Engineering Mathematics-I

L 3 C 3

Teachers Continuous Evaluation: as per university examination norms. End Term Theory Examination: as per university examination norms.

Course outcomes

• Ability of students to apply basic calculus [K1, K2, K3]
• Ability of students to apply vector calculus to solve engineering problems [K1, K2, K3, K4]
• Ability of students to understand complex analysis [K1,K2]
• Ability of students to understand laplace transforms and fourier analysis [K1, K2, K3]

Unit I (8 lectures)

Calculus I: Extreme values of a continuous function, mean value theorem, Solving definite and improper integrals: Area between two curves, Integration by parts and method of partial Fractions, Partial differentiation, Chain rule.

Unit II (8 lectures)

Calculus II: Total derivative, Directional derivatives and the gradient, divergence and curl, series, Taylor series (in one and two variables), maxima and minima of functions, Method of Lagrange multiplier, line and surface integrals, applications of Gauss, Stokes and Green’s theorem.

Unit III (8 lectures)

Complex Analysis: Complex numbers, polar form of complex numbers, Analytic functions Cauchy-Riemann Equations, Cauchy’s Integral Theorem, Cauchy’s Integral Formula, Taylor and Maclaurin Series, Laurent Series, Singularities and zeros, Residue Integration method.

Unit IV (8 lectures)

Laplace Transform: Basic definition, Linearity of Laplace transform, first shifting theorem (s-shifting), Transforms of derivatives and integrals, Using Laplace transform to solve ODE with initial value problems. Fourier Series and Transform: Basic definition of fourier series, Half range expansions, Fourier Cosine and sine transforms