Differential Calculus and Linear Algebra (1BMATM101)

Differential Calculus and Linear Algebra

Course Code 1BMATM101
CIE Marks 50
Teaching Hours/Week (L:T:P: S) 3:2:0:0
SEE Marks 50
Total Hours of Pedagogy 40Hours Theory + 20Hours Tutorials 
Total Marks 100
Credits 4 
Exam Hours 3 
Examination type (SEE) Theory

Module-1: Polar Curves and Curvature 

Polar coordinates, Polar curves, angle between the radius vector and the tangent, angle between two

curves. Pedal equations. Curvature and radius of curvature - Cartesian, parametric, polar and pedal

forms.

Textbook 1: Chapter 4 :4.7-4.11

Module-2: Series Expansion, Indeterminate Forms and Multivariable Calculus

Statement and problems on Taylor’s and Maclaurin’s series expansion for one variable. Indeterminate

forms - L’Hospital’s rule. Partial differentiation, total derivative – differentiation of composite

functions. Jacobian. Maxima and minima for the function of two variables.

Textbook 1: Chapter 4 :4.4,4.5, Chapter 5 :5.1-5.7

Module-3: Ordinary Differential Equations of First Order 

Linear and Bernoulli’s differential equation. Exact and reducible to exact differential equations

with integrating factor: 

Orthogonal trajectories, Law of natural growth and decay.

Textbook 1: Chapter 11:11.9-,11.12(4), Chapter 12:12.3-12.8, Textbook 2: Chapter 8: 8.17, 8.18

Module-4: Linear Algebra -1

Elementary row transformation of a matrix, Row echelon form and Rank of a matrix. Inverse of matrix

by Jordan method. Consistency and Solution of system of linear equations - Gauss- elimination

method, LU decomposition method and approximate solution by Gauss-Seidel method. Application to

traffic flow.

Textbook 1: Chapter 2 :2.7,2.10, Chapter 28 :28.6(1,2,3), 28.7(2)

Textbook 3: Chapter 7

Module-5: Linear Algebra -2

Eigenvalues and Eigenvectors, Rayleigh’s power method to find the dominant Eigenvalue and

Eigenvector. Model matrix, Diagonalization of the matrix, inverse of a matrix by Cayley-Hamilton

theorem, Characteristic and minimal polynomials of block matrices, Moore-Penrose pseudoinverse.

Textbook 3: Chapter 4: 4.0, Chapter 8 :8.1, Chapter 20: 20.8,

Textbook 1: Chapter 2:2.16(1),2.15, Chapter 28 :28.7(1)

Suggested Learning Resources: 

Textbooks:

1. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers,44ndEd., 2021.

2. Seymour Lipschutz and Marc Lipson, Linear Algebra, Schaum’s outlines series, 4th Ed., 2008.

3. E.Kreyszig, Advanced Engineering Mathematics, JohnWiley & Sons,10thEd.,2018.

4. Gilbert Strang, Linear Algebra and its Applications, Cengage Publications,4thEd.,2022.

Reference books:

1. Srimanta Pal & Subodh C.Bhunia, Engineering Mathematics, Oxford University Press, 3rd

Ed., 2016.

2. N. P.Bali and Manish Goyal, AText book of Engineering Mathematics, Laxmi

Publications,10thEd.,2022.

3. H.K.Dass and Er.RajnishVerma, Higher Engineering Mathematics,S.Chand Publication, 3rd

Ed., 2014.

4. Ray Wylie,Louis C.Barrett, Advanced Engineering Mathematics, McGrawHill Book Co.,

New York, 6th Ed., 2017.

5. David C Lay, Linear Algebra and its Applications, Pearson Publishers, 4thEd., 2018.

7. Gareth Williams, Linear Algebra with Applications”Jones Bartlett Publishers Inc.,6th Ed.,

2017.