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Old 16th November 2015, 02:35 PM
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Default 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
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Old 16th November 2015, 03:03 PM
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Join Date: May 2012
Default 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
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