SIM Classes provide coaching and guidance to students of Class BA/B.Sc (Mathematics). The Institute has an organized classroom program, where along with regular classes, regular tests and doubt clearing sessions are scheduled to help students get over their problems and face the exams with confidence. SIM Classes provide coaching for all three years to BA/B.Sc (Math’s- all Books).
Teaching Methodology
The distinct features of coaching at SIM Classes as described as under:
- Coaching as per the latest syllabus.
- Comprehensive study material.
- Regular tests, Problem solving / doubt removal sessions.
- Facility to check test scores online on SIM Classeswebsite at any time.
- Organized classrooms with all the facilities.
- Highly qualified and experienced faculty.
- Academics are planned in such a manner that the course finishes much in advance. This leaves enough time for self revision, polishing of examination temperament and removal of last moment doubts.
- Best guidance to students about further competitive exams.
- Limited seats for each Batch so that teacher can give personal attention to each individual.
To know about Batch Schedules, Call 9415009164
RECOMENDED UNIFIED SYLLABUS OF MATHEMATICS
For B.Sc. / B.A. ( From 2011 – 2012 onwards )
B.A. / B.Sc. First Year
Coming Soon
B.A. / B.Sc. Second Year
Paper I : LINEAR ALGEBRA and MATRICES
- Unit 1: Vector spaces and their elementary properties, Subspaces, Linear dependence and independence, Basis and dimension, Direct sum, Quotient space.
- Unit 2: Linear transformations and their algebra, Range and null space, Rank and nullity, Matrix representation of linear transformation, Change of basis.
- Unit 3: Linear functional, Dual space, Bi-dual space, Natural isomorphism, Annihilators, Bilinear and quadratic forms, Inner product spaces, Caucy-Schwarz’s inequality, Bessel’s inequality and orthogonality.
- Unit 4: Symmetric and skew-symmetric matrices, Hermitian and kew- Hermitian matrices, Orthogonal and unitary matrices, Triangular and diagonal matrices, Rank of a matrix, Elementary transformations, Echelon and normal forms, Inverse of a matrix by elementary transformations.
- Unit 5: Characteristic equation, Eigen values and eigen vectors of matrix, Cayley-Hamilton’s theorem and its use in finding inverse of a matrix, Application of matrices to solve a system of linear (both homogeneous and non-homogeneous) equations, Consistency and general solution, Diagonalization of square matrices with distinct eigen values, Quadratic forms.
PAPER II : DIFFERENTIAL EQUATIONS AND INTEGRAL TRANSFORMS
Differential Equations
- Unit 1. Formation of a differential (D.E.), Degree, order and solution of a D.E., Equations of first order and first degree : Separation of variables method, Solution of homogeneous equations, linear equations and exact equations, Linear differential equations with constant coefficients, Homogeneous linear differential equations,
- Unit 2 . Differential equations of the first order but not of the first degree, Clairaut’s equations and singular solutions, Orthogonal trajectories, simultaneous lineardifferential equation of the second order (including the method of variation of parameter).
- Unit 3 :Series solutions of second order differential equations, Legendre and Bessel functions (Pn and Jn only) and their properties. Order, degree and formation of partial differential equations, partial differential equations of the first order, Lagrange’s equations, Charpit’s general method, Linear partial differential equations with constant coefficients.
- Unti 4 : (i) Partial differential equations of the second order, Monge’s method.
Integral Transforms
- Unit 4 : (ii) The concept of transform, Integral transforms and kernel, Linearity property of transforms, Laplace transform, Inverse Laplace transform, Convolution theorem, Applications of Laplace transform to solve ordinary differential equations.
- Unit 5 : Fourier transforms (Finite and infinite), Fourier integral, Applications of Fourier transform to boundary value problems, Fourier series.
Paper III : MECHANICS
- Unit 1.Velocity and acceleration along radial and transverse directions, and along tangential and normal directions, Simple harmonic motion, motion under other laws of forces, Earth attraction, Elastic strings.
- Unit 2: Motion in resisting medium, Constrained motion (circular and cycloidal only).
- Unit 3: Moton on smooth and rough plane curves, Rocket motion, Central orbits and kepler’s law, Motion of a particle in three dimensions.
- Unit 4: Common catenary, Centre of gravity, Stable and unstable equilibrium, virtual work.
- Unit 5: Forces in three dimensions, Poinsot’s central axis, Wrenches, null line and null plane.
B.A. / B.Sc. Final Year
Paper I :- Real Analysis
- Unit 1. Axiomatic study of real numbers, Completeness property in R, Archimedean property, Countable and uncountable sets, Neighborhood, Interior points, Limit points, Open and closed sets, Derived sets, Dense sets, Perfect sets, Bolzano-Weierstrass theorem
- Unit 2. Sequences of real numbers, subsequences, Bounded and monotonic sequences, Convergent sequences, Cauchy’s theorems on limit, Cauchy sequence, Cauchy’s general principle of convergence, Uniform Convergence of sequences and series of functions, Weierstrass M-test, Abel’s and Dirichlet’s tests.
- Unit 3. Sequential continuity, Boundedness and intermediate value properties of continuous functions, Uniform continuity, Meaning of sign of two variables, Taylor’s theorem for functions of two functions, Maxima and minima of functions of three variables, Lagrange’s method of undetermined multipliers.
- Unit 4. Riemann integral, Integrality of continuous and monotonic functions, Fundamental theorem of integral calculus, Mean value theorems of integral calculus, Improper integrals and their convergence, Comparison test, I’-test, Abel’s test, Dirichlet’s test, Integral as a function of a parameter and its differentiability and integrability.
- Unit 5. Definition and examples and its metric spaces, Neighborhoods, Interior points, Limit points, Open and closed sets, Subspaces, Convergent and Cauchy Sequences, Completeness, Cantor’s intersection theorem.
Paper:- II COMPLEX ANALYSIS
- Unit 1. Functions of a complex variable, Concepts of limit, continuity and differentiability of complex functions, Analytic functions, Cauchy-Riemann equations (Cartesian and polar form), Harmonic functions, orthogonal system, and Power series as an analytic function.
- Unit 2. Elementary functions, Mapping by elementary functions, Linear and bilinear transformations, fixed points, Cross ratio, Inverse points and critical points, conformal transformations.
- Unit 3. Complex Integration, Line integral, Cauchy’s fundamental theorem, Cauchy’s integral formula, Morea’s theorem, Liouville theorem, Maximum Modulus theorem, Taylor and Laurent series.
- Unit 4. Singularities and zeros of an analytic function, Rouche’s theorem, Fundamental theorem of algebra, Analytic continuation.
- Unit 5. Residue theorem and its applications to the evaluation of definite integrals, Argument principle.
Paper III :- NUMERICALANALYSIS and PROGRAMMING
Numerical Analysis
- Unit 1. Shift operator, Forward and backward difference operator and their relationships, Fundamental theorem of difference calculus, Interpolation, Newton-Gregory’s forward and backward interpolation formulae.
- Unit 2. Divided differences, Newton’s divided difference formula, Lagrange’s interpolation formula, Central differences, Formulae based on central differences: Gauss, Striling’s Bessel’s and Everett’s interpolation formulae, Numerical differentiation.
- Unit 3. Numerical integration, General quadrature formula, Trapezoidal and Simpson’s riles, Weddle’s rule, Cote’s formula, Numerical solution of first order differential equations: Euler’s method, Picard’s method, Runge-Kutta method and Milne’s method, Numerical solution of linear, homogeneous and simultaneous difference equations, Generating function method.
- Unit 4. Solution of transcendental and polynomial equations by iteration, bisection, Regula-Falsi and Newton-Raphson methods, Algebraic Eigen value problems: Power method Jacobi’s method, Given’s method, Householder’s method and Q-R method, Approximation: Different types of approximations, Least square polynomial approximation, Polynomial approximation using orthogonal polynomials, Legendre approximation, Approximation with trigonometric functions, exponential functions, rational functions, Chebyshev polynomials.
Programming in C
- Unit 5. Programmer’s model of computer, Algorithms, Data type, Arithmetic and input/out instruction, Decisions, Control structures, Decision statements, Logical and conditional operators, Loop case control structures, Functions Recursion, Preprocessors, Arrays, Puppetting of strings Structures, Pointers, File formatting.
Simple and random sampling. Test of significance for large samples. Sampling distribution of Mean. Standard error, Test of significance based on. Test of significance based on distribution
IAS/IFoS MATHEMATICS OPTIONAL by Surendra Yadav
Regular and Weekend Time Table :
| TIMING | REGULAR (MON TO FRI) | WEEKEND (SAT & SUN) |
|---|---|---|
| 6:30 am to 8:00 am | -will be announced- | -will be announced- |
| 11:00 am to 12:00 pm | –B.Sc. Final Year Starting From 11 Aug CLICK HERE For Online Admission Form To join online classes CLICK HERE | -will be announced- |
| 10:00 am to 11:00 am | B.Sc. Second Year Starting From 11 Aug CLICK HERE For Online Admission Form To join online classes CLICK HERE | -will be announced- |
| 5:00 pm to 6:00 pm | -will be announced- | -will be announced- |
Note: Different Batches with different chapters (topics)
ONE DAY ONE CHAPTER PROGRAMME
SIM Classes CONDUCTS SPECIAL FAST TRACK CLASSES
(Occasionally) on Sunday from 8:00am to 8:00pm.
- The Fast Track batches students are strictly advised to attend the Regular and Weekend classes.
- With these classes (Fast Track + Regular + Weekend) SIM Classes ensures that the entire syllabus to be covered in just 4 months period.