Ordinary Differential Equations

Lecture 1: Introduction to Differential Equations [Slide] [Lecture]

Lecture 2: Variable Separable First Order Differential Equations [Slide] [Lecture]

Lecture 3: Homogeneous First Order Differential Equations [Slide] [Lecture]

Problem Sheet 1 [Slide] 

Lecture 4: Exact First Order Differential Equations [Slide] [Lecture]

Lecture 5: Computing Integrating Factor [Slide] [Lecture]

Lecture 6: Integrating Factor Related Exercises [Slide] [Lecture]

Lecture 7: Integrating Factor By Inspection [Slide] [Lecture]

Problem Sheet 2 [Slide] 

Lecture 8: Linear First Order DE [Slide] [Lecture]

Lecture 9: Bernoulli non-Linear First Order DE [Slide] [Lecture]

Lecture 10: Reduction of Order [Slide] [Lecture]

Problem Sheet 3 [Slide] 

Lecture 11: Introduction to 2nd Order DE [Slide] [Lecture]

Lecture 12: Wronskian [Slide] [Lecture]

Lecture 13: Computing y2 when y1 is known [Slide] [Lecture]

Lecture 14: 2nd Order DE with Constant Coefficients [Slide] [Lecture]

Lecture 15: Euler Equidimensional Equations [Slide] [Lecture]

Lecture 16: Transforming Given DE into DE with Constant Coefficients [Slide] [Lecture]

Problem Sheet 4 [Slide] 

Lecture 17: Methods of Undetermined Coefficients Part-I [Slide] [Lecture]

Lecture 18: Methods of Undetermined Coefficients Part-2 [Slide] [Lecture]

Problem Sheet 5 [Slide] 

Lecture 19: Methods of Variation of Parameters [Slide] [Lecture]

Problem Sheet 6 [Slide] 

Lecture 20: Operator Method Part-I [Slide] [Lecture]

Lecture 21: Operator Method Part-II [Slide] [Lecture]

Lecture 22: Qualitative Behavior of Solutions Part-I [Slide] [Lecture]

Lecture 23: Qualitative Behavior of Solutions Part-II [Slide] [Lecture]

Lecture 24: Sturm Comparison Theorem Part-I [Slide] [Lecture]

Lecture 25: Sturm Comparison Theorem Part-II [Slide] [Lecture]

Lecture 26: Power Series Solution for First Order DE [Slide] [Lecture]

Lecture 27: Ordinary Points-Power Series Solution for 2nd Order DE [Slide] [Lecture]

Lecture 28: Regular Singular Points and Indicial Equation [Slide] [Lecture]

Lecture 29: Frobenius Series Solutions Part-I [Slide] [Lecture]

Lecture 30: Frobenius Series Solutions Part-II [Slide] [Lecture]

Lecture 31: Hypergeometric Series Solutions Part-I [Slide] [Lecture]

Lecture 32: Hypergeometric Series Solutions Part-II [Slide] [Lecture]

Lecture 33: Legendre Equation and Rodrigue's Formula [Slide] [Lecture]

Lecture 34: Generating Function for Legendre Polynomial [Slide] [Lecture]

Lecture 35: Orthogonality Proof [Slide], Orthogonality Exercises [Slide] [Lecture]

Lecture 36: Legendre Series [Slide] [Lecture]

Problem Sheet 10 [Slide] 

Lecture 37: Bessel Functions [Slide] [Lecture]

Lecture 38: Properties of Bessel Functions [Slide] [Lecture]

Lecture 39: Orthogonality of Bessel Functions [Slide] [Lecture]

Lecture 40: Laplace Transform (LT) [Slide] [Lecture]

Lecture 41: Solving DE using LT Part-I [Slide] [Lecture]

Lecture 42: Solving DE using LT Part-II [Slide] [Lecture]

Lecture 43: Problem Sheet [Slide] [Lecture]

Lecture 44: Convolution Theorem [Slide] [Lecture]

Lecture 45: System of Equations [Slide] [Lecture]

Lecture 46: Solving Homogeneous System of Equations [Slide] [Lecture]

Lecture 47: Solving non-Homogeneous System of Equations [Slide] [Lecture]

Lecture 48: Fourier Series [Slide] [Lecture]

Lecture 49: Convergence of Fourier Series [Slide] [Lecture]

Lecture 50: Fourier Sine and Cosine Series [Slide] [Lecture]

Lecture 51: Eigenvalues and Eigenfunctions [Slide] [Lecture]

Lecture 52: Partial Differential Equations [Slide] [Lecture]