With the support of available solved study materials for partial differential equations and complex analysis, it's time to make sure you grasp everything. This course covers the fundamental concepts of partial differential equations, which have applications in all areas of engineering and are frequently utilized in the modelling and analysis of a wide range of physical events. to comprehend residue integration, conformal transformation, and the fundamental theory of complex variable functions.
| Board | KTU |
| Scheme | 2019 New Scheme |
| Year | Second Year |
| Semester | S3 |
| Subject | MAT 201 | Partial Differential Equation And Complex Analysis Notes |
| Credit | 4 Credit |
| Category | KTU S3 |
KTU S3 Partial Differential Equation And Complex Analysis | MAT 201 Notes (2019 Scheme)
Module 1
Module 1 - Syllabus
Partial Differential Equations: Partial differential equations, Formation of partial differential equations –elimination of arbitrary constants-elimination of arbitrary functions, Solutions of partial differential equations, Equations solvable by direct integration, Linear equations of the first order- Lagrange’s linear equation, Non-linear equations of the first order -Charpit’s method, Solution of the equation by the method of separation of variables.
Module 1 - Notes
Module 1 Partial Differential Equation And Complex Analysis | MAT 201 HANDWRITTEN Notes
Module 2
Module 2 - Syllabus
Applications of Partial Differential Equations: One dimensional wave equation- vibrations of a stretched string, derivation, solution of the wave equation using method of separation of variables, D’Alembert’s solution of the wave equation, One dimensional heat equation, derivation, solution of the heat equation
Module 2 - Notes
Module 2 Partial Differential Equation And Complex Analysis | MAT 201 HANDWRITTEN Notes
Module 3
Module 3 - Syllabus
Complex Variable – Differentiation : Complex function, limit, continuity, derivative, analytic functions, Cauchy-Riemann equations, harmonic functions, finding harmonic conjugate, Conformal mappings- mappings. Linear fractional transformation, fixed points, Transformation
Module 3 - Notes
Module 3 Partial Differential Equation And Complex Analysis | MAT 201 HANDWRITTEN Notes
Module 4
Module 4 - Syllabus
Complex Variable – Integration: Complex integration, Line integrals in the complex plane, Basic properties, First evaluation method-indefinite integration and substitution of limit, second evaluation method-use of a representation of a path, Contour integrals, Cauchy integral theorem (without proof) on the simply connected domain, Cauchy integral theorem (without proof) on multiply connected domain Cauchy Integral formula (without proof), Cauchy Integral formula for derivatives of an analytic function, Taylor’s series and Maclaurin series.
Module 4 - Notes
Module 4 Partial Differential Equation And Complex Analysis | MAT 201 HANDWRITTEN Notes
Module 5
Module 5 - Syllabus
Complex Variable – Residue Integration: Laurent’s series(without proof ), zeros of analytic functions, singularities, poles, removable singularities, essential singularities, Residues, Cauchy Residue theorem (without proof), Evaluation of definite integral using residue theorem, Residue integration of real integrals – integrals of rational functions, integrals of improper integrals of the form with no poles on the real axis.
Module 5 - Notes
Module 5 Partial Differential Equation And Complex Analysis | MAT 201 HANDWRITTEN Notes
- Recognize the idea behind and how to solve a partial differential equation.
- Analyze and resolve the heat equation and the wave equation in one dimension.
- Recognize complex functions and their continuity and differentiability using Cauchy-Riemann equations.
- Utilize Cauchy's integral theorem and formula to evaluate complex integrals, and be aware of the series expansion of analytic functions.
- Recognize the complex function's series expansion around a singularity and use the residue theorem to construct various real integrals of various types.
KTU S3 EC Related Links
| KTU S3 Syllabus | Click Here |
| KTU S3 Study Notes | Click Here |
| KTU S3 Reference Textbook | Click Here |
| KTU S3 Previous Year Solved Questions | Click Here |
| KTU S3 Study Materials | Click Here |
