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FE SEM 1 – ENGINEERING MATHS I

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Module 1 – Complex Numbers 8 Topics

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Pre-requisite 1: Review of Complex Numbers-Algebra of Complex Number

Pre-requisite 2: Cartesian

Pre-requisite 3: Polar

Pre-requisite 4: Exponential form of complex number

1.1 Statement of D’Moivre’s Theorem

1.2.1 Expansion of sinnθ, cosnθ in terms of sines and cosines of multiplesof θ

1.2.2 Expansion of sinnθ, cosnθ in powers of sinθ, cosθ

1.3 Powers and Roots of complex number

Module 2 – Hyperbolic function and Logarithm of Complex Numbers 7 Topics

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2.1.1 Circular functions of complex number

2.1.2 Circular functions of Hyperbolic functions

2.1.3 Inverse Circular and Inverse Hyperbolic functions

2.1.4 Separation of real and imaginary parts of all types of Functions

2.2.1 Logarithmic functions

2.2.2 Separation of real and Imaginary parts of Logarithmic Functions

2.3.1 Applications of complex number in Electrical circuits

Module 3 – Partial Differentiation 9 Topics

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3.1 Partial Differentiation

3.1.1 Function of several variables

3.1.2 Partial derivatives of first and higher order

3.1.3 Differentiation of composite function

3.2.1 Euler’s Theorem on Homogeneous functions with two independent variables (with proof)

3.2.2 Deductions from Euler’s Theorem

3.3.1 Total differentials

3.3.2 Implicit functions

3.3.3 Euler’s Theorem on Homogeneous functions with three independent variables

Module 4 – Applications of Partial Differentiation and Successive differentiation 6 Topics

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4.1.1 Maxima and Minima of a function of two independent variables

4.1.2 Lagrange’s method of undetermined multipliers with one constraint

4.2 Successive differentiation

4.2.1 nth derivative of standard functions

4.2.2 Leibnitz’s Theorem (without proof) and problems

4.3.1 Jacobian’s of two and three independent variables (simple problems)

Module 5 – Matrices 10 Topics

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Pre-requisite 1: Inverse of a matrix

Pre-requisite 2: Addition of a matrix

Pre-requisite 3: Multiplication of a matrix

Pre-requisite 4: Transpose of a matrix

5.1.2 Types of Matrices (symmetric, skew- symmetric, Hermitian, Skew Hermitian,Unitary and Orthogonal Matrices)

5.1.3 Rank of a Matrix using Echelon forms

5.1.4 Reduction to normal form

5.1.5 Reduction to PAQ form

5.2 System of homogeneous and non –homogeneous equations, their consistency and solutions

5.3.1 Application of inverse of a matrix to coding theory

Module 6 – Numerical Solutions of Transcendental Equations and System of Linear Equations and Expansion of Function 20 Topics

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6.1 Solution of Transcendental Equations

6.1.1 Solution by Newton Raphson method

6.1.2 Regula –Falsi method

6.2 Solution of system of linear algebraic equation

6.2.1 Gauss Jacobi Iteration Method

6.3.1 Taylor’s Theorem (Statement only)

6.3.2 Taylor’s series

6.3.3 Maclaurin’s series (Statement only)

6.3.4 Expansion of ??

6.3.4.4 sinh(x), cosh(x)

6.3.4.5 tanh(x)

6.3.4.6 log(1+x)

6.3.4.7 sin−1(?), cos−1(?) and tan−1(?)

6.4.1 Indeterminate forms

6.4.2 L- Hospital Rule

6.4.3 Gauss Elimination Method

6.4.4 Gauss Jordan Method

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