Semester 1 Maths weightage
Semester 1 Maths weightage

Chapter: Matrices

(Note: A very easy and high scoring chapter. A must for all students who want to pass M1)

Topics to be prepared

I want to Just Pass: Problems based on

  • Types of Matrices (symmetric, skew‐ symmetric, Hermitian, Skew Hermitian and properties of Matrices.
  • Unitary Matrix;
  • Orthogonal Matrix.
  • Rank of a Matrix using Echelon forms.
  • Reduction to Normal Form
  • PAQ in normal form

 

I want to get good Marks: (As above and plus)

  • Find constants k for Rank = 1, 2 or 3.
  • Theorems based on symmetric, skew‐ symmetric, Hermitian, Skew Hermitian Matrices

 

I want to Score Maximum: (As above and plus)

  • Inverse of a matrix
  • Definitions and Properties of Unitary Matrix, Orthogonal Matrix
  • Proving Properties of symmetric, skew‐ symmetric, Hermitian, Skew Hermitian Matrices

 

Chapter: Linear equations and Coding

(Note: A very easy and high scoring chapter. A must for all students who want to pass M1)

Topics to be prepared

I want to Just Pass: Problems based on

  • System of Homogeneous and Non–Homogeneous Equations, their consistency and solutions.
  • Linear Dependent and Independent Vectors.
  • Coding Decoding a message using Matrices

 

I want to get good Marks: (As above and plus)

 

 

I want to Score Maximum: (As above and plus)

  • Solving Linear equations using Adjoint and Inverse of a matrix.

Chapter: Numerical Solutions of Transcendental and System of Linear Equations

(Note: A very easy chapter. Only a fool will leave this chapter for Option)

Topics to be prepared

I want to Just Pass: Problems based on

  • Newton Raphson method
  • Gauss Elimination Method
  • Gauss Seidal Iteration Method.

 

I want to get good Marks: (As above and plus)

  • Regula –Falsi Equation
  • Gauss Jacobi Iteration Method

I want to Score Maximum: (As above and plus)

 


Chapter: Homogeneous Functions

(Note: Simple and Formula based chapter)

Topics to be prepared

I want to Just Pass: Problems based on

  • Euler’s Theorem and its corollaries with 2 & 3 independent variables
  • Evaluate using Euler’s Theorem
  • Verify Euler’s Theorem
  • Proving Euler’s Theorem with 2 & 3 independent variables

I want to get good Marks: (As above and plus)

I want to Score Maximum: (As above and plus)

  • Cauchy Homogenous functions
  • Lagrange’s Homogenous functions

 


 

Chapter: Applications of Partial Differentiation – Jacobian & Maxima-Minima

(Note: Small and easy chapter)

Topics to be prepared

I want to Just Pass: Problems based on

  • Jacobian

I want to get good Marks: (As above and plus)

  • Maxima and Minima of a function of two independent variables.

I want to Score Maximum: (As above and plus)

  • Maxima and Minima of a function using Lagrangian multiplier

 

 


Chapter: Partial Differentiation

(Note: A very Important and a major chapter)

 

Topics to be prepared

I want to Just Pass: Problems based on

  • Partial derivatives of
    1. First and Higher Order.
    2. Composite Functions.
    3. Implicit Functions.
  • Total differentials

I want to get good Marks: (As above and plus)

 

 

I want to Score Maximum: (As above and plus)

 

 


Chapter: Complex Numbers

(Note: Slightly Difficult chapter)

Topics to be prepared

I want to Just Pass: Problems based on

  • D’Moivre’s Theorem
  • Expansion of sin nθ, cos nθ in terms of sines and cosines of multiples of θ
  • Expansion of sin nθ, cos nθ in powers of sin θ, cos θ
  • Proving Euler’s Theorem with 2 & 3 independent variables

I want to get good Marks: (As above and plus)

  • Powers and Roots of Exponential and Trigonometric Functions.
  • Nth Root of unity esp. Cube Root
  • Finding roots of an nth order equation.
  • Continued Product of n roots

I want to Score Maximum: (As above and plus)

  • Algebra of Complex Number
  • Definitions
  • Magnitude and Amplitude of a Complex Number
  • Conjugate of a Complex Number

Chapter: Hyperbolic functions and Logarithm of Complex Numbers

(Note: Difficult chapter)

Topics to be prepared

I want to Just Pass: Problems based on

 

I want to get good Marks: (As above and plus)

  • Separation of real and imaginary parts of Logarithm of Complex Numbers

I want to Score Maximum: (As above and plus)

  • Inverse Circular functions
  • Inverse Hyperbolic functions.
  • Separation of real and imaginary parts of Hyperbolic functions

 


Chapter: Successive Differentiation

(Note: Difficult chapter)

Topics to be prepared

I want to Just Pass: Problems based on

  • Leibnitz’s Theorem. (Very Important. One problem will be surely asked)
  • Verify Euler’s Theorem
  • Proving Euler’s Theorem with 2 & 3 independent variables

I want to get good Marks: (As above and plus)

 

I want to Score Maximum: (As above and plus)

  • nth order derivative of standard functions like (ax + b)n; (ax + b)-n; log (a x + b); amx; emx; sin (ax + b); cos (ax + b); eax sin (bx + c); eax cos (bx + c); kax sin (bx + c); kax cos (bx + c);

Chapter: Expansion of Functions and Indeterminate forms

Topics to be prepared

I want to Just Pass: Problems based on

  • L‐ Hospital Rule
  • Finding constants a, b and c of a function whose indeterminate exists

I want to get good Marks: (As above and plus)

  • Taylor’s series
  • Maclaurin’s series

I want to Score Maximum: (As above and plus)

  • Expansion of ex, sin x, cos x, tan x, sinh x, cosh x, tanh x, log (1 + x), sin-1 x, cos-1 x, tan-1 x, Binomial series.
  • Indeterminate forms – Problems Involving Series

 

 

 

 

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