Course curriculum

  • 1

    MODULE 1 (KPG)

    • LEC 1
    • LEC 2
    • LEC 3
    • LEC 4
  • 2

    Module 2 (AKC)

    • some more problems of evaluating using defination
    • ImproperIntegral
    • PROBLEMS ON MEAN VALUE THEORY
    • .VOLUMES OF SOLIDS OF REVOLUTION CONT. 1
    • Reduction
    • Problems on Beta&Gamma func.(contd.1)
    • Integration; Area of surface of Revolution(Surface Area of Sphere)
    • Integration; Area of surface of Revolution
    • SUCCESSIVE DIFFERENTIATION; Standard Forms
    • Definition of the Definite Integral
    • Series Expansion of fns using Diffn. & Integration
    • Mean Value Theorem(Assorted Problems) Contd...
    • Rolle's th. verification & a different expression for 'c' in terms of theta
    • Integration; Area of surface of Revolution
    • SUCCESSIVE DIFFERENTIATION; Trigno Functions & Leibnitz Theorem
    • Rolle's Theorem with Geometrical Interpretation
    • Reduction Formulae Concepts & Examples(contd.)
    • properties of definite integrals with applications
    • contgeometrical meaning;with examples evaluating from defn.)
    • INTEGRAL CALCULAS AREA UNDER CURVES CONT.
    • Problems on Rolle's th. & Intro. to Lagrange's MVT theory
    • INTEGRAL CALCULAS AREA UNDER CURVES (Polar Co-ordinates)... CONT. 3
    • Reduction
    • Maclaurin's Series for Trigo Fn and applications
    • Taylor's and Maclaurin's series; With Remainder after 'n' terms
    • Problems on Beta&Gamma func.(contd.2)
    • Leibniz TheoremStatement and Problems
    • Reduction Formulae
    • SUCCESSIVE DIFFERENTIATION ; Meaning & Examples
    • Successive Differentiation REVISION & Problems
    • Problems on Beta&Gamma func.
    • ImproperIntegral
    • Series Expansion of fns using Diffn. & Integration.....contd.....
    • MAXIMA AND MINIMA;Method of Lagrangian Multiplier
    • Problems on Leibniz Theorem; Recurrence Relations
    • VOLUMES OF SOLIDS OF REVOLUTION
    • Reduction Formulae Concepts & Examples
    • Miscellaneous problems on Mean Value th
    • Expansion of fns by Special Methods
    • Integration; Area of surface of Revolution(Polar Co-ordinates)
    • Problems on Definite Integral using properties
    • Expansion of FnTaylor's & Maclaurin's Series
    • INTEGRAL CALCULAS AREA UNDER CURVES (Polar Co-ordinate)
    • Problems on Definite Integral using properties
    • 2.Problems on Definite Integral using properties & Introdn. to reduction formula
    • Mean Value Theorem(Assorted Problems)
    • INTEGRAL CALCULAS AREA UNDER CURVES
    • ImproperIntegral
    • Rolle's Theorem; One Special Problem
    • Relating LMVTh to algebraic & other calculus method
    • MAXIMA AND MINIMA; The Fisherman Problem
    • Cauchy's Mean Value Th; Discussion and Proof
    • Lagrange's Mean Value Th.(Proof & Discussion)
    • Cauchy's MVTh; LMVT as a special case of CMVT
    • MEAN VALUE Theory ; Some Problems
    • Assorted Problems on Beta and Gamma Function
    • ImproperIntegral
    • Definite Integrals used to Evaluate Infinite Series
  • 3

    MODULE 3 (KD)

    • Linear map,Matrix representation of linear map
    • Linear map , Rank Nullity Theorem
    • Linear map , Image
    • Linear map, Creation
    • Linear map ,Composition of linear map
    • Linear map, Kernel
    • Linear map, Defination and Examples
    • PARSEVAL'S IDENTITY FOR FOURIER SERIES 1
    • PROPERTIES OF FOURIER TRANSFORM 1
    • PROPERTIES OF FOURIER TRANSFORM 2
    • FOURIER SERIES
    • FOURIER SERIES
    • FOURIER SERIES 1
    • FOURIER SERIES 2
    • FOURIER TRANSFORM (SOME MORE IMPORTANT FOURIER TRANSFORM)
    • SOME QUESTIONS OF PARSEVAL'S IDENTITY FOR FOURIER SERIES (PART_2)
    • PROBLEMS RELATED TO FOURIER TRANSFORM
  • 4

    MODULE 4 (SPN)

    • VECTOR SPACE - LECTURE 1 - SPN
    • VECTOR SPACE - LECTURE 2 - SPN
    • VECTOR SPACE - LECTURE 3 - SPN
  • 5

    MODULE 5(SD)

    • LECTURE 2(POLAR REPRESENTATION OF COMPLEX NO.)
    • LECTURE 2(CAUCHY-RIEMANN EQUATION)
    • PART 1(HARMONIC FUNCTION)
    • LECTURE 1(FUNCTION OF COMPLEX VARIABLE)
    • PART 2(HARMONIC FUNCTION)
    • LECTURE 1(CONTINUITY OF A COMPLEX VALUED FUNCTIONS)
    • LECTURE(FINITE COMPLEX PLANE)
    • LECTURE(CONFORMAL MAPPING)MAIN
  • 6

    MODULE 6(PM)

    • Module 4- Cauchy's Root test
    • Module 5- Introduction to vector calculus
    • Module 5- Vector product
    • Module 4- Raabe's test
    • Module 1-Homogenous system of equations(examples)
    • Module 4- Comparison test
    • Module 5-Scalar Product
    • Module 4- D'Alembert Ratio test
    • Module 1- Cayley Hamilton Theorem
    • Module 4- Absolute and Conditional Convergence
    • Module 4- Alternating series and Lleibnitz's theorem
    • Module 1- Diagonalization of Matrix
    • Module 3 Homogenous functions
    • Module 1- Eigen values and Eigen vectors
    • Module 3-Jacobian
    • Module 3-Total Differentiation
    • Module 1-Rank of a matrix and System of linear equation
    • Module 1-Higher power of matrix using CHT
    • Module 1-System of linear equations(examples)
    • Module 3- Differentiation of composite function
    • Module 1-Homogenous system of equations
    • Module 1_Engineering Mathematics 1
    • Module 4- Infinite series(convergence & Divergence)
    • Module 3-Introduction to functions of several variables
    • Module 3-Euler's Theorem
    • Module 3- jacobian(examples)
    • Module 1- Determinant and Laplacian method
    • Module 4- Introduction to Infinite series
    • Module 3-Maxima and Minima
    • Module 1-Introduction to Matrix