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 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  
15Jun21  Day 1  Vector spaces over R and C, linear dependence and independence, subspaces, bases, dimension. 
16Jun21  Day 2  Linear transformations, rank and nullity, matrix of a linear transformation. 
17Jun21  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. 
18Jun21  Day 4  Eigenvalues and eigenvectors, characteristic polynomial, CayleyHamilton theorem, 
19Jun21  Day 5  Symmetric, skewsymmetric, Hermitian, skewHermitian, orthogonal, and unitary matrices and their eigenvalues. 
Calculus:  
21Jun21  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, 
22Jun21  Day 7  Asymptotes; curve tracing; functions of two or three variables: limits, continuity, partial derivatives, maxima and minima, Lagrange’s method of multipliers, Jacobian. 
23Jun21  Day 8  Riemann’s definition of definite integrals; indefinite integrals; infinite and improper integrals; 
24Jun21  Day 9  Double and triple integrals (evaluation techniques only); areas, surface, and volumes. 
Analytic Geometry:  
25Jun21  Day 10  Cartesian and polar coordinates in three dimensions, straight lines, shortest distance between two skew lines; plane, sphere, 
26Jun21  Day 11  Cone, cylinder, paraboloid, 
28Jun21  Day 12  Ellipsoid, hyperboloid of one and two sheets and their properties. 
29Jun21  Day 13  Second degree equations in three variables, reduction to canonical forms, 
Ordinary Differential Equations:  
30Jun21  Day 14  Formulation of differential equations; equations of first order and first degree, integrating factor; orthogonal trajectory. 
01Jul21  Day 15  Equations of first order but not of first degree, Clairaut’s equation, singular solution. 
02Jul21  Day 16  Second and higher order linear equations with constant coefficients, complementary function, particular integral, and general solution. 
03Jul21  Day 17  Second order linear equations with variable coefficients, EulerCauchy equation; determination of complete solution when one solution is known using method of variation of parameters. 
05Jul21  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:  
06Jul21  Day 19  Rectilinear motion, simple harmonic motion, motion in a plane, projectiles. 
07Jul21  Day 20  Constrained motion; work and energy, conservation of energy. 
08Jul21  Day 21  Kepler’s laws, orbits under central forces. 
Statics:  
09Jul21  Day 22  Equilibrium of a system of particles; work and potential energy, friction; principle of virtual work; 
10Jul21  Day 23  Common catenary, stability of equilibrium, equilibrium of forces in three dimensions. 
Vector Analysis:  
12Jul21  Day 24  Scalar and vector fields, differentiation of vector field of a scalar variable; vector identities and vector equations 
13Jul21  Day 25  Gradient, divergence, and curl in cartesian and cylindrical coordinates; higher order derivatives. 
14Jul21  Day 26  Application to geometry: curves in space, curvature, and torsion; SerretFrenet’s formulae. 
15Jul21  Day 27  Gauss and Stokes’ theorems, green’s identities. 
16Jul21  FLT1 (Full Length Test)  
PAPERII  
Algebra:  
19Jul21  Day 28  Groups, subgroups, cyclic groups, cosets, Lagrange’s Theorem, normal subgroups, quotient groups, 
20Jul21  Day 29  Homomorphism of groups, basic isomorphism theorems, permutation groups, Cayley’s theorem. 
21Jul21  Day 30  Rings, subrings, and ideals, homomorphisms of rings. 
22Jul21  Day 31  Integral domains, principal ideal domains, Euclidean domains, and unique factorization domains; 
23Jul21  Day 32  Fields, quotient fields. 
Real Analysis:  
24Jul21  Day 33  Real number system as an ordered field with least upper bound property; 
26Jul21  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. 
27Jul21  Day 35  Continuity and uniform continuity of functions, properties of continuous functions on compact sets. 
28Jul21  Day 36  Riemann integral, improper integrals; fundamental theorems of integral calculus. 
29Jul21  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:  
30Jul21  Day 38  Analytic functions, CauchyRiemann equations, 
31Jul21  Day 39  Power series representation of an analytic function, Taylor’s series; singularities; Laurent’s series. 
02Aug21  Day 40  Cauchy’s theorem, Cauchy’s integral formula Cauchy’s residue theorem; contour integration. 
Linear Programming:  
03Aug21  Day 41  Linear programming problems, basic solution, basic feasible solution, and optimal solution. 
04Aug21  Day 42  Graphical method and simplex method of solutions; duality. 
05Aug21  Day 43  Transportation and assignment problems. 
Partial differential equations:  
06Aug21  Day 44  Family of surfaces in three dimensions and formulation of partial differential equations. 
07Aug21  Day 45  Solution of quasilinear partial differential equations of the first order, 
09Aug21  Day 46  Linear partial differential equations of the second order with constant coefficients, canonical form; Cauchy’s method of characteristics 
10Aug21  Day 47  Equation of a vibrating string, heat equation, Laplace equation and their solutions. 
Numerical Analysis:  
11Aug21  Day 48  Numerical methods: solution of algebraic and transcendental equations of one variable by bisection, RegulaFalsi and NewtonRaphson methods; 
12Aug21  Day 49  Solution of system of linear equations by Gaussian elimination and GaussJordan (direct), GaussSeidel(iterative) methods. 
13Aug21  Day 50  Newton’s (forward and backward) interpolation, Lagrange’s interpolation. 
14Aug21  Day 51  Numerical integration: Trapezoidal rule, Simpson’s rules, Gaussian quadrature formula. 
15Aug21  Day 52  Numerical solution of ordinary differential equations: Euler and Runge Kuttamethods. 
Computer Programming:  
16Aug21  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. 
17Aug21  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. 
18Aug21  Day 55  Algorithms and flow charts for solving numerical analysis problems. 
Mechanics:  
19Aug21  Day 56  Generalized coordinates; D’ Alembert’s principle and Lagrange’s equations; Hamilton equations; 
20Aug21  Day 57  Moment of inertia; Motion of rigid bodies in two dimensions. 
Fluid Dynamics:  
21Aug21  Day 58  Equation of continuity; Streamlines, path of a particle. 
22Aug21  Day 59  Euler’s equation of motion for inviscid flow; Potential flow; Twodimensional and axisymmetric motion. 
23Aug21  Day 60  Sources and sinks, vortex motion; NavierStokes equation for a viscous fluid. 
24Aug21  FLT2 (Full Length Test) 
P.S.: Changes in the schedule may be made with a prior announcement to the students
Note:
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