Computational Method for Mechanical Engineering
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Computational Method for Mechanical Engineering Syllabus — Unit-wise Content
The official GTU curriculum for Computational Method for Mechanical Engineering (subject code 3710812) as prescribed for M(E · Semester 1 divides the course into 3 units, covering 44 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 (3710812)Unit 1 Differential Equations
- Basic Concepts: Modelling
- Differential Equations
- Ordinary and Partial differentiation
- Order of the equation
- Existence and Uniqueness of Solution
- Initial Value problem
- Boundary Value Problem
- Linear and Non-Linear Equation. 1st Order ODE: Geometric Meaning of y'= ƒ(x
- Direction Fields
- Euler’s Method
- Separable ODEs
- Exact ODEs (Integrating Factors Method
- Linear ODEs(Homogeneous and Non-Homogeneous
- Reduction to Linear problems)
- Orthogonal Trajectories. 2nd Order ODE: Linear Dependence and Linear Independence
- Homogeneous Linear ODEs of Second Order (Principal of Superposition
- Homogeneous Linear ODEs with Constant Coefficients (Euler's formula and review of the circular and hyperbolic function
- Exponential Solutions
- Repeated Roots and Stability)
- Differential Operator
- Modelling of Free Oscillations of Spring-Mass System
- Homogeneous Linear ODEs with Non-constant Coefficient (Cauchy-Euler Equation
- Existence and Uniqueness of Solutions)
Unit 2 Laplace Transforms
- Laplace Transform
- First Shifting Theorem (s-Shifting)
- Transforms of Derivatives and Integrals, ODE
- Unit Step Function (Heaviside Function)
- Second Shifting Theorem (t-Shifting)
- Short Impulses
- Dirac’s Delta Function
- Partial Fractions
- Integral Equations
- Differentiation and Integration of Transforms
- ODEs with Variable Coefficients
- Systems of ODEs
Unit 3 Linear Algebra
- Matrices and Vectors: Vectors in 2-Space and 3-Space
- Addition and Scalar Multiplication
- Matrix Multiplication
- Linear Systems of Equations and Gauss Elimination
- Ill- Conditioning
- Linear Independence
- Rank of a Matrix
- Solutions of Linear Systems: Existence 07 Subject Code: 3710812 w.e.f
- AY 2018-19 # Exam paper should be based on applications of above topics in Mechanical engineering rather than merely derivation of standard theory or its mathematical solution
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