# Course curriculum

• 1

• 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