Modules / Lectures

Sl.No Chapter Name English
1Definition and classification of linear integral equationsDownload
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2Conversion of IVP into integral equationsDownload
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3Conversion of BVP into an integral equationsDownload
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4Conversion of integral equations into differential equationsDownload
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5Integro-differential equationsDownload
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6Fredholm integral equation with separable kernel: TheoryDownload
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7Fredholm integral equation with separable kernel: ExamplesDownload
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8Solution of integral equations by successive substitutionsDownload
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9Solution of integral equations by successive approximationsDownload
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10Solution of integral equations by successive approximations: Resolvent kernelDownload
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11Fredholm integral equations with symmetric kernels: Properties of eigenvalues and eigenfunctionsDownload
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12Fredholm integral equations with symmetric kernels: Hilbert Schmidt theoryDownload
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13Fredholm integral equations with symmetric kernels: ExamplesDownload
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14 Construction of Green function-I Download
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15Construction of Green function-IIDownload
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16Green function for self adjoint linear differential equationsDownload
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17Green function for non-homogeneous boundary value problemDownload
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18Fredholm alternative theorem-IDownload
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19Fredholm alternative theorem-IIDownload
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20Fredholm method of solutionsDownload
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21Classical Fredholm theory: Fredholm first theorem-IDownload
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22Classical Fredholm theory: Fredholm first theorem-IIDownload
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23Classical Fredholm theory: Fredholm second theorem and third theoremDownload
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24Method of successive approximationsDownload
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25Neumann series and resolvent kernels-IDownload
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26Neumann series and resolvent kernels-IIDownload
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27Equations with convolution type kernels-IDownload
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28Equations with convolution type kernels-IIDownload
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29Singular integral equations-IDownload
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30Singular integral equations-IIDownload
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31Cauchy type integral equations-IDownload
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32Cauchy type integral equations-IIDownload
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33Cauchy type integral equations-IIIDownload
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34Cauchy type integral equations-IVDownload
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35Cauchy type integral equations-VDownload
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36Solution of integral equations using Fourier transformDownload
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37Solution of integral equations using Hilbert transform-IDownload
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38Solution of integral equations using Hilbert transform-IIDownload
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39Calculus of variations: IntroductionDownload
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40Calculus of variations: Basic concepts-IDownload
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41Calculus of variations: Basic concepts-IIDownload
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42Calculus of variations: Basic concepts and Euler equationDownload
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43Euler equation: Some particular casesDownload
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44Euler equation : A particular case and GeodesicsDownload
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45Brachistochrone problem and Euler equation-IDownload
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46Euler's equation-IIDownload
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47Functions of several independent variables Download
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48Variational problems in parametric form Download
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49Variational problems of general type Download
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50Variational derivative and invariance of Euler's equation Download
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51Invariance of Euler's equation and isoperimetric problem-I Download
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52Isoperimetric problem-II Download
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53Variational problem involving a conditional extremum-I Download
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54Variational problem involving a conditional extremum-II Download
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55Variational problems with moving boundaries-IDownload
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56Variational problems with moving boundaries-II Download
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57Variational problems with moving boundaries-III Download
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58Variational problems with moving boundaries; One sided variationDownload
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59Variational problem with a movable boundary for a functional dependent on two functions Download
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60Hamilton's principle: Variational principle of least action Download
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