மனனோன்மணியம் சுந் தரனோர் பல் கலலக் கழகம்
MANONMANIAM SUNDARANAR UNIVERSITY
TIRUNELVELI-627 012
த ொலைநிலைத ொடர் கல் வி இயக்ககம்
DIRECTORATE OF DISTANCE AND
CONTINUING EDUCATION
B.Sc. (Allied Mathematics)
I YEAR
ALGEBRA AND DIFFERENTIAL EQUATIONS
Sub. Code: JEMA11 (For Private Circulation only)
, B.Sc. (Allied Mathematics) –I YEAR
JEMA11 - ALGEBRA AND DIFFERENTIAL EQUATIONS
SYLLABUS
Unit-I:
Theory of Equations – Formation of Equations – Relation between
roots and coefficients – Reciprocal equations.
Unit-II:
Transformation of Equations – Approximate solutions to equations
– Newton’s method and Horner’s method.
Unit-III:
Matrices – Characteristic equation of a matrix – Eigen values and Eigen
vectors – Cayley Hamilton theorem and simple problems.
Unit-IV:
Differential equation of first order but of higher degree – Equations
solvable for 𝑝, 𝑥, 𝑦 – Partial differential equations – formations – solutions –
Standard form 𝑃𝑝 + 𝑄𝑞 = 𝑅.
Unit-V:
Laplace transformation – Inverse Laplace transform.
Recommended Text:
1. Dr.S. Arumugam & Isaac – Allied Mathematics Paper – I, New
Gamma Publishing House (2012), Palayamkottai.
1
Manonmaniam Sundaranar University, Directorate of Distance & Continuing Education, Tirunelveli.
, 2
Manonmaniam Sundaranar University, Directorate of Distance & Continuing Education, Tirunelveli.
, JEMA11 - ALGEBRA AND DIFFERENTIAL EQUATIONS
CONTENTS
UNIT-1
1.1 Theory of Equations 5
1.2 Formation of Equations 5
1.3 Relation between roots and coefficients 9
1.4 Reciprocal equations 16
UNIT-2
2.1 Transformation of Equations 23
2.2 Approximate solutions to equations 27
2.3 Newton’s method 27
2.4 Horner’s method 33
UNIT-3
3.1 Matrices 35
3.2 Characteristic equation of a matrix 37
3.3 Cayley Hamilton theorem and simple problems 40
3.4 Eigenvalues and Eigen vectors 45
UNIT-4
4.1 Differential equation of first order but of higher degree 47
4.2 Differential Equations which are solvable for 𝑝 47
4.3 Differential Equations which are solvable for 𝑦 50
4.4 Differential Equations which are solvable for 𝑥 52
4.5 Partial differential equations 55
3
Manonmaniam Sundaranar University, Directorate of Distance & Continuing Education, Tirunelveli.
MANONMANIAM SUNDARANAR UNIVERSITY
TIRUNELVELI-627 012
த ொலைநிலைத ொடர் கல் வி இயக்ககம்
DIRECTORATE OF DISTANCE AND
CONTINUING EDUCATION
B.Sc. (Allied Mathematics)
I YEAR
ALGEBRA AND DIFFERENTIAL EQUATIONS
Sub. Code: JEMA11 (For Private Circulation only)
, B.Sc. (Allied Mathematics) –I YEAR
JEMA11 - ALGEBRA AND DIFFERENTIAL EQUATIONS
SYLLABUS
Unit-I:
Theory of Equations – Formation of Equations – Relation between
roots and coefficients – Reciprocal equations.
Unit-II:
Transformation of Equations – Approximate solutions to equations
– Newton’s method and Horner’s method.
Unit-III:
Matrices – Characteristic equation of a matrix – Eigen values and Eigen
vectors – Cayley Hamilton theorem and simple problems.
Unit-IV:
Differential equation of first order but of higher degree – Equations
solvable for 𝑝, 𝑥, 𝑦 – Partial differential equations – formations – solutions –
Standard form 𝑃𝑝 + 𝑄𝑞 = 𝑅.
Unit-V:
Laplace transformation – Inverse Laplace transform.
Recommended Text:
1. Dr.S. Arumugam & Isaac – Allied Mathematics Paper – I, New
Gamma Publishing House (2012), Palayamkottai.
1
Manonmaniam Sundaranar University, Directorate of Distance & Continuing Education, Tirunelveli.
, 2
Manonmaniam Sundaranar University, Directorate of Distance & Continuing Education, Tirunelveli.
, JEMA11 - ALGEBRA AND DIFFERENTIAL EQUATIONS
CONTENTS
UNIT-1
1.1 Theory of Equations 5
1.2 Formation of Equations 5
1.3 Relation between roots and coefficients 9
1.4 Reciprocal equations 16
UNIT-2
2.1 Transformation of Equations 23
2.2 Approximate solutions to equations 27
2.3 Newton’s method 27
2.4 Horner’s method 33
UNIT-3
3.1 Matrices 35
3.2 Characteristic equation of a matrix 37
3.3 Cayley Hamilton theorem and simple problems 40
3.4 Eigenvalues and Eigen vectors 45
UNIT-4
4.1 Differential equation of first order but of higher degree 47
4.2 Differential Equations which are solvable for 𝑝 47
4.3 Differential Equations which are solvable for 𝑦 50
4.4 Differential Equations which are solvable for 𝑥 52
4.5 Partial differential equations 55
3
Manonmaniam Sundaranar University, Directorate of Distance & Continuing Education, Tirunelveli.
