Engineering Mathematics-I (BSC-101)
Program: B.Tech Computer Science Engineering
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_1 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
Updated on: 2026-05-05
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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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