| 16th November 2015 03:03 PM | |
| Saksham | Re: Engineering Maths In Mumbai University The University of Mumbai is one of the first three state universities in India and the oldest in Maharashtra. As you said that you want Final year SEM 1st Engineering Maths syllabus of the Mumbai University so here I am giving you the same Module 1 Complex numbers. 1.1.1 Review of complex numbers. Cartesian, Polar and Exponential form of a complex number. 1.1.2 De Moiver’s Theorem (without proof). Powers and roots of Exponential and Trigonometric functions. 1.1.3 Circular and Hyperbolic functions. 1.2 Module 2 Complex numbers and successive differentiation. 1.2.1 Inverse circular and Inverse Hyperbolic Functions Logarithmic functions 1.2.2 Separation of real and imaginary parts of all types of functions. 1.2.3 Successive differentiation –nth derivative of standard functions-eax, (ax=b)-1, (ax=b)m , (ax=b)-m, log (ax + b) sin (ax + b) Cos (ax+b). eax sin (bx+c). eax cos (bx+c). 1.2.4 Leibnitz’s theorem (without proot) and problems. 1.3 Module 3 Partial differentiation 1.3.1 Partial derivatives of first and higher order, total differential coefficients, total differentials, differentiation of composite and implicit functions. 1.3.2 Euler’s theorem on Homogeneous function with two and three independent Variables (with proof), deductions from Euler’s theorem. 1.4 Module 4 Application of partial differentiation, Mean Value theorems 1.4.1 Errors and approximations. Maxima and Minima of a function of two independent variables. Lagrange’s method of undetermined multipliers with one constraint. 1.4.2 Rolle’s theorem, Lagrange’s mean value theorem, Cauchy’s mean value theorem (all theorems without proof). Geometrical interpretation and problems. 1.5 Module 5 Vector algebra & Vector calculus 1.5.1 Vector triple product and product of four vectors. 1.5.2 Differentiation of a vector function of a single scalar variable. Theorems on derivatives (without proof). curves in space concept of a tangent vector (without problems) 1.5.3 Scalar point function and vector point function. Vector differential operator del. Gradient, Divergence and curl- definitions, Properties and problems. Applications-Normal, directional derivatives, Solenoidal and lrrotational fields. 1.6 Module 6 Infinite series, Expansion of functions and indeterminate forms. 1.6.1 Infinite series-Idea of convergence and divergence. D’ Alembert’s root test, Cauchy’s root test. 1.6.2 Taylor’s theorem (Without proof) Taylor’s series and Maclaurin’s series (without proof) Expansion of standard series such as ex , sinx, cosx, tanx, sinhx, coshx, tanhx, log(1+x), sin-1x – tan-1x, binomial series, expansion of functions in power series. Indeterminate forms-BHospitalsrule problem volvingseriesalso Recommended Books: • A textbook of Applied Mathematies. P.N. & J.N wartikar, volume 1 & 2 pune Vidyarthi Griha. •Higher Engineering Mathematics Dr. B.S. Grewal, Khanna Pulications. •Advanced Engineering Mathematics, Erwai Kreyszing, Wiley Eastern Limited, 8th Ed. •Vector analysis- Murray R., Spiegal- Scham series •Higher Engineering mathematics by B.V. Ramana-Tata McGraw Hill |
| 16th November 2015 02:35 PM | |
| Unregistered | Engineering Maths In Mumbai University Sir I want the Final year SEM 1st Engineering Maths syllabus of the Mumbai University so can you please provide me the same |
