University of Mumbai

Class – F.E. (all Branches of Engineering)

Semester – I Subject – Applied Mathematics -I


all syllabus in single PDF file free download 

Periods per week(each of 60 minutes) Lecture

4

Practical

Tutorial

1

Hours

marks

Evaluation System Theory Examination

3

100

Practical and OralExamination

Oral Examination

Term Work

25

Total

125

 


 

Details of Syllabus –

Sr. No. Detailed Syllabus: Lectures/We ek
1.1 Module 1Complex 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.

 

02

 

03

1.2 Module 2Complex 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.

 

03

 

02

 

04

 

 

 

03

1.3 Module 3Partial differentiation1.3.1   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.

 

 

05

 

 

 

03

Total:08

1.4 Module 4Application of partial differentiation, Mean Value theorems1.4.1   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.

 

 

04

 

 

 

03

Total:07

 

 

1.5 Module 5Vector algebra & Vector calculus1.5.1    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.

 

01

 

02

 

06

 

Total:09

1.6 Module 6Infinite 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.

1.6.3    Indeterminate forms-

x

0 , x ,0 x ∞, ∞ − ∞, 0 0     , ∞ 0  ,1x     BHospitalsrule problem sin volvingseriesalso.

−   x

 

02

 

 

 

04

 

 

 

 

 

02

 

Total-08

Recommended Books:• A textbook of Applied Mathematies. P.N. & J.N wartikar, volume1 & 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.

Theory Examination:

1.        Question paper will comprise of total 7 questions, each of 20 marks.

2.         Only 5 questions need to be solved.

3.         Q, 1 will be compulsory and based on entire syllabus

4.         Remaining questions will be mixed in nature (e.g. suppose Q.2 has part (a) form, module 3 then part (b) will be form any module other then module3)

5.         In question paper weightage of each module will be proportional to number of respective lecture hours as mentioned in the syllabus.

Term Work.

Term work will beshall consist of minimum five experiments and a written test. The distribution of marks for term work shall be as follows:

•        Laboratory work (Experiments and journal                                  : 10 Marks

•        Test (at least one)                                                                         : 10 Marks

•       Attendance (Theory and Theory)                                                   : 05 Marks

Total                                                                                              : 25 Marks

•                The final certification and acceptance of term-work ensures the satisfactory performance of laboratory work and minimum passing in the term –work.


all syllabus in single PDF file free download