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Ordinary Differential Equations
Course Code:
MAT4300104MJ
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Unit: 1
First Order Ordinary Differential Equations
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➔
Unit: 2
Second Order Linear Differential Equations
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➔
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Notice / ঘোষণা
প্ৰিয় ছাত্ৰ-ছাত্ৰীসকল,
সম্পূৰ্ণ অধ্যায়ভিত্তিক Notes বোৰ অতি শীঘ্ৰেই এই ৱেবছাইটত আপডেট কৰা হ’ব। অনুগ্ৰহ কৰি অলপ অপেক্ষা কৰক।
Ordinary Differential Equations
Course Code:
MAT4300104MJ
Click on the topics below to view the questions and answers for this paper:
Unit: 1
First Order Ordinary Differential Equations
View Notes
➔
Unit: 2
Second Order Linear Differential Equations
View Notes
➔
Previous Year Question Papers
Download past question papers to test your preparation
⏳
Notice / ঘোষণা
প্ৰিয় ছাত্ৰ-ছাত্ৰীসকল,
সম্পূৰ্ণ অধ্যায়ভিত্তিক Notes বোৰ অতি শীঘ্ৰেই এই ৱেবছাইটত আপডেট কৰা হ’ব। অনুগ্ৰহ কৰি অলপ অপেক্ষা কৰক।
Ordinary Differential Equations Paper Solution 2025
✨ FYUGP Verified Study Material
Ordinary Differential Equations Paper Solution 2025
✨ FYUGP Verified Study Material
Abstract Algebra
Course Code:
MAT4300204MJ
Click on the topics below to view the questions and answers for this paper:
Unit: 1
Definition and examples of groups
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➔
Unit: 2
Permutations, Permutation group
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➔
Unit: 3
Isomorphism of groups
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➔
Unit: 4
Rings, Examples of rings, Properties of rings
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➔
Previous Year Question Papers
Download past question papers to test your preparation
Abstract Algebra
Course Code:
MAT4300204MJ
Click on the topics below to view the questions and answers for this paper:
Unit: 1
Definition and examples of groups
View Notes
➔
Unit: 2
Permutations, Permutation group
View Notes
➔
Unit: 3
Isomorphism of groups
View Notes
➔
Unit: 4
Rings, Examples of rings, Properties of rings
View Notes
➔
Previous Year Question Papers
Download past question papers to test your preparation
Ordinary Differential Equations
SEMESTER-III
Course Code: MAT4300104MJ
Scheme of Evaluation
Total Marks: 100 (External 60, Internal Assessment 40)
Course Content
UNIT 1: First Order Ordinary Differential Equations
30 Marks | 30 Classes
Classification of differential equations; their origin and application. Solutions. First order exact differential equation. Integrating factors, Rules to find an integrating factor.
[1] Chapter 1 (Sections 1.1 and 1.2) Chapter 2 (Sections 2.1, 2.2 and 2.4)
Linear equations and Bernoulli equations. Basic theory of higher order linear differential equations. Solving differential equation by reducing its order. Wronskian and its properties.
[1] Chapter 2 (Section 2.3), Chapter 4 (Sections 4.1 and 4.6)
UNIT 2: Second Order Linear Differential Equations
30 Marks | 30 Classes
Linear homogenous equations with constant coefficients. Linear non- homogenous equations; the method of undetermined coefficients, the method of Variation of Parameters. The Cauchy-Euler equations.
[1] Chapter 4 (Sections 4.2, 4.3, 4.4 and 4.5)
Text Book
- Ross, Shepley L. (1984). Differential Equations (3rd Ed.), John Wiley & Sons, Inc.
Reference Book
- Kreyszig, Erwin (2011). Advanced Engineering Mathematics (10th ed.). John Wiley & Sons, Inc. Wiley India Edition 2015.
Ordinary Differential Equations
SEMESTER-III
Course Code: MAT4300104MJ
Scheme of Evaluation
Total Marks: 100 (External 60, Internal Assessment 40)
Course Content
UNIT 1: First Order Ordinary Differential Equations
30 Marks | 30 Classes
Classification of differential equations; their origin and application. Solutions. First order exact differential equation. Integrating factors, Rules to find an integrating factor.
[1] Chapter 1 (Sections 1.1 and 1.2) Chapter 2 (Sections 2.1, 2.2 and 2.4)
Linear equations and Bernoulli equations. Basic theory of higher order linear differential equations. Solving differential equation by reducing its order. Wronskian and its properties.
[1] Chapter 2 (Section 2.3), Chapter 4 (Sections 4.1 and 4.6)
UNIT 2: Second Order Linear Differential Equations
30 Marks | 30 Classes
Linear homogenous equations with constant coefficients. Linear non- homogenous equations; the method of undetermined coefficients, the method of Variation of Parameters. The Cauchy-Euler equations.
[1] Chapter 4 (Sections 4.2, 4.3, 4.4 and 4.5)
Text Book
- Ross, Shepley L. (1984). Differential Equations (3rd Ed.), John Wiley & Sons, Inc.
Reference Book
- Kreyszig, Erwin (2011). Advanced Engineering Mathematics (10th ed.). John Wiley & Sons, Inc. Wiley India Edition 2015.
Abstract Algebra
Course Code: MAT4300204MJ
Scheme of Evaluation
Total Marks: 100 (External 60, Internal Assessment 40)
Course Content
Unit 1: Groups & Subgroups
15 Marks | 15 Classes
Definition and examples of groups, Elementary properties of groups, Symmetries of a square, Dihedral groups, order of a group, Order of an element in a group, Subgroups, Subgroup Tests, Subgroup generated by an element of a group, Centre of a group, Centralizer of an element in a group, Cyclic groups, Properties of cyclic groups, Fundamental theorem of cyclic groups.
[1] Chapter 1 to Chapter 4.
Unit 2: Permutations, Cosets & Lagrange's Theorem
15 Marks | 15 Classes
Permutations, Permutation group, Properties of permutations, Even and odd permutations, Alternating groups, Cosets, Properties of cosets, Lagrange’s Theorem, Fermat’s Little Theorem, Normal subgroups, Factor groups.
[1] Chapter 5 (up to theorem 5.7), Chapter 7 (up to theorem 7.2), Chapter 9 (up to theorem 9.2)
Unit 3: Homomorphisms & Isomorphisms
15 Marks | 15 Classes
Isomorphism of groups, Cayley’s Theorem, Properties of isomorphism, Group homomorphism, Kernal of a group homomorphism, Properties of group homomorphism, First isomorphism Theorem of groups.
[1] Chapter 6 (up to theorem 6.3), Chapter 10 (up to theorem 10.4).
Unit 4: Rings, Ideals & Fields
15 Marks | 15 Classes
Rings, Examples of rings, Properties of rings, Subrings, Zero-Divisors in a ring, Integral domains, Fields, Characteristic of a ring, Ideals, Ideal Test, Factor rings, Prime ideals and maximal ideals of a ring.
[1] Chapter 12 to Chapter 14.
Text Books
-
Gallian Joseph A., Contemporary Abstract Algebra (8th Edition), Cengage Learning India Private limited, Delhi, Fourth impression, 2015.
Online link: https://ict.iitk.ac.in/wp-content/uploads/CS203-Mathematics-for-Computer-Science-III-Gallian.pdf
Reference Books
- David S. Dummit and Richard M. Foote, Abstract Algebra (2nd Edition), John Wiley and Sons (Asia) Pvt. Ltd., Singapore, 2003.
- John B. Fraleigh, A First course in Abstract Algebra, 7th Edition, Pearson, 2002.
- G. Santhanam. Algebra, Narosa Publishing House, 2017.
Abstract Algebra
Course Code: MAT4300204MJ
Scheme of Evaluation
Total Marks: 100 (External 60, Internal Assessment 40)
Course Content
Unit 1: Groups & Subgroups
15 Marks | 15 Classes
Definition and examples of groups, Elementary properties of groups, Symmetries of a square, Dihedral groups, order of a group, Order of an element in a group, Subgroups, Subgroup Tests, Subgroup generated by an element of a group, Centre of a group, Centralizer of an element in a group, Cyclic groups, Properties of cyclic groups, Fundamental theorem of cyclic groups.
[1] Chapter 1 to Chapter 4.
Unit 2: Permutations, Cosets & Lagrange's Theorem
15 Marks | 15 Classes
Permutations, Permutation group, Properties of permutations, Even and odd permutations, Alternating groups, Cosets, Properties of cosets, Lagrange’s Theorem, Fermat’s Little Theorem, Normal subgroups, Factor groups.
[1] Chapter 5 (up to theorem 5.7), Chapter 7 (up to theorem 7.2), Chapter 9 (up to theorem 9.2)
Unit 3: Homomorphisms & Isomorphisms
15 Marks | 15 Classes
Isomorphism of groups, Cayley’s Theorem, Properties of isomorphism, Group homomorphism, Kernal of a group homomorphism, Properties of group homomorphism, First isomorphism Theorem of groups.
[1] Chapter 6 (up to theorem 6.3), Chapter 10 (up to theorem 10.4).
Unit 4: Rings, Ideals & Fields
15 Marks | 15 Classes
Rings, Examples of rings, Properties of rings, Subrings, Zero-Divisors in a ring, Integral domains, Fields, Characteristic of a ring, Ideals, Ideal Test, Factor rings, Prime ideals and maximal ideals of a ring.
[1] Chapter 12 to Chapter 14.
Text Books
-
Gallian Joseph A., Contemporary Abstract Algebra (8th Edition), Cengage Learning India Private limited, Delhi, Fourth impression, 2015.
Online link: https://ict.iitk.ac.in/wp-content/uploads/CS203-Mathematics-for-Computer-Science-III-Gallian.pdf
Reference Books
- David S. Dummit and Richard M. Foote, Abstract Algebra (2nd Edition), John Wiley and Sons (Asia) Pvt. Ltd., Singapore, 2003.
- John B. Fraleigh, A First course in Abstract Algebra, 7th Edition, Pearson, 2002.
- G. Santhanam. Algebra, Narosa Publishing House, 2017.
Computer Algebra Systems and Related Software
SEMESTER-III
Course Code: SEC0316303
Scheme of Evaluation
Total Marks: 75 (Theory 30, Practical 25, Internal-20)
Course Content
Unit 1: Introduction to CAS and Applications
15 Classes
Computer Algebra System (CAS), Use of a CAS as a calculator, Computing and plotting functions in 2D, plotting functions of two variables using Plot 3 D and Contour Plot, plotting para metric curves surfaces, customizing plots, animating plots, producing tables of values, working with piecewise defined functions, Combining graphics.
[1] Chapter 12 (Sections 12.1 to 12.5)
[2] Chapter1, and Chapter 3 (Sections 3.1to 3.6, and 3.8) Chapter 6(Sections 6.2 and 6.3)
[2] Chapter1, and Chapter 3 (Sections 3.1to 3.6, and 3.8) Chapter 6(Sections 6.2 and 6.3)
Unit 2: Working with Matrices
15 Classes
Simple programming in a CAS, working with matrices, addition, subtraction, multiplication of matrices, Minors and cofactors, working with 3x3 matrices, Solving system of linear equations of three variables.
[2] Chapter7(Sections7.1to7.8)
Practical
Practical Exercises
15 Classes
Six practicals should be done by each student. The teacher can assign practical from the exercises from [1,2].
Text Book
- Bindner, Donald & Erickson, Martin. (2011). A Student’s Guide to the Study, Practice, and Tools of Modern Mathematics. CRC Press, Taylor & Francis Group, LLC.
- Torrence, Bruce F., & Torrence, Eve A. (2009). The Student’s Introduction to Mathematica: A Handbook for Precalculus, Calculus and Linear Algebra (2nd ed.). Cambridge University Press
Computer Algebra Systems and Related Software
SEMESTER-III
Course Code: SEC0316303
Scheme of Evaluation
Total Marks: 75 (Theory 30, Practical 25, Internal-20)
Course Content
Unit 1: Introduction to CAS and Applications
15 Classes
Computer Algebra System (CAS), Use of a CAS as a calculator, Computing and plotting functions in 2D, plotting functions of two variables using Plot 3 D and Contour Plot, plotting para metric curves surfaces, customizing plots, animating plots, producing tables of values, working with piecewise defined functions, Combining graphics.
[1] Chapter 12 (Sections 12.1 to 12.5)
[2] Chapter1, and Chapter 3 (Sections 3.1to 3.6, and 3.8) Chapter 6(Sections 6.2 and 6.3)
[2] Chapter1, and Chapter 3 (Sections 3.1to 3.6, and 3.8) Chapter 6(Sections 6.2 and 6.3)
Unit 2: Working with Matrices
15 Classes
Simple programming in a CAS, working with matrices, addition, subtraction, multiplication of matrices, Minors and cofactors, working with 3x3 matrices, Solving system of linear equations of three variables.
[2] Chapter7(Sections7.1to7.8)
Practical
Practical Exercises
15 Classes
Six practicals should be done by each student. The teacher can assign practical from the exercises from [1,2].
Text Book
- Bindner, Donald & Erickson, Martin. (2011). A Student’s Guide to the Study, Practice, and Tools of Modern Mathematics. CRC Press, Taylor & Francis Group, LLC.
- Torrence, Bruce F., & Torrence, Eve A. (2009). The Student’s Introduction to Mathematica: A Handbook for Precalculus, Calculus and Linear Algebra (2nd ed.). Cambridge University Press