Nagpur University Syllabus :- Engineering FIRST YEAR | FIRST YEAR Applied Mathematics-I Section-A

FIRST YEAR

Applied Mathematics-I

Section-A

1-1

1. Differential Calculus:

Unit-I:

Successive differentiation, Taylor's and Maclaurin's series for one variable, Tan­gents and Normals, subtangent and subnormal (Cartesian form), Curvature and Radius of curvature (Cartesian, Parametric and polar form), centre of curvature (Cartesian form only), L'Hospital's rule. Maxima and Minima of function of one variable.

Unit-II:

Partial differentiation, Function of several variables, first and higher order deriva­tives, Euler's theorem, chain rules and total differential co-efficient, Jacobians, Taylor's and Maclaurin's series of two variables, Maxima & Minima of function of two variables, Lagrange's method of undetermined multipliers. Differentiation of definite integrals.

             

2. Analytical Trigonometry:

Unit-III:

Cartesian and polar forms of complex numbers, D-Moivre's theorem, hyperbolic functions and their inverse, Logarithm of complex quantities, summation of series.( C + is Method).

Section-B

3. Theory of equations:

Unit-IV:

General properties of polynomial equations, relation between roots & coefficients, transformation of equations, Horner's method of synthetic division.

4. Integral Calculus:

Unit V

Beta Gamma functions, Differentiation of definite Integral, Tracing of curves (Cartesian & Polar curves) rectification of simple curves, quadrature, volumes and surface of solids of revolutions (Cartesian, Polar & parametric forms). Theorem of Pappus and Guldin, mean value and root mean square values.

5. Analytical solid Geometry:

Unit-VI:

Cartesian, cylindrical and spherical system of co-ordinates and their transformations, Detail study of lines of planes in Cartesian system. Shift of origin, projection of segment, projection of plane closed cure, projection of lines and planes. Shortest distance between two lines, Equations of sphere, Right circular cylinder and right circular cone.

Books Recommended:

1.      Plane Trigonometry Part II : S. L. Loni, (S.Chand & Co)

2.      Engg. Mathematics: H.K.Das. (S.Chand & Co)

3.      Higher Algebra: Hall & Knight

4.      Analytical solid Geometry: Shantinarayan. (S.Chand & Co)

5.      Applied mathematics : Ramana murthy Srinivas

Reference Books:

1.      Engineering Mathematics Voll.. II : Shantinarayan(S.Chand & Co)

2.      Mathematics for Engineers: Chandrika Prasad (Prasad Mudranalaya, Allahabad)

3.      Higher Engineering Mathematics: B. S. Grewal (Khanna Publishers, N Delhi)

4.      The text book Applied Mathematics vol. I & II : Prof. D. T. Deshmukh