**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
- First and Higher Order.
- Composite Functions.
- 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)

__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); a^{mx}; e^{mx}; sin (ax + b); cos (ax + b); e^{ax}sin (bx + c); e^{ax}cos (bx + c); k^{ax}sin (bx + c); k^{ax}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 e
^{x}, 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