Engineering Mathematics -II
10 MAT 21
Dr. V. Lokesha
2012
Engineering Mathematics – II
(10 MAT21)
LECTURE NOTES
(FOR II SEMESTER B E OF VTU)
VTU-EDUSAT Programme-16
Dr. V. Lokesha
Professor of Mathematics
DEPARTMENT OF MATHEMATICS
ACHARYA INSTITUTE OF TECNOLOGY
Soldevanahalli, Bangalore – 90
Partial Differential Equation
1
10 MAT 21
Dr. V. Lokesha
2012
ENGNEERING MATHEMATICS – II Content
CHAPTER
UNIT IV
PARTIAL DIFFERENTIAL EQUATIONS
Partial Differential Equation
2
10 MAT 21
Dr. V. Lokesha
2012
Unit‐IV
PARTIAL DIFFERENTIAL EQUATIONS
Overview:
In this unit we study how to form a P.D.E and various methods of obtaining solutions of P.D.E. This unit consists of 6 sections. In section 1, we learn how to form the P.D.E. by eliminating arbitrary constants and in section 2 we learn the formation of P.D.E by eliminating arbitrary functions. In section 3, the solution of non homogeneous P.D.E by the method of direct integration is discussed. In section 4, the solution of homogeneous equations is discussed. In section 5 we learn the method of separation of variables to solve homogeneous equations. In section 6 we discuss the Lagrange’s linear equation and the solution by the method of grouping and multipliers, at end some muliple choice questions prominence the comprehensive unit.
Objective:
At the finish of this unit, we will be able to:
•
•
•
•
Form Partial differential equation.
Solve the first order linear partial differential equation
Obtain the solution of homogeneous P.D.E by different methods.
Obtain the solution of non homogeneous P.D.E
Partial Differential Equation
3
10 MAT 21
Dr. V. Lokesha
2012
Section 1:
Formation of P.D.E by eliminating arbitrary constants
Objective:
At the closing stages of this Section, we
Dr. V. Lokesha
2012
Engineering Mathematics – II
(10 MAT21)
LECTURE NOTES
(FOR II SEMESTER B E OF VTU)
VTU-EDUSAT Programme-16
Dr. V. Lokesha
Professor of Mathematics
DEPARTMENT OF MATHEMATICS
ACHARYA INSTITUTE OF TECNOLOGY
Soldevanahalli, Bangalore – 90
Partial Differential Equation
1
10 MAT 21
Dr. V. Lokesha
2012
ENGNEERING MATHEMATICS – II Content
CHAPTER
UNIT IV
PARTIAL DIFFERENTIAL EQUATIONS
Partial Differential Equation
2
10 MAT 21
Dr. V. Lokesha
2012
Unit‐IV
PARTIAL DIFFERENTIAL EQUATIONS
Overview:
In this unit we study how to form a P.D.E and various methods of obtaining solutions of P.D.E. This unit consists of 6 sections. In section 1, we learn how to form the P.D.E. by eliminating arbitrary constants and in section 2 we learn the formation of P.D.E by eliminating arbitrary functions. In section 3, the solution of non homogeneous P.D.E by the method of direct integration is discussed. In section 4, the solution of homogeneous equations is discussed. In section 5 we learn the method of separation of variables to solve homogeneous equations. In section 6 we discuss the Lagrange’s linear equation and the solution by the method of grouping and multipliers, at end some muliple choice questions prominence the comprehensive unit.
Objective:
At the finish of this unit, we will be able to:
•
•
•
•
Form Partial differential equation.
Solve the first order linear partial differential equation
Obtain the solution of homogeneous P.D.E by different methods.
Obtain the solution of non homogeneous P.D.E
Partial Differential Equation
3
10 MAT 21
Dr. V. Lokesha
2012
Section 1:
Formation of P.D.E by eliminating arbitrary constants
Objective:
At the closing stages of this Section, we