Applied Mathematics-I Revised Syllabus 2012 | Mumbai University Engineering | SEM 1
Detailed Engineering Syllabus for Applied Mathemtics 1 in Sem 1:
Pre‐requisite: Review on Complex Number‐Algebra of Complex Number, Different representations of a Complex number and other definitions, D’Moivre’s Theorem.
||Module‐1: Complex Numbers:‐
1.1: Powers and Roots of Exponential and Trigonometric Functions. 2Hr
1.2: Circular functions of complex number and Hyperbolic functions.Inverse
Circular and Inverse Hyperbolic functions. Logarithmic functions.6Hr.
1.3: Separation of real and Imaginary parts of all types of Functions.3Hr.
1.4: Expansion of sinnθ,cosnθ in terms of sines and cosines of 2Hr.
multiples of θ and Expansion of sinnθ, cosnθ in powers of sinθ, cosθ
||Module‐2: Matrices and Numerical Methods:‐
2.1: Types of Matrices(symmetric, skew‐ symmetric, Hermitian, Skew Hermitian,Unitary, Orthogonal Matrices and properties of Matrices).Rank of a Matrix using Echelon forms, reduction to normal form, PAQ forms, system of
homogeneous and non –homogeneous equations, their consistency and solutions. Linear dependent and independent vectors. 9Hr.
2.2: Solution of system of linear algebraic equations, by (1) Gauss Elimination Method (Review) (2) Guass Jordan Method (3) Crouts Method (LU)
(4) Gauss Seidal Method and (5) Jacobi iteration (Scilab programming for
above methods is to be taught during lecture hours) 6Hr.
3.1: Successive differentiation: nth derivative of standard functions.
Leibnitz’s Thoerem (without proof) and problems.
3.2: Partial Differentiation: Partial derivatives of first and higher order, total
differentials, differentiation of composite and implicit functions.
3.3: Euler’s Theorem on Homogeneous functions with two and three
independent variables (with proof)deductions from Euler’s Theorem.
||Module‐4: Application of Partial differentiation, Expansion of functions , Indeterminate forms and curve fitting:‐
4.1.: Maxima and Minima of a function of two independent variables.
Lagrange’s method of undetermined multipliers with one constraint. Jacobian,
Jacobian of implicit function. Partial derivative of implicit function using
4.2: Taylor’s Theorem(Statement only) and Taylor’s series,Maclaurin’s series (Statement only).Expansion of ex, sinx, cosx, tanx, sinhx,coshx, tanhx, log(1+x), sin‐1x,cos1x, Binomial series. Indeterminate forms, L‐Hospital Rule, problems involving series also.
4.3: Fitting of curves by least square method for linear, parabolic,and exponential. Regression Analysis(to be introduced for estimation only)
(Scilab programming related to fitting of curves is to be taught during
1: A text book of Applied Mathematics, P.N.Wartikar and J.N.Wartikar,Vol – I and –II by Pune Vidyarthi
2: Higher Engineering Mathematics, Dr.B.S.Grewal, Khanna Publication
3: Advanced Engineering Mathematics, Erwin Kreyszig, Wiley EasternLimited,9th Ed.
4: Matrices by Shanti Narayan.
5: Numerical by S.S.Sastry, Prentice Hall
1. Question paper will comprise of 6 questions, each carrying 20 marks.
2. Total 4 questions need to be solved.
3: Question No.1 will be compulsory and based on entire syllabus wherein sub questions of 2 to 3 marks
will be asked.
4: Remaining question will be randomly selected from all the modules.
5: Weightage of marks should be proportional to number of hours assigned to each
(1) Batch wise tutorials are to be conducted. The number of students per batch should
be as per University pattern for practicals.
(2) Students must be encouraged to write Scilab Programs in tutorial class only. Each
Student has to write at least 4 Scilab tutorials (including print out) and at least
6 class tutorials on entire syllabus.
(3) SciLab Tutorials will be based on (1) Guass Jordan Method (2) Crouts
Method (LU) (3) Guass Seidal Method and (4) Jacobi iteration (5) Curve Fitting
for linear, parabolic and exponential functions
The distribution of marks for term work will be as follows,
Attendance (Theory and Tutorial) :05 marks
Class Tutorials on entire syllabus :10 marks
SciLab Tutorials :10
The final certification and acceptance of term‐work ensures the satisfactory
Performance of laboratory work and minimum passing in the term work.