Engineering: Subjects and Syllabus
ENGINEERING MATHEMATICS – I Sub Code Hrs/ Week Total Hrs. : : : 10MAT11 04 52 IA Marks Exam Hours Exam Marks : : : 25 03 100
PART-A UNIT – 1 Differential Calculus - 1 Determination of nth derivative of standard functions-illustrative examples*. Leibnitz’s theorem (without proof) and problems. Rolle’s Theorem – Geometrical interpretation. Lagrange’s and Cauchy’s mean value theorems. Taylor’s and Maclaurin’s series expansions of function of one variable (without proof). 6 Hours UNIT – 2 Differential Calculus - 2 Indeterminate forms – L’Hospital’s rule (without proof), Polar curves: Angle between polar curves, Pedal equation for polar curves. Derivative of arc length – concept and formulae without proof. Radius of curvature - Cartesian, parametric, polar and pedal forms. 7 Hours UNIT – 3 Differential Calculus - 3 Partial differentiation: Partial derivatives, total derivative and chain rule, Jacobians-direct evaluation. Taylor’s expansion of a function of two variables-illustrative examples*. Maxima and Minima for function of two variables. Applications – Errors and approximations. 6 Hours UNIT – 4 Vector Calculus Scalar and vector point functions – Gradient, Divergence, Curl, Laplacian, Solenoidal and Irrotational vectors. Vector Identities: div (øA), Curl (øA) Curl (grad ø ) div (CurlA) div (A x B ) & Curl (Curl A) . Orthogonal Curvilinear Coordinates – Definition, unit vectors, scale factors, orthogonality of Cylindrical and Spherical Systems. Expression for Gradient, Divergence, Curl, Laplacian in an orthogonal system and also in Cartesian, Cylindrical and Spherical System as particular cases – No problems 7 Hours 5
PART-B UNIT – V Integral Calculus Differentiation under the integral sign – simple problems with constant limits. Reduction formulae for the integrals of n x , cos n x, m n x and evaluation of these integrals with sin s in x cos standard limits - Problems. Tracing of curves in Cartesian, Parametric and polar forms – illustrative examples*.
PART-A UNIT – 1 Differential Calculus - 1 Determination of nth derivative of standard functions-illustrative examples*. Leibnitz’s theorem (without proof) and problems. Rolle’s Theorem – Geometrical interpretation. Lagrange’s and Cauchy’s mean value theorems. Taylor’s and Maclaurin’s series expansions of function of one variable (without proof). 6 Hours UNIT – 2 Differential Calculus - 2 Indeterminate forms – L’Hospital’s rule (without proof), Polar curves: Angle between polar curves, Pedal equation for polar curves. Derivative of arc length – concept and formulae without proof. Radius of curvature - Cartesian, parametric, polar and pedal forms. 7 Hours UNIT – 3 Differential Calculus - 3 Partial differentiation: Partial derivatives, total derivative and chain rule, Jacobians-direct evaluation. Taylor’s expansion of a function of two variables-illustrative examples*. Maxima and Minima for function of two variables. Applications – Errors and approximations. 6 Hours UNIT – 4 Vector Calculus Scalar and vector point functions – Gradient, Divergence, Curl, Laplacian, Solenoidal and Irrotational vectors. Vector Identities: div (øA), Curl (øA) Curl (grad ø ) div (CurlA) div (A x B ) & Curl (Curl A) . Orthogonal Curvilinear Coordinates – Definition, unit vectors, scale factors, orthogonality of Cylindrical and Spherical Systems. Expression for Gradient, Divergence, Curl, Laplacian in an orthogonal system and also in Cartesian, Cylindrical and Spherical System as particular cases – No problems 7 Hours 5
PART-B UNIT – V Integral Calculus Differentiation under the integral sign – simple problems with constant limits. Reduction formulae for the integrals of n x , cos n x, m n x and evaluation of these integrals with sin s in x cos standard limits - Problems. Tracing of curves in Cartesian, Parametric and polar forms – illustrative examples*.