DAMP™

DAMP™ Mathematics

By S. Avi Sir

Start Date: 15 June 2021
Duration: 2 Months
Delivery Mode: Online
Validity: Till 10 Oct, 2021

Course Fee: ₹ 6500 + GST (18%)

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Features of the Program:

  • 2 Months (Paper 1 – 4 Weeks | Paper 2 – 4 Weeks)
  • Daily – Three Questions |Three Evaluations |Five Practice Questions I Three Discussions
  • 2 Full Length Tests
  • 6 Days a week | Completely online module 
  • Comprehensive coverage of Entire Mathematics Syllabus
  • Individual Evaluation, Feedback + Personalised Mentoring 

Structure of the Program:

    • Question will be released at 12.00 pm (Afternoon)
    • Answer can be uploaded till 12:00pm (Next Day Afternoon)
    • Answer Discussion video will be released at 12:00pm (Next Day Afternoon)

For complete Terms and Conditions scroll to the bottom

MATHEMATICS SYLLABUS

PAPER – I
Linear Algebra
15-Jun-21 Day 1 Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension.
16-Jun-21 Day 2 Linear transformations, rank and nullity, matrix of a linear transformation.
17-Jun-21 Day 3 Algebra of Matrices; row and column reduction, echelon form, congruence, and similarity; rank of a matrix; inverse of a matrix; solution of system of linear equations.
18-Jun-21 Day 4 Eigenvalues and eigenvectors, characteristic polynomial, Cayley-Hamilton theorem,
19-Jun-21 Day 5 Symmetric, skew-symmetric, Hermitian, skew-Hermitian, orthogonal, and unitary matrices and their eigenvalues.
Calculus:
21-Jun-21 Day 6 Real numbers, functions of a real variable, limits, continuity, differentiability, mean value theorem, Taylor’s theorem with remainders, indeterminate forms, maxima, and minima,
22-Jun-21 Day 7 Asymptotes; curve tracing; functions of two or three variables: limits, continuity, partial derivatives, maxima and minima, Lagrange’s method of multipliers, Jacobian.
23-Jun-21 Day 8 Riemann’s definition of definite integrals; indefinite integrals; infinite and improper integrals;
24-Jun-21 Day 9 Double and triple integrals (evaluation techniques only); areas, surface, and volumes.
Analytic Geometry:
25-Jun-21 Day 10 Cartesian and polar coordinates in three dimensions, straight lines, shortest distance between two skew lines; plane, sphere,
26-Jun-21 Day 11 Cone, cylinder, paraboloid,
28-Jun-21 Day 12 Ellipsoid, hyperboloid of one and two sheets and their properties.
29-Jun-21 Day 13 Second degree equations in three variables, reduction to canonical forms,
Ordinary Differential Equations:
30-Jun-21 Day 14 Formulation of differential equations; equations of first order and first degree, integrating factor; orthogonal trajectory.
01-Jul-21 Day 15 Equations of first order but not of first degree, Clairaut’s equation, singular solution.
02-Jul-21 Day 16 Second and higher order linear equations with constant coefficients, complementary function, particular integral, and general solution.
03-Jul-21 Day 17 Second order linear equations with variable coefficients, Euler-Cauchy equation; determination of complete solution when one solution is known using method of variation of parameters.
05-Jul-21 Day 18 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.
Dynamics:
06-Jul-21 Day 19 Rectilinear motion, simple harmonic motion, motion in a plane, projectiles.
07-Jul-21 Day 20 Constrained motion; work and energy, conservation of energy.
08-Jul-21 Day 21 Kepler’s laws, orbits under central forces.
Statics:
09-Jul-21 Day 22 Equilibrium of a system of particles; work and potential energy, friction; principle of virtual work;
10-Jul-21 Day 23 Common catenary, stability of equilibrium, equilibrium of forces in three dimensions.
Vector Analysis:
12-Jul-21 Day 24 Scalar and vector fields, differentiation of vector field of a scalar variable; vector identities and vector equations
13-Jul-21 Day 25 Gradient, divergence, and curl in cartesian and cylindrical coordinates; higher order derivatives.
14-Jul-21 Day 26 Application to geometry: curves in space, curvature, and torsion; Serret-Frenet’s formulae.
15-Jul-21 Day 27 Gauss and Stokes’ theorems, green’s identities.
16-Jul-21 FLT-1 (Full Length Test)
PAPER-II
Algebra:
19-Jul-21 Day 28 Groups, subgroups, cyclic groups, cosets, Lagrange’s Theorem, normal subgroups, quotient groups,
20-Jul-21 Day 29 Homomorphism of groups, basic isomorphism theorems, permutation groups, Cayley’s theorem.
21-Jul-21 Day 30 Rings, subrings, and ideals, homomorphisms of rings.
22-Jul-21 Day 31 Integral domains, principal ideal domains, Euclidean domains, and unique factorization domains;
23-Jul-21 Day 32 Fields, quotient fields.
Real Analysis:
24-Jul-21 Day 33 Real number system as an ordered field with least upper bound property;
26-Jul-21 Day 34 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.
27-Jul-21 Day 35 Continuity and uniform continuity of functions, properties of continuous functions on compact sets.
28-Jul-21 Day 36 Riemann integral, improper integrals; fundamental theorems of integral calculus.
29-Jul-21 Day 37 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.
Complex Analysis:
30-Jul-21 Day 38 Analytic functions, Cauchy-Riemann equations,
31-Jul-21 Day 39 Power series representation of an analytic function, Taylor’s series; singularities; Laurent’s series.
02-Aug-21 Day 40 Cauchy’s theorem, Cauchy’s integral formula Cauchy’s residue theorem; contour integration.
Linear Programming:
03-Aug-21 Day 41 Linear programming problems, basic solution, basic feasible solution, and optimal solution.
04-Aug-21 Day 42 Graphical method and simplex method of solutions; duality.
05-Aug-21 Day 43 Transportation and assignment problems.
Partial differential equations:
06-Aug-21 Day 44 Family of surfaces in three dimensions and formulation of partial differential equations.
07-Aug-21 Day 45 Solution of quasilinear partial differential equations of the first order,
09-Aug-21 Day 46 Linear partial differential equations of the second order with constant coefficients, canonical form; Cauchy’s method of characteristics
10-Aug-21 Day 47 Equation of a vibrating string, heat equation, Laplace equation and their solutions.
Numerical Analysis:
11-Aug-21 Day 48 Numerical methods: solution of algebraic and transcendental equations of one variable by bisection, Regula-Falsi and Newton-Raphson methods;
12-Aug-21 Day 49 Solution of system of linear equations by Gaussian elimination and Gauss-Jordan (direct), Gauss-Seidel(iterative) methods.
13-Aug-21 Day 50 Newton’s (forward and backward) interpolation, Lagrange’s interpolation.
14-Aug-21 Day 51 Numerical integration: Trapezoidal rule, Simpson’s rules, Gaussian quadrature formula.
15-Aug-21 Day 52 Numerical solution of ordinary differential equations: Euler and Runge Kutta-methods.
Computer Programming:
16-Aug-21 Day 53 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.
17-Aug-21 Day 54 Basic logic gates and truth tables, Boolean algebra, normal forms. Representation of unsigned integers signed integers and reals, double precision reals and long integers.
18-Aug-21 Day 55 Algorithms and flow charts for solving numerical analysis problems.
Mechanics:
19-Aug-21 Day 56 Generalized coordinates; D’ Alembert’s principle and Lagrange’s equations; Hamilton equations;
20-Aug-21 Day 57 Moment of inertia; Motion of rigid bodies in two dimensions.
Fluid Dynamics:
21-Aug-21 Day 58 Equation of continuity; Stream-lines, path of a particle.
22-Aug-21 Day 59 Euler’s equation of motion for inviscid flow; Potential flow; Two-dimensional and axisymmetric motion.
23-Aug-21 Day 60 Sources and sinks, vortex motion; Navier-Stokes equation for a viscous fluid.
24-Aug-21 FLT-2 (Full Length Test)

P.S.: Changes in the schedule may be made with a prior announcement to the students

Note:

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