ENGINEERING SEM 1
APPIED MATHEMATICS I
SYLLABUS IN DETAIL:-
1.1 Module 1
1.1.1 Review of complex numbers. Cartesian, Polar and 02
Exponential form of a complex number.
1.1.2 De Moiver’s Theorem (without proof). Powers and roots 03
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 03
1.2.2 Separation of real and imaginary parts of all types of 02
1.2.3 Successive differentiation –nth derivative of standard 04
ax -1 m -m
functions-e , (ax=b) , (ax=b) , (ax=b) , 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. 03
1.3 Module 3
1.3.1 Partial derivatives of first and higher order, total differential
coefficients, total differentials, differentiation of composite 05
and implicit functions.
1.3.2 Euler’s theorem on Homogeneous function with two and
three independent Variables (with proof), deductions from 03
Euler’s theorem. Total:08
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 04
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 03
proof). Geometrical interpretation and problems. Total:07
1.5 Module 5
Vector algebra & Vector calculus
1.5.1 Vector triple product and product of four vectors. 01
1.5.2 Differentiation of a vector function of a single scalar
variable. Theorems on derivatives (without proof). curves 02
in space concept of a tangent vector (without problems)
1.5.3 Scalar point function and vector point function. Vector 06
differential operator del. Gradient, Divergence and curl-
definitions, Properties and problems. Applications-Normal, Total:09
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’ 02
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 04
series such as e , sinx, cosx, tanx, sinhx, coshx, tanhx,
log(1+x), sin-1x – tan-1x, binomial series, expansion of
functions in power series.
1.6.3 Indeterminate forms-
0 x x 02
0 0 x
, ,0 x 8, 8 – 8, 0 , 8 ,1 BHospitalsrule – problem sin volvingseriesalso.
• A textbook of Applied Mathematies. P.N. & J.N wartikar, volume
1 & 2 pune Vidyarthi Griha.
•Higher Engineering Mathematics Dr. B.S. Grewal, Khanna
•Advanced Engineering Mathematics, Erwai Kreyszing, Wiley
Eastern Limited, 8 Ed.
•Vector analysis- Murray R., Spiegal- Scham series
•Higher Engineering mathematics by B.V. Ramana-Tata McGraw