Engineering Mathematics-I (BSC-101)
Program: B.Tech Computer Science and Engineering (Artificial Intelligence and Machine Learning)
Category: Basic Science Course
Semester: 1
Credits: 5
L-T-P: 4- 1- 0
Description
Instructor

Dr. Ashish Kumar

Assistant Professor
Department Of Applied Sciences
Course Outcomes
  • Apply the knowledge of calculus to plot graphs of functions and solve the problem of maxima and minima.
  • Determine the convergence/divergence of infinite series, approximation of functions using power and Taylor’s series expansion and error estimation.
  • Apply the concept of definite integrals to calculate area under the curves.
  • Understand and apply the concepts of matrices.
  • Demonstrate knowledge of vector space by solving associated problems.
Evaluation Scheme
MST 10
MST 10
Assignment 20
Attendance 10
Total Internal 50
Total External 100
Overall Total 150
Course Materials

Unit 1

Differential Calculus -I
Applications of Euler’s Theorem
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Asymptotes – Concept and Classification
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Curvature and Radius of Curvature
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Curve Tracing – Cartesian Form
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Curve Tracing – Polar Form
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Double Points – Types and Identification
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Euler’s Theorem on Homogeneous Functions
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Introduction to Differential Calculus – I
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Leibnitz’s Theorem (statement and usage)
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Partial Derivatives – Basics
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Unit 2

Differential Calculus -I
Curve Tracing – Parametric Form
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Differential Calculus -II
Expansion of Two-variable Functions
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Indeterminate Forms – L'Hospital Rule
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Maclaurin’s Series (with remainder)
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Maxima & Minima (Two Variables)
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Mean Value Theorem (Lagrange and Cauchy)
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Rolle’s Theorem
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Second Derivative Test
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Taylor Series for Two Variables – Introduction
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Taylor’s Series (Single Variable)
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Unit 3

Differential Calculus -II
Applications of Lagrange’s Multipliers
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Lagrange’s Method of Multipliers – Concept
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Integral Calculus
Applications: Area under Curves
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Applications: Length of Curves
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Beta Function – Relation to Gamma
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Differentiation Under Integral Sign (Leibnitz Rule)
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Double & Triple Integrals – Simple Problems
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Error Function – Basic Concepts
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Gamma Function – Definition and Simple Problems
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Properties of Definite Integrals
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Transformation of Coordinates
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Volume and Surface Area of Revolution
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Matrices
Linear System of Equations
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Matrix Basics: Types, Notation
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Matrix Multiplication Rules
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Vector Addition and Scalar Multiplication
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Unit 4

Matrices
Consistent and Inconsistent system of equations
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Cramer’s Rule – Applications
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Determinants – Properties
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Gauss Elimination Method
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Gauss-Jordan Elimination
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Homogeneous system of equations
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Inverse of Matrix using Adjoint Method
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Linear Independence of Vectors
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Rank of a Matrix – Row Echelon Form
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Special Matrices: Diagonal, Triangular
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System Solving using Matrix Inversion
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Vector Space
Basis and Dimension of a Vector Space
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Linear Dependence and Independence
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Linear Transformations: Basics
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Vector Space: Definition, Examples
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Unit 5

Vector Space
Composition of Linear Transformations
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Eigenvalues and Eigenvectors
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Inverse of a Linear Transformation
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Range and Kernel of Linear Maps
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Rank and Nullity; Rank-Nullity Theorem
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Symmetric, Skew-Symmetric, Orthogonal Matrices, Eigenbases
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