# GTU Maths 3 Equations Of All Chapters | AEM

0
26
views

## 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