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) Download PDF

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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