Mathematics 3 (Mechanical)
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Follow on Instagram for UpdatesMathematics 3 (Mechanical) Syllabus — Unit-wise Content
The official GTU curriculum for Mathematics 3 (Mechanical) (subject code BE03000211) as prescribed for Metallurgy · Semester 3 divides the course into 6 units, covering 38 listed topics. The unit-wise breakdown below is read from the GTU syllabus document for this subject code, so you can check what the course actually covers before deciding which papers to attempt.
Download the official syllabus PDF (BE03000211)Unit 1 Fourier Series
- Periodic functions
- Fourier series of functions of 2π or any other period
- Dirichlet’s condition for convergence of Fourier series
- Fourier series of even and odd functions
- Half-range Fourier series
Unit 2 Partial Differential Equations (PDEs)
- Formation of partial differential equations
- solution of first order linear and non-linear partial differential equations
- Charpit’s method
- Solution of homogeneous and nonhomogeneous linear partial differential equations of second and higher order by complementary function and particular integral method
- classification of second order linear partial differential equations
- method of separation of variables
- one-dimensional wave equation and heat equation
Unit 3 Finite Differences and Interpolation
- Finite difference operators and their relations
- Newton’s forward and backward difference methods
- Lagrange’s interpolation method
- Inverse interpolation
- Newton’s divided difference method
Unit 4 Numerical Differentiation and Integration
- Numerical Differentiation: Derivatives using forward difference and backward difference formulae Numerical Integration: Newton-Cotes quadrature formulae
- Trapezoidal rule
- Simpson’s rules
- Gaussian integration
- Case studies
Unit 5 Numerical Solution of Ordinary Differential Equations
- Picard’s method
- Euler’s method
- Runge-Kutta 2nd and 4th order method
- Case studies
Unit 6 Laplace Transforms
- Laplace transform and Inverse Laplace transform
- first shifting theorem (s-shifting)
- transforms of derivatives and integrals
- unit step function (Heaviside function)
- second shifting theorem (t-Shifting)
- Laplace transform of periodic functions
- short impulses
- Dirac’s delta function
- integral equations
- differentiation and integration of transforms
- ODEs with variable coefficients
- systems of ODEs
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