  ## 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%)

#### 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 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:

All our lectures are under the license of copyright protection, under the Copyright Act 1957 (the Act), supported by the Copyright Rules 1958 (the Rules), International Copyright Order, 1999 and Copyright Act in 2012. So copying our videos, illegal piracy, downloads, sharing, distribution etc. are strictly not allowed. We will take strict legal action against people doing so.

We have embedded tracking of video usage with the location, IP and we collect data on the video usage to check if there are any suspicious downloads of video happening with some third-party software. In such cases, the culprits will not be given any warning from our end; instead, strict legal action will be enforced.

Sharing of the user’s login and password is strictly prohibited. If any student is found doing so, his account would be suspended, and we will file a legal case of data theft and piracy against the student. Please do not share logins with your friends; else you will be in deep trouble.

There is access limit for each student – based on the course validity (date mentioned in the course features) and the total duration for which a student can watch any particular video (three times of the length of the video). Under no circumstance requests to extend the validity or increase the view duration will be entertained.

You may be mandatorily required to register the device from which you will be permitted to access the student portal to consume the online services. LevelUP IAS withholds the right to keep the number of devices registered limited.

Students are advised to have minimum internet speed of 2 Mbps for smooth experience. For mobile, videos run efficiently on 4G networks.