Mathematics

Complete Syllabus of First semester

 Mathematic I (3–1–0)

1. Calculus-Iuccessive differentiation of one variable and Leibnitz theorem, Taylor’s and Maclaurin’s expansion of functions of single variable, Functions of several variables, partial derivatives, Euler’s theorem, derivatives of composite and implicit functions, total derivatives, Jacobian’s, Taylor’s and Maclaurin’s expansion of functions of several variables, Maxima and minima of functions of several variables, Lagrange’s method of undetermined multipliers, Curvature and asymptotes, concavity, convexity and point of inflection, Curve tracing.
2. Calculus-II: Improper integrals, convergence of improper integrals, test of convergence, Beta and Gamma functions and its properties, Differentiation under integral sign, differentiation of integrals with constant and variable limits, Leibinitz rule. Evaluation of double integrals, Change of order of integrations, change of coordinates, evaluation of area using double integrals, Evaluation of triple integrals, change of coordinates, evaluation of volumes of solids and curved surfaces using double and triple integrals. Mass, center of gravity, moment of inertia and product of inertia of two and three-dimensional bodies and principal axes.
3. Trigonometry of Complex Number, 3D Geometry and Algebra: Function of complex arguments, Hyperbolic functions and summation of trigonometrical series.
4. 3D Geometry: Cones, cylinders and conicoids, Central conicoids, normals and conjugate diameters.
5. Algebra: Convergency and divergency of Infinite series. Comparison test, D’ Alembert’s Ratio test, Raabe’s test, logarithmic test, Cauchy’s root test, Alternating series, Leibinitz test, absolute and conditional convergence, power series, uniform convergence.

Complete syllabus of Second semester

Mathematics II  (3–1–0)

1. Vector Calculus: Scalar and vector fields, Level surfaces, differentiation of vectors, Directionalderivatives, gradient, divergence and curl and their physical meaning, vector operators and expansion formulae, Line, surface and volume integrations, Theorems of Green, Stokes and Gauss, Application of vector calculus in engineering problems, orthogonal curvilinear coordinates, expressions of gradient, divergence and curl in curvilinear coordinates.
2. Fourier Series: Periodic functions, Euler’s formulae, Dirichlet’s conditions, expansion of even and odd functions, half range Fourier series, Perseval’s formula, complex form of Fourier series.
3. Matrix Theory: Orthogonal, Hermitian, skew- Hermitian and unitary matrices, Elementary row and column transformations, rank and consistency conditions and solution of simultaneous equations, linear dependence and consistency conditions and solution of simultaneous equations, linear dependence and independence of vectors, Linear and orthogonal transformations, Eigen values and Eigen vectors, properties of Eigen values, Cayley-Hamilton theorem, reduction to normal forms, quadratic forms, reduction of quadratic forms to canonical forms, index, signature,Matrix calculus & its applications in solving differential equations.
4. Differential Equations: Differential Equations of first order and higher degree, Linear independence and dependence of functions. Higher order differential equations with constant coefficient, Rules of finding C.F. and P.I., Method of variation of parameter Cauchy and Legendre’s linear equations, Simultaneous linear equations with constant coefficients, Linear differential equations of second order with variable coefficients; Removal of first derivative (Normal form), Change of independent varaiable, Applications of higher order differential equations in solution of engineering problems.
5. Partial Differential equations: Formation of P.D.E, Equations solvable by direct integration,Linear and non-linear equations of first order, Lagrange’s equations, and Charpit’s method,Homogeneous and non-homogeneous linear P.D.E. with constant coefficients, Rules for finding C.F. & P.I.

 Previous years Exam Papers

Higher Engineering Mathematics