# BE/B.Tech First Year Mathematics-I

Periods/week : 3 Periods & 1 Tut /week. Ses. : 30 Exam : 70

Examination (Practical): 3hrs. Credits: 4

**Partial Differentiation and its Applications **

Functions of two or more variables, partial derivatives, homogenous functions – Eular’s Theorem, Total Derivative, Differentiation of implicit functions, Geometrical interpretation – Tangent plane and normal to a surface. Change of variables, Jacobians, Taylor’s theorem for functions of two variables, Jacobians, Taylor’s theorem for functions of two variables, Errors and approximations, Total differential, Maxima and minima of functions two variables, Lagrange’s method of undetermined multiples, Differentiation under the integral sign – Leibnitz Rule, Involutes and evolutes.

**Multiple Integrals and their Applications**

Double integrals, Change of order of integration, Double integrals in polar coordinates, Areas enclosed by plane curves, Triple integrals, Volume of solids, Change of variables, Area of a curve of a curved surface, Calculation of mass, center of gravity, center pressure, Moment of inertia, Product of inertia, Principle axes, Beta function, Gamma function, Relation between Beta and Gamma functions, Error function or probability integral.

**Solid Geometry (Vector Treatment)**

Equation of a plane, Equation of straight line, Condition for a line to lie in a plane, Coplanar lines, Shortest distance between two lines, Interaction of three planes, Equation of sphere, Tangent plane to a sphere, Cone, Cylinder, Quadric surfaces.

**Infinite Series**

Definitions, Convergence, Divergence and oscillation of a series, General properties, Series of positive terms, comparison tests, Integral test, D’Alembert’s ratio test, Raabe’s test, Logarithmic test, Cauchy’s root test, Alternating series – Leibnitz’s rule, Series of positive or negative terms, Power series, Convergence of exponential, Logerithmic and bionomial series, Uniform convergence, Weirstrass M-test, Properties of uniformly convergent series.

**Fourier Series**

Eular’s formulae, Conditions for a Fourier expansion, Functions having point of discontinuity, Change of interval, Odd and even functions – Expansions of odd or even periodic function, Half range series, Parseval formula, Practical harmonic analysis.

**Textbooks:**

Higher Engineering mathematics by B.S. Grewal

Mathematics for Engineering by Chandrica Prasad

**Reference Books:**

Higher Engineering Mathematics by M.K. Venkatraman

Advanced Engineering Mathematics by Erwin Kreyzig

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