B.Tech. (ECE '15), IIT Kharagpur,
AIR 34 in AIEEE - 2011,
Qualified RMO - 2009,
CSE Mains 2017: Essay - 153, Maths - 252

Asim Anand

In this course I would be covering another topic from the Mathematics Optional syllabus - Ordinary Differential Equations and Partial Differential Equations.

Crack UPSC CSE Prelims and Mains Exams. Know how to prepare for UPSC 2019 and 2020, complete syllabus, exam patterns, latest notifications to join IAS, IFS, IPS and other cadres of Civil Services.

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English

Mathematics Optional for UPSC - ODE And PDE

Strategy for Mains

Preparation Strategy

Practice & Strategy

UPSC CSE

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Test Preparation

Union Public Service Commission Exams (UPSC)

Syllabus

In this video we would be seeing a brief overview of what this course has in store.

Overview

In this lecture we introduce the ODE, its degree, order, Uniqueness Theorem, linear dependence and Independence.

Formulation of Differential Equations - I

Some more theorems on linear dependence and independence.

Formulation of Differential Equations - II

Formulation of Differential Equations - III

Formulation of Differential Equations - IV

Some solved examples on Formulation of Differential Equations.

Solved Examples - I

Some more solved examples from Formulation of Differential Equations.

Solved Examples - II

We introduce equations of first order and first degree.

Equations of First Order and First Degree - I

Homogeneous & exact Differential Equations.

Equations of First Order and First Degree - II

Equations of First Order and First Degree - III

Equations of First Order and First Degree - IV

Please omit this lesson.

Equations of First Order and First Degree - V

Equations of First Order and First Degree - VI

Equations of First Order and First Degree - VII

Important facts for a Cartesian curve y = f(x).

Equations of First Order and First Degree - VIII

Solved Examples on Equations of First Order and First Degree.

Solved Examples - III

Solved Examples - IV

Solved Examples - V

Solved Examples - VI

Concluding problems on Equations of First Order and First Degree.

Solved Examples - VII

Trajectories, orthogonal trajectories in Cartesian coordinates.

Trajectories - I

Determination of orthogonal Trajectories in polar coordinates.

Trajectories - II

Trajectories - III

Equations of First Order but not of First Degree - I

Equations of First Order but not of First Degree - II

Equations of First Order but not of First Degree - III

Clairaut's Equation

Equations reducible to the Clairaut's Form

Singular Solutions introduction.

Correction - In the explanation for the 'a' in y^2 = 4ax, I mentioned that 'a' is a parameter. However it should be read as 'a is a constant mentioned in the given differential equation'.

Singular Solutions - Introduction

c - discriminant and p - discriminant relations.

C - discriminant and p - discriminant Relations

Determination of Singular Solutions

Working rule - Method I

Working rule - Method II

Singular Solution of Clairaut's Equation

Solved Examples

Linear Differential Equations with Constant Coefficients - Notations

Linear Differential Equations with Constant Coefficients - Introduction

Linear Differential Equations with Constant Coefficients - Complementary Function (C.F.)

Auxiliary Equation - Case of Real & Distinct roots

Auxiliary Equation - Case of Equal roots

Auxiliary Equation - Case of Complex Roots

Auxiliary Equation - Case of Surd Roots

Complementary Function - Working Rule & Summary

The Symbolic Function 1/f(D)

Linear Differential Equations with Constant Coefficients - Particular Integral (P.I.)

Particular Integral - Working Rule

Solved Example

Particular Integral - Short Method I

Particular Integral - Short Method II

Particular Integral - Short Method III

Particular Integral - Short Method IV

Particular Integral - Short Method V

Method of Undetermined Coefficients

Method of Undetermined Coefficients - Modifications to the Trial solution

Cauchy-Euler Equations - Introduction

Cauchy-Euler Equations - Method of solution

Cauchy-Euler Equations - Particular Integral

Particular cases

Legendre's Linear Equation - Introduction

Legendre's Linear Equations - Method of Solution

Legendre's Linear Equation - Working Rule

Method of Variation of Parameters - First Order Equations

Working Rule & Illustrative Example

Method of Variation of Parameters for second order Linear Differential Equation.

Method of Variation of Parameters - Second Order Equations

Working Rule

Simultaneous Differential Equations - Introduction

Simultaneous Differential Equations - Method I & Example

Simultaneous Differential Equations - Method II & Example

Simultaneous Differential Equations involving x•d/dx or t•d/dt

Exact Differential Equation - Introduction

Condition of Exactness

Integrating Factor

Exactness of Non-Linear Equations - I

Exactness of Non-Linear Equations - II

Equations of the form (d^n y/dx^n) = f(x)

Equations of the form (d^2 y/dx^2) = f(y)

Reduction of Order - Equations that don't contain y directly

Equations that don't contain x directly

Linear Equations of Second Order - Motivation

Complete Solution of y'' + Py' + Qy = R in terms of one known Integral

Rules for getting an Integral belonging to C.F.

Theorem

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Priya Tiwari

In this course, the educator discusses idioms, phrases and proverbs with meaning and easy explanation. The course will be beneficial for UPSC CSE Aspirants.

(Hindi) Idioms and Phrases: UPSC CSE

MA in Applied Human Rights from Sheffield Hallam University, BA (Hons.) History from LSR, reader, dancer, love to teach, AIR 42 in 2018 UPSC

Nandini Maharaj

In this course, the educator will give history optional students a detailed strategy for preparation. We will discuss lists of maps, then the syllabus point by point with relevant sources to study from and previous year questions.

Strategy for History Optional: UPSC CSE

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Anuj Garg

In this course I will be discussing some important questions asked in UPSC mains from modern history section

(Hindi) Modern History Previous Year Paper Analysis (2014-2018)

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▪️Founder - STUDY IAS ( 4.5 Lakh Followers )
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Aman Sharma

Two important factors decide the good outcome of your answer: one, understanding the question completely. Second, sticking to the word limit.

To understand a question fully, one must know that a question has keywords. Every question has a ‘topic’ and a ‘directive’.

(Hindi) Understanding the Keywords for UPSC Mains Answer Writing

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Amit Ranjan

In this course we will be focussing on the preparations for UPSC mains for the optional paper Physics.

(Hindi) Mains Optional Physics - UPSC CSE

Kapil Sharma

(Hindi) l important Previous Years Question for UPPCS,RAS,MPPSC.UGC NET, SSC.CGL examination

Lessons

118 lessons • 8h 30m