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What you will learn

☑ GTU maths-3

Description

This Course Made for specially GTU (Gujarat Technological University) students, based on that we have covered the full course of GTU Maths-3.

The topics cover are as below,

1.First Order (ODE)

2.Higher-Order (O.D.E)

3.Laplace

4.Power Series

5.Fourier Series

6.Partial Differential Equation (PDE)

Ordinary Differential Equations and Applications: First order differential equations: basic concepts, Geometric meaning of y’ = f(x,y) Direction fields, Exact differential equations, Integrating factor, Linear differential equations, Bernoulli equations, Modeling, Orthogonal trajectories of curves.Linear differential equations of second and higher-order: Homogeneous linear differential equations of second order, Modeling: Free Oscillations, Euler- Cauchy Equations, Wronskian, Non-homogeneous equations, Solution by undetermined coefficients, Solution by variation of parameters, Modeling: free Oscillations resonance and Electric circuits, Higher order linear differential equations, Higher-order homogeneous with constant coefficient, Higher-order non-homogeneous equations. Solution by [1/f(D)] r(x) method for finding particular integral.

Fourier Series and Fourier integral: Periodic function, Trigonometric series, Fourier series, Functions of any period, Even and odd functions, Half-range Expansion, Forced oscillations, Fourier integral

Series Solution of Differential Equations: Power series method, Theory of power series methods, Frobenius method.

Laplace Transforms and Applications: Definition of the Laplace transform, Inverse Laplace transform, Linearity, Shifting theorem, Transforms of derivatives and integrals Differential equations, Unit step function Second shifting theorem, 09 15 Dirac’s delta function, Differentiation, and integration of transforms, Convolution and integral equations, Partial fraction differential equations, Systems of differential equations

Partial Differential Equations and Applications: Formation PDEs, Solution of Partial Differential equations f(x,y,z,p,q) = 0, Nonlinear PDEs first order, Some standard forms of nonlinear PDE, Linear PDEs with constant coefficients, Equations reducible to Homogeneous linear form, Classification of second-order linear PDEs.Separation of variables use of Fourier series, D’Alembert’s solution of the wave equation, Heat equation: Solution by Fourier series and Fourier integral

we have also added Basic Of Differentiation and basic Integration for a better understanding of Basics Mathematics.

Content

1.First Order(ODE)

Chart

1.Order & Degree

2.Formation Of Differential Equation

(3.1)Variable Saparable Part 1

(3.2)Variable Saparable Part 2

(3.3)Variable Saparable Part 3

(4.1)Homogeneous part 1

(4.2)Homogeneous part 2

(5.1)Exact & Non Exact part 1

(5.2)Exact & Non Exact part 2

(5.3)Exact & Non Exact part 3

(5.4)Exact & Non Exact part 4

(5.5)Exact & Non Exact part 5

(6.1)Linear Equation part 1

(6.2)Linear Equation part 2

(6.3)Linear Equation part 3

(6.4)Linear Equation part 4

(7.1)Miscellaneous Problems part 1

(7.2)Miscellaneous Problems part 2

2.Higher Order (O.D.E)

1.Linear Dependence & Independence

2.Definition

3. Use Of Know solution To Find Another

(4.1.1) Homogeneous Linear Equation_Second Order_Part1

(4.1.2)Homogeneous Linear Equation_Second Order_Part2

(4.2.1)Homogeneous Linear Equation_Higher Order_Part1

(4.2.2)Homogeneous Linear Equation_Higher Order_Part2

(4.2.3)Homogeneous Linear Equation_Higher Order_Part3

(5.0)Non Homogeneous Linear Equation_Definition

(5.1)Non Homogeneous Linear Equation_1.General Method

(5.2.1.1)Non Homogeneous Linear Equation_2.Shortcut Method_Case1_Part1

(5.2.1.2)Non Homogeneous Linear Equation_2.Shortcut Method_Case1_Part2

(5.2.2.1)Non Homogeneous Linear Equation_2.Shortcut Method_Case2_Part1

(5.2.2.2)Non Homogeneous Linear Equation_2.Shortcut Method_Case2_Part2

(5.2.3.1)Non Homogeneous Linear Equation_2.Shortcut Method_Case3_Part1

(5.2.3.2)Non Homogeneous Linear Equation_2.Shortcut Method_Case3_Part2

(5.2.3.3)Non Homogeneous Linear Equation_2.Shortcut Method_Case3_Part3

(5.2.4)Non Homogeneous Linear Equation_2.Shortcut Method_Case4

(5.2.5.1)Non Homogeneous Linear Equation_2.Shortcut Method_Case5_Part1

(5.2.5.2)Non Homogeneous Linear Equation_2.Shortcut Method_Case5_Part2

(5.3.1)Non Homogeneous Linear Equation_3.Undetermined Coefficent_Part1

(5.3.2)Non Homogeneous Linear Equation_3.Undetermined Coefficent_Part2

(5.4.1)Non Homogeneous Linear Equation_4.Variation Of Parameters_Part1

(5.4.2)Non Homogeneous Linear Equation_4.Variation Of Parameters_Part2

(5.4.3)Non Homogeneous Linear Equation_4.Variation Of Parameters_Part3

6.Cauchy-Euler Equation

7.Legendre's Equation

3.Laplace

(1.1)lp trannform n example_part1

(1.2)lp trannform n example_part2

(1.3)lp trannform n example_part3

(1.4)lp trannform n example_part4

(2.1)first shifting theorem_part1

(2.2)first shifting theorem_part2

(2.3)first shifting theorem_part3

3.Change Scale Of Property

(4.1)Inverse LPT_part1

(4.2)Inverse LPT_part2

(4.3)Inverse LPT_part3

(4.4)Inverse LPT_part4

(4.5)Inverse LPT_part5

(4.6)Inverse LPT_part6

(5.1)Derivative & Integral_part1

(5.2)Derivative & Integral_part2

(5.3)Derivative & Integral_part3

(6.1)Multiplication & Divided by T_part1

(6.2)Multiplication & Divided by T_part2

(6.3)Multiplication & Divided by T_part3

(6.4)Multiplication & Divided by T_part4

(6.5)Multiplication & Divided by T_part5

7.Evaluation of Integral by LT

(8.1)Convolution Theorem_part1

(8.2)Convolution Theorem_part2

(8.3)Convolution Theorem_part3

(9.1)Application Of difference equation_part1

(9.2)Application Of difference equation_part2

10.Periodic Function

11.Unit Step Function

12.Unit Impulse Function

4.Power Series

(1)Ordinary & Singular Point

(2.1).Power Series Example_Part1

(2.2)Power Series Example_Part2

5.Fourier Series

(1.1)Fourier Example_part1

(1.2)Fourier Example_part2

(1.3)Fourier Example_part3

(1.4)Fourier Example_part4

(2.1)Discontinuos Function_part1

(2.2)Discontinuos Function_part2

(2.3)Discontinuos Function_part3

(3.1)Change Of Interval_part1

(3.2)Change Of Interval_part2

(4.1)Even & Odd Function_part1

(4.2)Even & Odd Function_part2

(4.3)Even & Odd Function_part3

(5.1)Half Range Series-Part1

(5.2)Half Range Series-Part2

(5.3)Half Range Series-Part3

(6.1)Compex Fourier_part1

(6.2)Compex Fourier_part2

(7.1)Fourier Integral_part1

(7.2)Fourier Integral_part2

(7.3)Fourier Integral_part3

(7.4)Fourier Integral_part4

6.Partial Differential Equation (PDE)

1.Introduction

(2.1)Formating Of PDE_Eliminating Arbitary Constant

(2.2)Formating Of PDE_Eliminating Arbitary Function

3.Linear Diff Eq In First Order

(4.1)Non Linear Diff Eq_Introduction

(4.2)Non Linear Diff Eq_FORM I

(4.3)Non Linear Diff Eq_FORM II

(4.4)Non Linear Diff Eq_FORM III

(4.5)Non Linear Diff Eq_FORM IV

5.Direct Integration

6.Separation Of Variable

Basic Of Differentiation and Integration

Basic Of Differentiation

Basic Of Integration

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