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Engineering Mathematics

BI 1452

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Engineering Mathematics

Corresponding Marathi & Hindi Meanings for each difficult English words.

Book Id: 1452

Author: Anantmali S. Patil, Dr. Prakash M.Patil, Rekha V. Gujar, Shubhangi R. Kanbarkar

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Contents

1. Complex Number

1. Introduction

Definition of Complex Number

Polar form of a Complex Number

Polar Form of z = x + iy for Different Values of x and y   

2. Algebra of Complex Number

Addition

Subtraction

Scalar Multiplication

Multiplication

Conjugate of Complex Number

Division

Solved Examples

3. De'moivre's Theorem

Powers of Complex Number

The Roots of a Complex Number

nth Roots of Unity

Solved Examples

4. Euler's Theorem

Euler's Theorem for Real or Complex

Hyperbolic Functions

Solved Examples

2. Function

1. Definition of Function

1.1  Domain, Co-domain and Range

2.   Types of Functions

Solved Examples

3. Intervals

Solved Examples

3. Limits

1. Definition of Limit

2. Properties of Limits

Standard Results

Limits of Algebraic Functions

By Direct Substitution

Limits of Exponential Functions

Limits of Logarithmic Functions

Limits of Trigonometric Functions

4. Derivatives

1. Concept of Derivatives

Definition

Notation

2. Derivative of Standard Functions by I Principle

Solved Examples

3. Laws of Differentiation

Solved Examples

4. Derivative of Composite Functions or Chain Rule

Solved Examples

5. Derivatives of Inverse and Inverse Trigonometric Functions

Derivative of Inverse Trigonometric Functions

Some Properties of Inverse Trigonometric Functions

Relation between Inverse and Circular Functions

Solved Examples

6. Derivative of Implicit Function

Methods to Differentiate Implicit Function

Solved Examples

7. Logarithmic Differentiation

Solved Examples

8. Derivative of Parametric Functions

Solved Examples

9. Derivative of one Function with Respect to Another Function

Solved Examples

10.  Second Order Differentiation

Solved Examples

5. Numerical Solution of Algebraic Equation

1. Introduction

Algebraic Equation

Method of Iteration2

Working Rule

2. Bisection Method

Solved Examples

3. Method of False Position or (Regula- Falsi Method)

Solved Examples

4. Newton-Raphson Method

Solved Examples

6.   Numerical Solution of Simultaneous Equation

1. Introduction

2. Elimination Method

Gauss Elimination Method

Solved Examples

Gauss-Seidal Method (Iterative Method)

Solved Examples

Jacobi's Method (Iterative Method)

Working Rule

Solved Examples

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