MA25C09 Computational Differential Equations – Semester III – Mech / Aero / Auto / Mfg / Marine / Mechatronics / MechAuto / Robotics / Aerospace / Mech(Auto) / Mech(Smart) – R-2025

Subject Code & Name: MA25C09 – Computational Differential Equations

Regulation: R-2025

Semester: III (Third Semester)

Branch: B.E. Mechanical Engineering (Mech) / B.E. Aeronautical Engineering (Aero) / B.E. Automobile Engineering (Auto) / B.E. Manufacturing Engineering (Mfg) / B.E. Marine Engineering (Marine) / B.E. Mechatronics Engineering (Mechatronics) / B.E. Mechanical and Automation Engineering (MechAuto) / B.E. Robotics and Automation Engineering (Robotics) / B.E. Aerospace Engineering (Aerospace) / B.E. Mechanical Engineering (Automobile) (Mech(Auto)) / B.E. Mechanical Engineering (Smart Manufacturing) (Mech(Smart))

Credits / L-T-P: 4 Credits | L-T-P: 3-1-0

Course Objectives

  • The Objectives of the course are to equip students with the ability to formulate and solve various types of Ordinary and Partial Differential Equations (ODEs & PDEs) and to develop proficiency in applying numerical methods and computational tools for solving differential equations encountered in engineering problems.

Full Unit-wise Syllabus

Unit I – First Order Ordinary Differential Equations

Basic concepts of ordinary differential equations–Formation of first order differential equations from physical problems–First order and first-degree ODE: Variables separable–Exact equations–Leibnitz’s equation – Bernoulli’s equation – Numerical Methods: Solving first order ODE by Euler's formula, Taylor series and Runge Kutta method of 4th order.

Activities: Application and Visualization of the first order ODE using open-source software and solving Competitive Examination questions

Unit II – Higher Order Ordinary Differential Equations

Formation of second order differential equations from physical problems–Linear equations of second and higher order with constant coefficients – Euler’s linear equations – Method of variation of parameters–Numerical Methods: Solving second order ODE by Runge-Kutta method of 4th order and finite difference method.

Activities: solving ordinary differential equations using open-source software and solving of Competitive Examination questions

Unit III – First Order Partial Differential Equations

Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions - Solution of PDE by variable separable method – Solution of standard types of first order partial differential equations (excluding reducible to standard types) – Lagrange’s linear equation – Numerical Methods for first order PDE by Method of lines with Runge- Kutta method of order fourth.

Activities: Application and Visualization of the Partial Differential Equations using open-source software and solving Competitive Examination questions

Unit IV – Higher Order Partial Differential Equations

Linear homogeneous partial differential equations of second and higher order with constant coefficients. Numerical Methods: Finite difference techniques for the solution of two-dimensional Laplace’s and Poisson’s equations on rectangular domain—Solution of one- dimensional heat equation using Bender Schmidt and Crank Nicholson difference schemes—Solution of one-dimensional wave equation by explicit scheme.

Activities: Application of the second order PDE using open-source software of 1-D wave, 1-D heat equations, Laplace and Poisson equations and Solving Competitive Examination questions

Course Outcomes (COs)

  • CO1: Explain first and higher order ODEs using appropriate analytical and numerical techniques.
  • CO2: Solve higher order PDEs using classical and finite difference methods.
  • CO3: Apply various solution methods to differential equations arising in engineering contexts.
  • CO4: Interpretation of numerical solutions for partial differential equations and using open source software.

Assessment Pattern (Quick Note)

  • Weightage: Continuous Assessment 40% | End Semester Examinations 60%
  • Internal methodology: Assignments (20%), Solution to application-oriented problems using software (20%), Solving Competitive Examination questions (20%), Internal Examinations (40%)

Source: Official Anna University – B.E. Mechanical Engineering R-2025 Syllabus
Last Updated: September 2026

Subject Code & Name: MA25C09 – Computational Differential Equations

Regulation: R-2025

Semester: III (Third Semester)

Branch: B.E. Mechanical Engineering (Mech) / B.E. Aeronautical Engineering (Aero) / B.E. Automobile Engineering (Auto) / B.E. Manufacturing Engineering (Mfg) / B.E. Marine Engineering (Marine) / B.E. Mechatronics Engineering (Mechatronics) / B.E. Mechanical and Automation Engineering (MechAuto) / B.E. Robotics and Automation (Robotics) / B.E. Aerospace Engineering (Aerospace) / B.E. Mechanical Engineering (Automobile) (Mech(Auto)) / B.E. Mechanical Engineering (Smart Manufacturing) (Mech(Smart))

Credits / L-T-P: 4 Credits | L-T-P: 3-1-0

Course Objectives

  • The Objectives of the course are to equip students with the ability to formulate and solve various types of Ordinary and Partial Differential Equations (ODEs & PDEs) and to develop proficiency in applying numerical methods and computational tools for solving differential equations encountered in engineering problems.

Full Unit-wise Syllabus

Unit I – First Order Ordinary Differential Equations

Basic concepts of ordinary differential equations–Formation of first order differential equations from physical problems–First order and first-degree ODE: Variables separable–Exact equations–Leibnitz’s equation – Bernoulli’s equation – Numerical Methods: Solving first order ODE by Euler's formula, Taylor series and Runge Kutta method of 4th order.

Activities: Application and Visualization of the first order ODE using open-source software and solving Competitive Examination questions

Unit II – Higher Order Ordinary Differential Equations

Formation of second order differential equations from physical problems–Linear equations of second and higher order with constant coefficients – Euler’s linear equations – Method of variation of parameters–Numerical Methods: Solving second order ODE by Runge-Kutta method of 4th order and finite difference method.

Activities: solving ordinary differential equations using open-source software and solving of Competitive Examination questions

Unit III – First Order Partial Differential Equations

Formation of partial differential equations by elimination of arbitrary constants and arbitrary functions - Solution of PDE by variable separable method – Solution of standard types of first order partial differential equations (excluding reducible to standard types) – Lagrange’s linear equation – Numerical Methods for first order PDE by Method of lines with Runge- Kutta method of order fourth.

Activities: Application and Visualization of the Partial Differential Equations using open-source software and solving Competitive Examination questions

Unit IV – Higher Order Partial Differential Equations

Linear homogeneous partial differential equations of second and higher order with constant coefficients. Numerical Methods: Finite difference techniques for the solution of two-dimensional Laplace’s and Poisson’s equations on rectangular domain—Solution of one- dimensional heat equation using Bender Schmidt and Crank Nicholson difference schemes—Solution of one-dimensional wave equation by explicit scheme.

Activities: Application of the second order PDE using open-source software of 1-D wave, 1-D heat equations, Laplace and Poisson equations and Solving Competitive Examination questions

Course Outcomes (COs)

  • CO1: Explain first and higher order ODEs using appropriate analytical and numerical techniques.
  • CO2: Solve higher order PDEs using classical and finite difference methods.
  • CO3: Apply various solution methods to differential equations arising in engineering contexts.
  • CO4: Interpretation of numerical solutions for partial differential equations and using open source software.

Assessment Pattern (Quick Note)

  • Weightage: Continuous Assessment 40% | End Semester Examinations 60%
  • Internal methodology: Assignments (20%), Solution to application-oriented problems using software (20%), Solving Competitive Examination questions (20%), Internal Examinations (40%)

Source: Official Anna University – B.E. Mechanical Engineering R-2025 Syllabus
Last Updated: September 2026

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