Differential Calculus & Linear Algebra (1BMATE101)

Differential Calculus & Linear Algebra

Course Code 1BMATE101 
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 04 
Exam Hours 3 Hours
Examination type (SEE) Theory

Module-1: Differential Calculus

Polar curves, angle between the radius vector and the tangent, angle between the polar curves,

Pedal equations. Curvature and radius of curvature in cartesian, polar, parametric and Pedal

forms.

Textbook-1: Chapter- 4.7- 4.11

Module-2: Power series Expansions, 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: Partial derivatives, total derivative, differentiation of composite

functions, Jacobians. Maxima and minima for functions of two variables.

Textbook-1: Chapter- 4.4(1,2,3),4.5(1,2,3), 5.1- 5.11.

Module-3: Ordinary Differential Equations (ODE) of first order and first degree and nonlinear ODE 

Exact and reducible to exact differential equations- Integrating factors on 

 only. Linear and Bernoulli’s differential equations. Orthogonal trajectories, L-R and

C-R circuits.

Non-linear differential equations: Introduction to general and singular solutions, Solvable for p

only, Clairaut’s equations, reducible to Clairaut’s equations.

Textbook-1: Chapter-11.9-11.14- 12.3,12.5.

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, L-C-R circuits.

Textbook-1: Chapter-13.1-13.9, 14.5.

Module-5: Linear Algebra

Elementary transformations of a matrix, Echelon form, rank of a matrix, consistency of system of

linear equations. Gauss elimination and Gauss –Seidel method to solve system of linear

equations. Eigen values and eigen vectors of a matrix, Rayleigh’s power method to determine the

dominant eigen value and corresponding eigen vector of a matrix. Applications: Traffic flow.

Textbook-1: Chapter-2.7-2.13, 28.5,28.6(1),28.7(2),28.9.

Textbook-2: Chapter-7

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,4thEd.,2022.

Reference books / Manuals:

1. B. V. Ramana, HigherEngineeringMathematics, McGraw-HillEducation,11thEd., 2017

2. Srimanta Pal & Subodh C. Bhunia, Engineering Mathematics, Oxford University

Press, 3rd Ed., 2016.

3. N. P. Baliand Manish Goyal, A Textbook of Engineering Mathematics, Laxmi

Publications, 10thEd.,2022.

4. H.K. Das and Er. Rajnish Verma, Higher Engineering Mathematics, S. Chand

Publication, 3rd Ed., 2014.

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