MCL704: Applied Mathematics for Thermofluids

Lecture Notes

PRE-MAJOR TOTAL

Syllabus & References

EVALUATION POLICY

MCL 704 : Applied Mathematics for Thermofluids: 3-0-0-2 : Introduction

Selection of A Suitable Branch of Mathematics for Thermofluids

Simple DEs for Conservative Thermofluids

Development of FO-ODEs for Selected Thermofluid Systems

First Order Inhomogeneous ODEs to Study Thermofluids

First Order Nonlinear ODEs

First Order Nonlinear & Non-autonomous ODEs

First Order Exact Nonlinear ODEs

First Order Semi-Exact Nonlinear ODEs

Second Order ODEs

Soloved Examples:FO ODEs

Second Order Linear ODEs

Study of Denominated Linear SO-ODEs

Study of Non-Homogeneous Linear SO-ODEs with CC

The Variation of Parameters Method

Series Solutions to Linear SO-ODE

Designated Series Functions as Solutions to Special Linear SO-ODE

Orthogonal Series Functions as Solutions to Special Linear SO-ODE

Family of Sturm-Liouville Problems

Basics of Nonlinear SO-ODE

Introduction to Partial Differential Equations

Laplacian Operator : A Mathematical Key to Thermofluids

First Order Linear PDEs

First Order Linear PDEs

Quasi-Linear FO-Partial Differential Equations

Non-Linear FO-Partial Differential Equations

Second Order-Partial Differential Equations

Solution to More Thermo-Mechanical Problems using Laplace Equations

Analysis of Parabolic SO-PDES

Analysis of Hyperbolic SO-PDES

Problem Sheets for Practice

Basic Calculus of Vectors

First order ODEs

Basics of Second order ODEs

Reduction of Order Method for Second Order Linear ODEs

Second Order Linear ODEs with CC

Non-homogeneous Second Order Linear ODEs with CC

Second Order Linear ODEs with VC

Reading Material

Basic Calculus of Vectors

First Order ODEs with applications

Basics of First Order ODEs

Autonomous First Order ODEs

Nonlinear First Order ODEs

Second Order ODEs

FROBENIUS SERIES SOLUTIONS

Series Methods and Approximations

Bessel Functions

Chebyshev Polynomials