AM 203 : PARTIAL DIFFERENTIAL EQUATIONS (Common with paper MA 203 of Branch I(A) Mathematics) UNIT : –I Ordinary Differential Equations in more than two variables : Methods of solutions of dx/P =dy/Q = dz/R-Orthogonal trajectories of a system of curves on asuface-Pfaffian differential forms and equations in Three variables . (Sections 3,4,5 and of Chapter 1) UNIT II: – Partial Differential Equations of the First order: Partial Differential equations-Origins of first order partial differential equations- problems for first order Cauchy’s equations-Linear equations of first order-Integral surfaces passing through a given curve orthogonal to a given system of surfaces-Charpit’s –Surfaces method.(Sections 1,2,3, 4,5,6 and 10 of Chapter 2) UNIT III: – Partial Differential Equations of the Second order: The Origin of second order equations partial differential with constant coefficients-Equations with –Linear variable coefficients.(Sections 1,4 and 5 of Chapter 3) UNIT-IV: Equations : Elementary solution of equation-Families of Laplace’s Laplace’s equipotential surfaces-Boundary value problems Separation of variables.( Sections – 2,3,4 and 5 of Chapter 4) Scope and Standard as in Elements of Partial Differential by IAN “ Equations” Sneddon Chapter 1: Section 1 to 6, Chapter 2: Sections 1,2,4,5,6,10 Chapter 3: Sections 1,4,5, chapter 4: Sections 2,3,4,5, Chapter 5: Sec2, Chapter 6: Section 3 and 4. Reference : 1. Ordinary and Partial Differential Equations by M.D. Raisinghania
AM 203 : PARTIAL DIFFERENTIAL EQUATIONS (Common with paper MA 203 of Branch I(A) Mathematics) UNIT –I : Ordinary Differential Equations in more than two variables : Methods of solutions of dx/P =dy/Q = dz/R-Orthogonal trajectories of a system of curves on asuface-Pfaffian differential forms and equations in Three variables . (Sections 3,4,5 and of Chapter 1) UNIT – II: Partial Differential Equations of the First order: Partial Differential equations-Origins of first order partial differential equations- Cauchy’s problems for first order equations-Linear equations of first order-Integral surfaces passing through a given curve –Surfaces orthogonal to a given system of surfaces-Charpit’s method.(Sections 1,2,3, 4,5,6 and 10 of Chapter 2) UNIT – III: Partial Differential Equations of the Second order: The Origin of second order equations –Linear partial differential with constant coefficients-Equations with variable coefficients.(Sections 1,4 and 5 of Chapter 3) UNIT-IV: Laplace’s Equations : Elementary solution of Laplace’s equation-Families of equipotential surfaces-Boundary value problems – Separation of variables.( Sections 2,3,4 and 5 of Chapter 4) Scope and Standard as in “ Elements of Partial Differential Equations” by IAN Sneddon Chapter 1: Section 1 to 6, Chapter 2: Sections 1,2,4,5,6,10 Chapter 3: Sections 1,4,5, chapter 4: Sections 2,3,4,5, Chapter 5: Sec2, Chapter 6: Section 3 and 4. Reference : 1. Ordinary and Partial Differential Equations by M.D. Raisinghania