Modules / Lectures


Sl.No Chapter Name MP4 Download
1Lecture 1.1: Partial Differential Equations - Basic concepts and NomenclatureDownload
2Lecture 2.1:First Order Partial Differential Equations- How they arise? Cauchy Problems, IVPs, IBVPsDownload
3Lecture 2.2: First order Partial Differential Equations - Geometry of Quasilinear equationsDownload
4Lecture 2.3: FOPDE's - General Solutions to Linear and Semilinear equationsDownload
5Lecture 2.4: First order Partial Differential Equations- Lagrange's method for Quasilinear equationsDownload
6Lecture 2.5: Relation between Characteristic curves and Integral surfaces for Quasilinear equationsDownload
7Lecture 2.5: Relation between Characteristic curves and Integral surfaces for Quasilinear equationsDownload
8Lecture 2.6: FOPDE's - Method of characteristics for Quasilinear equations - 1Download
9Lecture 2.8: First order Partial Differential Equations - Failure of transversality conditionDownload
10Lecture 2.9: First order Partial Differential Equations - Tutorial of Quasilinear equationsDownload
11Lecture 2.10: FOPDE's- General nonlinear equations 1 - Search for a characteristic directionDownload
12Lecture 2.11:FOPDE's-General nonlinear equations 2-Characteristic direction and characteristic stripDownload
13Lecture 2.12: FOPDE's - General nonlinear equations 3 - Finding an initial stripDownload
14Lecture 2.13: FOPDE's - General nonlinear equations 4 - Local existence and uniqueness theoremDownload
15Lecture 2.14: First order Partial Differential Equations - Tutorial on General nonlinear equationsDownload
16Lecture 2.15: First order Partial Differential Equations-Initial value problems for Burgers equationDownload
17Lecture 2.16: FOPDE's - Conservation laws with a view towards global solutions to Burgers equationDownload
18Lecture: 3.1: Second Order Partial Differential Equations - Special Curves associated to a PDEDownload
19Lecture: 3.2: Second Order Partial Differential Equations - Curves of discontinuityDownload
20Lecture 3.3: Second Order Partial Differential Equations - ClassificationDownload
21Lecture 3.4: SOPDE's - Canonical form for an equation of Hyperbolic typeDownload
22Lecture 3.5: SOPDE's - Canonical form for an equation of Parabolic typeDownload
23Lecture 3.6: SOPDE's - Canonical form for an equation of Elliptic typeDownload
24Lecture 3.7: Second Order Partial Differential Equations - Characteristic SurfacesDownload
25Lecture 3.8: SOPDE's - Canonical forms for constant coefficient PDEsDownload
26Lecture 4.1: Wave Equation - A mathematical model for vibrating stringsDownload
27Lecture 4.2: Wave Equation in one space dimension - d'Alembert formulaDownload
28Lecture 4.3: Tutorial on One dimensional wave equationDownload
29Lecture 4.4: Wave Equation in d space dimensions - Equivalent Cauchy problems via Spherical meansDownload
30Lecture 4.5: Cauchy problem for Wave Equation in 3 space dimensions - Poisson-Kirchhoff formulaeDownload
31Lecture 4.6: Cauchy problem for Wave Equation in 2 space dimensions - Hadamard's method of descentDownload
32Lecture 4.7: Nonhomogeneous Wave Equation - Duhamel principleDownload
33Lecture 4.8: Wellposedness of Cauchy problem for Wave EquationDownload
34Lecture 4.9: Wave Equation on an interval in ? - Solution to an IBVP from first principlesDownload
35Lecture 4.10: Tutorial on IBVPs for wave equationDownload
36Lecture 4.11: IBVP for Wave Equation - Separation of Variables MethodDownload
37Lecture 4.12: Tutorial on Separation of variables method for wave equationDownload
38Lecture 5.1: Qualitative analysis of Wave equation - Parallelogram identityDownload
39Lecture 5.2: Qualitative analysis of Wave equation - Domain of dependence, domain of influenceDownload

Sl.No Chapter Name English
1Lecture 1.1: Partial Differential Equations - Basic concepts and NomenclatureDownload
Verified
2Lecture 2.1:First Order Partial Differential Equations- How they arise? Cauchy Problems, IVPs, IBVPsPDF unavailable
3Lecture 2.2: First order Partial Differential Equations - Geometry of Quasilinear equationsPDF unavailable
4Lecture 2.3: FOPDE's - General Solutions to Linear and Semilinear equationsPDF unavailable
5Lecture 2.4: First order Partial Differential Equations- Lagrange's method for Quasilinear equationsPDF unavailable
6Lecture 2.5: Relation between Characteristic curves and Integral surfaces for Quasilinear equationsPDF unavailable
7Lecture 2.5: Relation between Characteristic curves and Integral surfaces for Quasilinear equationsPDF unavailable
8Lecture 2.6: FOPDE's - Method of characteristics for Quasilinear equations - 1PDF unavailable
9Lecture 2.8: First order Partial Differential Equations - Failure of transversality conditionPDF unavailable
10Lecture 2.9: First order Partial Differential Equations - Tutorial of Quasilinear equationsPDF unavailable
11Lecture 2.10: FOPDE's- General nonlinear equations 1 - Search for a characteristic directionPDF unavailable
12Lecture 2.11:FOPDE's-General nonlinear equations 2-Characteristic direction and characteristic stripPDF unavailable
13Lecture 2.12: FOPDE's - General nonlinear equations 3 - Finding an initial stripPDF unavailable
14Lecture 2.13: FOPDE's - General nonlinear equations 4 - Local existence and uniqueness theoremPDF unavailable
15Lecture 2.14: First order Partial Differential Equations - Tutorial on General nonlinear equationsPDF unavailable
16Lecture 2.15: First order Partial Differential Equations-Initial value problems for Burgers equationPDF unavailable
17Lecture 2.16: FOPDE's - Conservation laws with a view towards global solutions to Burgers equationPDF unavailable
18Lecture: 3.1: Second Order Partial Differential Equations - Special Curves associated to a PDEPDF unavailable
19Lecture: 3.2: Second Order Partial Differential Equations - Curves of discontinuityPDF unavailable
20Lecture 3.3: Second Order Partial Differential Equations - ClassificationPDF unavailable
21Lecture 3.4: SOPDE's - Canonical form for an equation of Hyperbolic typePDF unavailable
22Lecture 3.5: SOPDE's - Canonical form for an equation of Parabolic typePDF unavailable
23Lecture 3.6: SOPDE's - Canonical form for an equation of Elliptic typePDF unavailable
24Lecture 3.7: Second Order Partial Differential Equations - Characteristic SurfacesPDF unavailable
25Lecture 3.8: SOPDE's - Canonical forms for constant coefficient PDEsPDF unavailable
26Lecture 4.1: Wave Equation - A mathematical model for vibrating stringsPDF unavailable
27Lecture 4.2: Wave Equation in one space dimension - d'Alembert formulaPDF unavailable
28Lecture 4.3: Tutorial on One dimensional wave equationPDF unavailable
29Lecture 4.4: Wave Equation in d space dimensions - Equivalent Cauchy problems via Spherical meansPDF unavailable
30Lecture 4.5: Cauchy problem for Wave Equation in 3 space dimensions - Poisson-Kirchhoff formulaePDF unavailable
31Lecture 4.6: Cauchy problem for Wave Equation in 2 space dimensions - Hadamard's method of descentPDF unavailable
32Lecture 4.7: Nonhomogeneous Wave Equation - Duhamel principlePDF unavailable
33Lecture 4.8: Wellposedness of Cauchy problem for Wave EquationPDF unavailable
34Lecture 4.9: Wave Equation on an interval in ? - Solution to an IBVP from first principlesPDF unavailable
35Lecture 4.10: Tutorial on IBVPs for wave equationPDF unavailable
36Lecture 4.11: IBVP for Wave Equation - Separation of Variables MethodPDF unavailable
37Lecture 4.12: Tutorial on Separation of variables method for wave equationPDF unavailable
38Lecture 5.1: Qualitative analysis of Wave equation - Parallelogram identityPDF unavailable
39Lecture 5.2: Qualitative analysis of Wave equation - Domain of dependence, domain of influencePDF unavailable


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