## GTU Maths 3 Equations Of All Chapters | AEM

**GTU Maths 3 Equations :**

Here, we providing all chapters equations related to mathematics 3 or we know as AEM (2130002).

We know syllabus is changed but methods was not changed equations are not changed so, in this article provided equations are related to chapters.

### Chapter 1 : Introduction to Some Special Functions:

- Gamma – Beta and Bessel-Error Functions
- Some special Wave Functions for Mathematics
- Some Special Functions For Advanced Maths

### Chapter 2 : Fourier Series and Fourier integral:

- Periodic function
- Trigonometric series
- Fourier series
- Functions of any perioday
- Even and odd functions
- Half-range Expansion
- Fourier integral

### Chapter 3 : Ordinary Differential Equations and Applications:

- First order differential equations: basic concepts, Geometric meaning of y’ = f(x,y) Direction field
- 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.

### Chapter 4 : Series Solution of Differential Equations:

- Power series method,Theory of power series methods
- Frobenius method

### Chapter 5 : 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
- Dirac’s delta function
- Differentiation and integration of transforms
- Convolution and integral equations
- Partial fraction differential equations
- Systems of differential equations

### Chapter 6 : 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