BS 111 is a 4-credit course on Applied Mathematics I taught in the first semester. The course covers topics including partial differentiation, differential calculus, linear algebra, and vector calculus. The syllabus outlines 4 units that will be covered over the semester, including partial derivatives, ordinary differential equations, linear algebra concepts, and vector calculus topics. The course is taught by Ms. Bharti Seth who has over 13 years of teaching experience and is pursuing her PhD. Evaluation will include assignments, tests, and an exam.

2. BS 111: APPLIED MATHEMATICS I
Faculty: Ms Bharti Seth
Semester: I
Credits: 4 (4-0-0)
BTech AI & ML

3. Faculty Coordinator: Ms. BHARTI SETH
• Teaching and Research Experience
• 13 years (Aug 2009 onwards)
• Pursuing PhD (2017 onwards) from Indira Gandhi Delhi Technical University
for Women, Delhi
• Educational Qualifications
• Qualified the CSIR-UGC NET(JRF) exam in Dec 2008
• (2007-2009) MSc Maths from IIT Delhi
• (2004-2007) BSc Maths Honours from Sri Venkateswara College, Univ. of Delhi

4. Partial Differentiation
Differential Calculus
Linear Algebra
Vector Calculus
Contents

5. Syllabus
• Unit I
Partial derivatives, Chain rule, Differentiation of Implicit functions, Exact
differentials. Maxima, Minima and saddle points, Method of Lagrange multipliers.
Differentiation under Integral sign, Jacobians and transformations of coordinates.
[8 Hrs]
• Unit II
Ordinary Differential Equations (ODEs): Basic Concepts. Geometric Meaning of y’=
ƒ(x, y). Direction Fields, Euler’s Method, Separable ODEs. Exact ODEs. Integrating
Factors, Linear ODEs. Bernoulli Equation. Population Dynamics, Orthogonal
Trajectories. Homogeneous Linear ODEs with Constant Coefficients. Differential
Operators. Modeling of Free Oscillations of a Mass–Spring System, Euler–Cauchy
Equations. Wronskian, Non-homogeneous ODEs, Solution by Variation of Parameters.
Power Series Method for solution of ODEs: Legendre’s Equation. Legendre
Polynomials, Bessel’s Equation, Bessel's functions Jn(x) and Yn(x). Gamma Function
[12 Hrs]

6. Syllabus
• Unit III
Linear Algebra: Matrices and Determinants, Gauss Elimination, Linear Independence. Rank of
a Matrix. Vector Space. Solutions of Linear Systems and concept of Existence, Uniqueness,
Determinants. Cramer’s Rule, Gauss–Jordan Elimination. The Matrix Eigen-value Problem.
Determining Eigen-values and Eigen-vectors, Symmetric, Skew-Symmetric, and Orthogonal
Matrices. Eigen-bases. Diagonalization. Quadratic Forms. Cayley – Hamilton Theorem
(without proof)
[10 Hrs]
• Unit IV
Vector Calculus: Vector and Scalar Functions and Their Fields. Derivatives, Curves. Arc
Length. Curvature. Torsion, Gradient of a Scalar Field. Directional Derivative, Divergence of a
Vector Field, Curl of a Vector Field, Line Integrals, Path Independence of Line Integrals,
Double Integrals, Green’s Theorem in the Plane, Surfaces for Surface Integrals, Surface
Integrals, Triple Integrals, Stokes Theorem. Divergence Theorem of Gauss.
[10 Hrs]

7. Textbooks and Reference Books

8. Evaluation Scheme

9. Introduction to Partial Derivatives
First Derivative of y=f(x) For two variable function z=f(x,y)
• How to calculate the derivative of z?
• For example if z=x+y
• Two independent variables
• We differentiate partially with respect
to each of the independent variable
• Partial differentiation is the process of
finding partial derivatives.

10. Unit I Partial Differentiation
• A partial derivative of a function of several variables is the ordinary
derivative with respect to one of the variables when all the remaining
variables are held constant.
• Partial differentiation is the process of finding partial derivatives.
• All the rules of differentiation applicable to function of a single
independent variable are also applicable in partial differentiation with
the only difference that while differentiating (partially) with respect to
one variable, all the other variables are treated (temporarily) as
constants

11. Unit I Partial Differentiation

12. Unit I Partial Differentiation

13. Geometrical Interpretation
https://www.geogebra.org/m/uc5avdac

14. Useful Links
• Assignment Sheets Folder Link
https://drive.google.com/drive/folders/1gbMSRbD7oHsgdGK2PYXTo_u
wB9_lwGkj?usp=sharing
• PPT Folder Link
https://drive.google.com/drive/folders/1FfSTTXtpN-
HR3vC_PqFfHhAYVMcMovgm?usp=sharing