | CA |

Test-32 | Taylor’s series; Singularities; Laurent’s series; Cauchy’s residue theorem; Contour integration. | |

Test-33 | Scalar and vector fields, differentiation of vector field of a scalar variable; Gradient, divergence and curl in Cartesian and cylindrical coordinates; Higher order derivatives; | VA |

Test-34 | Vector identities and vector equations. Application to geometry: Curves in space, Curvature and torsion; Serret-Frenet’s formulae. Gauss and Stokes’ theorems, Green’s identities. | |

Test-35 | Rectilinear motion, simple harmonic motion, motion in a plane, projectiles; constrained motion; | D & S |

Test-36 | Work and energy, conservation of energy; Kepler’s laws, orbits under central forces. Equilibrium of a system of particles; | |

Test-37 | Work and potential energy, friction; common catenary; Principle of virtual work; Stability of equilibrium, equilibrium of forces in three dimensions. | |

Test-38 | Generalized coordinates; D’ Alembert’s principle and Lagrange’s equations; Hamilton equations; Moment of inertia; | M & FD |

Test-39 | Motion of rigid bodies in two dimensions. Equation of continuity; Euler’s equation of motion for in viscid flow; Stream-lines, path of a particle; Potential flow; | |

Test-40 | Two-dimensional and axisymmetric motion; Sources and sinks, vortex motion; Navier-Stokes Equation for a viscous fluid. |

**TO MOST EFFECTIVELY INCORPORATE SELF STUDYING INTO YOURS LIFE, MAKE SURE YOU HAVE THE FOLLOWING TOOLS ON HAND**

**A study area**is crucial for effective self studying. This might mean a home office, or a desk in the aspirant’s bedroom. No matter where it is, it should include a tidy work space – free of clutter and distractions – with good lighting.**A computer**or tab or Android phone with internet connection is necessary for many methods of self study, especially where reading, watching or listening to online resources are concerned. However if yourself studier prefers completing work by hand, non-digital substitutes (ex. Pen, pencils and notebooks) can be used.**Note-taking tools**such as highlighters, coloured pens and sticky notes are useful tools for an aspirant studying at home or in their room. Keeping notes while learning will enable you to retain the information longer, and help to build valuable organizational skills.

If you are struggling when test time comes around, **Ramanasri IAS/IFoS Institute’s Self Study program** is here to help! Contact us today to learn more and many things daily.

Finally you can reach your dream of becoming an IAS officer !!!

**How to Register Self-Study Program**

- Fill the Ramanasri UPSC Maths Optional Coaching Application/Admission Form. For this Click on this Link:
**Admission Form of Ramanasri Maths Optional** - Upload the passport size of photo of yours top right of the corner (select your image).
Fill all the details of the of the Ramanasri UPSC Maths Optional Coaching Application/Admission Form.- Click on the Submit button below.

**FEE STRUCTURE **

Price of the Self-Study Program (40 Tests) along with Study Materials: Rs.27,500/-

Price of the Self-Study Program (40 Tests): Rs.17,500/-