The Advanced Numerical Methods in Thermal Engineering (MEngg 6111) course aims to equip students with essential mathematical analysis techniques pertinent to thermal engineering. Key topics encompass linear algebra, tensor calculus, and both ordinary and partial differential equations, emphasizing analytical and numerical solution methods to model engineering systems. Students will learn to apply differential equations, use Taylor’s series for error analysis, and employ numerical techniques for various mathematical challenges, including root finding and curve fitting. The course adopts a blended learning approach spanning 10 weeks, with 9 weeks online and 1 week of face-to-face laboratory sessions. Assessments include mid-exams, individual projects, and final exams, with a strong emphasis on engaging with mandatory online materials. Active participation, alongside maintaining required scores in assessments, is crucial for success in this course, fostering deep understanding and practical application of advanced numerical methods in thermal engineering contexts.

Course Overview: Advanced Numerical Methods in Thermal Engineering (Course Code: MEngg 6111)

- Credits: 3 credit hours / 6 ECTS  

Objective:

Develop foundational mathematical analysis methods relevant for Thermal engineers.

Topics Covered: 

  - Linear algebra and vector spaces

  - Tensorial calculus: Limit and continuity, Mean  value theorems, Evaluation of Improper Definite Differentials and Integral 

  - Ordinary and partial differential equations: First  (linear  and  nonlinear) and Higher Order Equations, 

  - Numerical methods and solutions for linear algebraic equations: Floating  point  operations  and  errors,  Interpolation,  Root  finding  of linear  and  non-linear  algebraic  equations,  Numerical  differentiation and integration,  and Systems of linear algebraic equations:

 Learning Outcomes: 

  1. Apply first and second-order differential equations, solving analytically and numerically for engineering system modeling.

  2. Utilize Taylor’s series for approximations and error analysis.

  3. Implement numerical methods for root finding, curve fitting, differentiation, and integration.

  4. Solve linear and non-linear algebraic equations, ordinary and partial differential equations on computers.

  5. Understand computational complexity, accuracy, stability, and errors in solution procedures.

Resources:

Lecture notes (PDFs, eBooks), videos, articles, books, online reading materials, lab manuals, and assignments.

Delivery Method: 

  - 10 weeks total; 9 weeks online (including project submission/presentation) and 1 week of face-to-face demonstrations in a computer lab.

  - Suggested flexibility in pacing, with a focus on independent project work.

Assessment Structure: 

  1. Mid Exam (Online) – 20%

  2. Individual Project Submission (Online) – 30%

  3. Assignment/Presentation (Individual Project Online) – 20%

  4. Final/End Semester Exam – 30%

- Requirements: 

  - Minimum 80% scores in online quizzes and ORA submissions.

  - 100% attendance at practical computer lab sessions, barring unforeseen circumstances.