Differential Calculus and Linear Algebra (1BMATC101)

Differential Calculus and Linear Algebra

Course Code 1BMATC101 
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 Hours
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- 4.7-4.11

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- 4.4-5.11

Module-3: Ordinary Differential Equations of First Order

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

with integrating factors 

Orthogonal trajectories, Law of natural growth and decay.

Textbook-1: Chapter- 11.9-11.12

Module-4: Ordinary Differential Equations of Higher Order

Higher-order linear ordinary differential equations with constant coefficients, homogeneous and

non-homogeneous equations (eax, sin(ax+b), cos(ax+b), xn only), Method of variation of

parameters, Cauchy’s and Legendre’s homogeneous differential equations. Applications: Solving

governing differential equations of Mass Spring.

Textbook-1: Chapter-13.1-13.8

Module-5: Linear Algebra

Elementary row transformation of a matrix, Rank of a matrix. Consistency and Solution of system

of linear equations - Gauss-elimination method and approximate solution by Gauss-Seidel method.

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

Eigenvector. Applications: Traffic flow.

Textbook-1: Chapter-2.7-2.13, 28.6-28.9

Suggested Learning Resources: 

Textbooks:

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

2. E. Kreyszig, Advanced Engineering Mathematics, John Wiley & Sons, 10th Ed., 2018.

3. Gilbert Strang, Linear Algebra and its Applications, Cengage Publications, 4th Ed., 2022.

Reference books:

1. B.V. Ramana, Higher Engineering Mathematics, McGraw-Hill Education, 11th Ed., 2017

2. Srimanta Pal & Subodh C.Bhunia, Engineering Mathematics, Oxford University Press, 3rd Ed., 2016.

3. N. P. Bali and Manish Goyal, A Textbook of Engineering Mathematics, Laxmi Publications, 10th Ed.,

2022.

4. H. K. Dass and Er. Rajnish Verma, Higher Engineering Mathematics, S. Chand Publication, 3rd

Ed., 2014.

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