Central Library

MATRICIES

• • Fundamental
  • Transpose of Matrix
  • Determinant
  • Adjoint of a Square Matrix
  • Rank of a Matrix

Linear System of Equations

• • System of Linear Equation
  • Eigen Value and Eigen Vectors
  • Complex Matrices
  • Cayley Hamilton Theorem

Differential Calculus

• • Lagranges Mean Value Theorem
  • Taylor’s Theorem
  • L Hospitals Rule (E-1)
  • L Hospitals Rule (E-2)
  • Maclurin’s theorem
  • Improper integrals
  • Gamma functions
  • Beeta Function
  • Improper integrals (Questions for practice)
  • Functions of Two variables
  • Partial derivatives
  • Total derivatives
  • Tangent plane and normal line
  • Maxima & Minima of function of two variables

Calculus of Several Variables

• • Functions of Two Variables
  • Partial Derivative E-1
  • Limit and Continuity of Higher Dimensions
  • Total derivative
  • Tangent Plane and Normal Line
  • Maxima & minima of Functions of Two Variables
  • Lagrange’s method of understanding Multipliers

Numerical Analysis

• • General Formula for Errors
  • Significant Digit
  • Error Analysis
  • Method of Iteration
  • Regula False Position
  • Secant Method
  • Numerical Analysis MCQ

Numerical Differentiation

• • Numerical Differentiation
  • MCQ: Interpolation and Finite Differences
  • Numerical for Practice on Numerical Integrations

Numerical Integration & Numerical Differential Equations

• • General Quadrature Formula
  • Trapezoidal  rule
  • Numerical Solution of Ordinary Differential Equation (MCQ)
  • Extrapolation Method 
  • Romberg Integration
  • Taylor’s Series Method
  • Euler’s Method
  • Euler’s Modified Method
  • Runge-Kutta Method

FINITE DIFFERENCE OPERATORS

• • Finite differences
  • Central difference & mean operators with relations

NUMERICAL METHODS: CONVERGENCE-QUESTIONS FOR PRACTICE

• • Solution for Equations
  • Interpolation & finite differences
  • Error Analysis (MCQ)
  • NA Solution of Algebraic Equations(MCQ)
  • Non Linear Equations (MCQ)
  • Numerical Solution of DE & NI (MCQ-1)
  • Numerical Solution of DE & NI (MCQ-2)
  • Convergence of Regula-False position method

COMPLEX ANALYSIS

• • Function of a Complex Variable (CR Equations)
  • Practice question for Analytic Functions
  • Contour Integrals
  • Cauchy’s Integral theorem 
  • Lowville’s Theorem
  • Laurent’s Series 
  • Singularities and Poles 
  • Numerical: Cauchy’s residue theorem
  • Complex analysis (MCQ-1)
  • Vector Analysis (MCQ-2)

MATHEMATICAL MODELLING

• • Mathematical Modelling (Vol-1)
  • Mathematical Modelling (Vol-2)
  • Mathematical Modelling (Vol-3)
  • Mathematical Modelling (Vol-4) Calculating Population Growth using Differential Equation

MATRIX ALGEBRA & SOLUTION OF LINEAR  SYSTEM OF EQUATIONS

• • System of Linear Equations
  • Eigen values and Eigen vectors
  • Gauss Elimination method
  • Jacobi’s method
  • Gauss-Seidel method
  • Solution of non-homogeneous system of equations
  • Power Method
  • Linear System of Equations (Questions for practice)

INTERPOLATIONS

• • Newton forward Interpolation formula
  • Newton Backward Interpolation formula
  • Concept of Divided difference
  • Lagrange’s Interpolation
  • Newton’s divided difference formulae

STATISTICS & PROBABILITY THEORY

• • Theory of Probability (Vol.1)
  • Theory of Probability (Vol.2) : Conditional Probability
  • Theory of Probability (Vol.3) : Baye’s Theorem
  • Mean deviation
  • Carl-Pearson coefficients of correlation
  • Probability distributions
  • Moment and Kurtosis
  • Binomial distributions
  • Poisson distributions
  • Normal distribution
  • Karl-Pearson Standard deviation
  • Measure of dispersion
  • Partition values
  • Measure of Central tendency (Vol.1)
  • Measure of Central tendency(Vol.2)

CONCEPT OF CURVE FITTING

• • Concept of curve fitting
  • Method of least square (Vol.1)
  • Method of least square (Vol.2)

VECTOR CALCULUS

• • Line Integral
  • Divergence of a vector point function
  • Scalar and vector field
  • Gradient
  • Green’s Theorem
  • Surface Integral
  • Volume integral
  • Stokes Theorem

SEQUENCE & SERIES

• • Sequence & Series
  • Comparison test
  • D’Alembert’s Ratio test
  • Cauchy’s root test

DIFFERENTIAL GEOMETRY

• • Theory of Space Curves
  • Curvature
  • Torsion (Mathematics of twisting)
  • Scalar & Vector field (Vol.1)
  • Scalar & Vector field (Vol.2)
  • Serret-Frenet Formulae
  • Theorems of Space curves
  • Contact between curves and surface
  • Osculating Circle & Sphere
  • Differential geometry (Examples)
  • Involutes & Evolutes
  • Bertrand curves
  • Relation between Curvature & Torsion
  • Spherical Indicatrix
  • Spherical Indicatrix (in case of Binormal)
  • Intrinsic equations of curve
  • Fundamental existence theorem for Space curves
  • Example for practice
  • Surface in Geometry
  • Nature of a point in Surface
  • Representation of a surface
  • Tangent plane and Surface normal
  • Metric on a surface (Vol.1)
  • Metric on a surface (Vol.2)
  • Metric on a surface (Vol.3)
  • Direction coefficients on a surface(Vol.1)
  • Direction coefficients on a surface(Vol.2)
  • Families of curves
  • Orthogonal Trajectories
  • Double family of curves
  • Isometric correspondence
  • Intrinsic properties of surface
  • Geodesics on surface (Condition)
  • Geodesics on surface (Theorems-1)
  • Geodesics on surface (Theorems-2)
  • Canonical Geodesic Equation
  • Normal property of Geodesic
  • Differential Equations of Geodesics
  • Important result of Geodesics
  • Geodesics Parallel
  • Geodesics Polar coordinate
  • Geodesic Coordinate

NEW EDUCATION POLICY

• • Webinar on New Education Policy@SLIET-Session-1
  • Webinar on New Education Policy@ SLIET-Session-2
  • NEP-2020