CALCULUS AND LINEAR ALGEBRA (1BMATS101)

CALCULUS AND LINEAR ALGEBRA

Course Code 1BMATS101 
CIE Marks 50
Teaching Hours/Week (L:T:P: S) 3:2:0:0 
SEE Marks 50
Total Hours of Pedagogy 40Hours Theory + 20Hours Tutorial 
Total Marks 100
Credits 4 
Exam Hours 3 hrs
Examination type (SEE) Theory

Module-1: Calculus

Partial differentiation, total derivative, differentiation of composite functions, Jacobian,

Statement of Taylor’s and Maclaurin’s series expansion for two variables. Maxima and

minima for the function of two variables.

Textbook-1: Chapter 5: Sections 5.1- 5.11

Module-2: Vector Calculus 

Scalar and vector fields, Gradient, directional derivatives, divergence and curl - physical

interpretation, solenoidal vector fields, irrotational vector fields and scalar potential.

Introduction to polar coordinates and polar curves.

Curvilinear coordinates: Scale factors, base vectors, Cylindrical polar coordinates, Spherical

polar coordinates, transformation between cartesian and curvilinear systems, orthogonality.

Module-3: System of Linear Equations, Eigenvalues and Eigenvectors

Elementary row transformation of a matrix, Echelon form, rank of a matrix. Consistency and

solution of system of linear equations: Gauss elimination method, Gauss Jordan method.

Applications: Traffic flow.

Eigenvalues and Eigenvectors, diagonalization of the matrix, modal matrix.

Textbook-1: Chapter 2: Sections 2.7-2.16, Chapter 28: Sections 28.6 and 28.7

Textbook-2: Chapter-7

Module-4: Vector Space

Vector spaces: definition and examples, subspace: definition and examples. Linear

Combinations, linear span, linearly independent and dependent sets, basis and dimension, row

space and column space of a matrix, Coordinates vector, inner products and orthogonality.

Textbook-3: Chapter 4: Sections 4.1 to 4.9 and 4.11

Module-5: Linear Transformation 

Definition and examples, algebra of linear transformations, matrix of a linear transformation.

Singular, non-singular linear transformations and invertible linear transformations. Rank and nullity

of linear transformations, Rank-Nullity theorem.

Textbook-3: Chapter 5: Sections 5.3- 5.7 Chapter 6: Sections-6.1-6.2

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

Reference books:

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

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

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

10th Ed., 2022.

4. James Stewart, Calculus, Cengage Publications, 7thEd., 2019.

5. David Poole, Linear Algebra, a modern introduction, Cengage publishers, 4th Ed., 2014.

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

7. Gareth Williams, Linear Algebra with applications, Jones Bartlett Publishers Inc., 6th Ed., 2017.