Web Course
:
Mathematics-I
Prof. Inder K Rana (IITB)
Mathematics-III
Prof. Durga C Dalal (IITG)
Mathematics-II
Prof. P. Chandra (IITK)
Engineering Mechanics
Prof. U.S.Dixit (IITG)
Engineering Mechanics
Prof. P. Chandra (IITK)
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APPLIED MATHEMATICS-I
Module
Topics
Differential Calculus
Expansion by Maclaurin's and Taylor's series
Taylor's series:
M5 L14
Taylor's series:
M9 L27
Maclaurin's series:
M9 L27
Indeterminate forms
M7 L20
Functions of two variables:
M1 L1
Limit:
M2 L4, L5
Continuity:
M2 L5 L6
Partial derivative:
M11 L31
Total derivative:
M11 L31
Euler's theorem for homogeneous functions:
M11 L31
Composite functions:
M11 L32
Taylor's series for two independent variables:
M5 L14
Maxima and minima of functions of two variables:
M4 L11
Maxima and minima of functions of two variables:
M3 L37
Maxima and minima of functions of two variables:
M3 L38
Maxima and minima of functions of two variables:
M3 L39
Errors and increments:
M5 L13
Tangents and Normals
Tangents and normals:
M12 L35
Equations of tangents and normals
Derivative of length of the arc:
M8 L22
Curve tracing:
M4 L12
Catenary Cycloid Asteroid:
M8 L22
Algebraic aids
Convergence and Divergence of infinite series:
M1 L2-3
Convergence and Divergence of infinite series:
M9 L25-26
Cauclur's root test:
M9 L26
D'Alembart's ratio test:
M9 L26
Separation of Trigonometric, Hyperbolic and Logarithmic functions into real and imaginery parts:
Mathematics-3 Module- Elementary analytic function
Analytical Geometry of Three Dimensions
Equation of a cone with vertex at origin
Right circular cone
Equation of right circular cone
Equation of cylinder and right circular cylinder
Equation of central conicoids
Standard surfaces of revolution
Multiple Integrals
Double integrals (rectangular and polar coordinates) :
M14 L40
Double integrals (rectangular and polar coordinates) :
M14 L42
Change in order of integration:
M14 L40
Change of variable:
M14 L42
Triple integrals:
M14 L41
Surface and volumes of revolution:
M14 L41
Centroids of arcs:
M14 L41
Plane areas:
M14 L41
Matrices
Vectors
Vectors
Linear dependence of vectors
Rank of a matrix:
Rank of a matrix
(For additional information about matrix operation)
Linearly independent vectors of a matrix
Characteristics of vectors and characteristics roots of a matrix
Cayley-Hamilton theorem
Inverse of a matrix
Diagonalization of a matrix
Statics
Vector function, differential and line integral:
M15 L43
Vector function, differential and line integral:
M16 L46
Force and moments:
M15 L43
Parallel forces:
M1 L3
Couple:
M1 L3
Resultant of coplanar and non coplanar force systems and their equilibrium:
M1 L4, L5
Friction
Frictional phenomena:
M2 L7
Types of friction:
M4 L9
Dry friction:
M4 L9
Mechanism of friction:
M4 L9
Friction on inclined planes:
M2 L7
Coefficient and angle of friction:
M4 L9
Angle of repose:
M4 L9
Laws of friction:
M4 L9
Belt friction:
M2 L7
Simple problems:
M4 L9- L10 Quiz and Problems
Virtual Work
Principle of virtual work:
M4 L10
Conditions for stability of equilibrium:
M4 L10
Application to simple problems:
M4 L10
Vectorial Dynamics
Kinetics and Kinematics:
Kinetics:
M9 L21, M10 L26
Kinematics:
M8 L17, 18, 19, 20
Velocity and acceleration as derivatives of a vector:
M15 L45
Tangential and normal components:
M15 L45
Radial and transverse components:
M5 L11
Work:
M6 L15, L16
Power:
M6 L15, L16
Energy:
M6 L15, L16
Momentum:
M6 L14
Moment of momentum:
M9 L23
Impulse:
M9 L23
Impulsive motion:
M9 L23
Impact:
M9 L24
Direct and oblique (Impact):
M9 L24
Angular momentum and energy of rotation:
M7 L18, L19
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