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I am teaching the following courses for UG/PG programs at Crescent Institute of Science and Technology.
I am teaching the following courses for UG/PG programs at Crescent Institute of Science and Technology.
If you have any specific questions about course topics, feel free to message me at
If you have any specific questions about course topics, feel free to message me at
ravinder.maths@crescent.education
ravinder.maths@crescent.education
so that I can respond as soon as possible.
so that I can respond as soon as possible.
MAE 1283 - Probability & Statistical Data Analysis
MAE 1283 - Probability & Statistical Data Analysis
Semester: Even
Semester: Even
Offered: B.Tech
Offered: B.Tech
Course Learning Objectives:
To introduce the fundamental principles of probability and the concept of
random variables.
To understand various discrete and continuous probability distributions and their
real-world applications.
To evaluate bi-variate dependencies and transformations in computational problems.
To introduce the concept of hypothesis testing, including the formulation of null
and alternative hypotheses.
To design the experiment for various types of data.
Syllabus : MAE 1283 - Probability & Statistical Data Analysis
Text Books : 1) Fundamentals of Mathematical Statistics - S.C.Gupta & V.K.Kapoor
2) Probability and Statistics for Engineers - Miller & Freund's
Module-1 : Probability & Random Variables
1.1 Lecture Notes - 01 : Basic Probability Concepts
1.2 Lecture Notes - 02 : Random Variables and Distributions
Module-2 : Probability Distributions
2.1 Lecture Notes - 01 : Standard Discrete Probability Distributions
2.2 Lecture Notes - 02 : Standard Continuous Probability Distributions
Module-3 : Two Dimensional Random Variables
3.1 Lecture Notes
Module-4 : Sampling & Theory of Inference
Module-5 : Design of Experiment
Assignments : Assignment-01 (Feb 2026) : Problem Set-01 Solutions
Assignment-02 (Feb 2026) : MCQ Test-01 Solutions
Assignment-03 (April 2026) : Problem Set-02 Solutions
Assignment-04 (April 2026) : MCQ Test-02 Solutions
Old Question Papers : CAT-1 (September 2025) & Answer Key
CAT-1 (September 2023) & Answer Key
CAT-2 (October 2023) & Answer Key
Sem Exam (January 2023) & Answer Key
MAF 6187 - Applied Probability & Statistics for Computer Applications
MAF 6187 - Applied Probability & Statistics for Computer Applications
Semester: Odd
Semester: Odd
Offered: M.C.A.
Offered: M.C.A.
Course Learning Objectives:
To impart the knowledge of probability and random variables.
To learn the techniques to carry out probability calculations and identify probability distributions.
To understand the basic knowledge of statistics.
To have the knowledge of sampling techniques and estimation.
To familiarize with the application of statistical inference in practical data analysis.
Syllabus : MAF 6187 - Applied Probability & Statistics for Computer Applications
Text Books : 1) Fundamentals of Mathematical Statistics - S.C.Gupta & V.K.Kapoor
2) Probability and Statistics for Engineers - Miller & Freund's
Module-1 : Probability & Random Variables
1.1 Lecture Notes : Basic Probability Concepts
1.2 Lecture Notes : Random Variable and Distributions
Module-2 : Standard Distributions
2.1 Lecture Notes: Discrete & Continuous Distributions
Module-3 : Descriptive Statistics
3.3 Video Lecture - 01
3.4 Video Lecture - 02
Module-4 : Sampling & Estimation
Module-5 : Testing of Hypothesis
Assignments : Assignment-01 (Oct. 2025) : On Basic Definitions & Formulas Solutions
Assignment-02 (Oct. 2025) : Quiz Assignment Solutions
Assignment-03 (Nov. 2025) : Problem Set
Assignment-04 (Nov 2025) : Problem Set
MAE 1183 - Linear Algebra and Calculus
MAE 1183 - Linear Algebra and Calculus
Semester: Odd
Semester: Odd
Offered: 2025
Offered: 2025
Course Learning Objectives:
To introduce eigenvalues and eigenvectors of a matrix.
To introduce the methods to solve linear algebra problems in practice.
To introduce the fundamental concepts of linear transformations and their matrix representations.
To understand the concept of functions of several variables and its applications.
To impart the knowledge in solving problems in double and triple integrations.
Syllabus : MAE 1183 - Linear Algebra and Calculus
Text Books : 1) B.V. Ramana, "Higher Engineering Mathematics"
2) B.S. Grewal, "Higher Engineering Mathematics"
Module - I : Matrices
1.1 Lecture Notes
1.2 Video Lectures
1.2.1 Eigenvalues : Link-01
1.2.2 Eigenvectors : Link-02 Link-03 Link-04
1.2.3 Orthogonal Diagonalization : Link-05 Link-06 Link-07
1.2.4 Cayley-Hamilton Theorem : Link-08
Module - II : Vector Space
Module - III : Linear Transformations and Applications
Module - IV : Function of Several Variables
4.2 Jacobian
4.3 Taylor's Series
Module - V : Multiple Integrals
5.2 Multiple Integral to Compute Area and Volume
5.3 Change of Order of Integration
Question Bank : Module-1 Module-2 Module-3 Module-4 Module-5
Assignments : Assignment-01 (Oct. 2025) : Problem Set Solutions
Assignment-02 (Oct. 2025) : Quiz Assignment Solutions
Assignment-03 (Nov 2025) : Problem Set
Assignment-04 (Nov 2025) : Problem Set
MAD 2182 - Probability & Statistics
MAD 2182 - Probability & Statistics
Semester: Odd
Semester: Odd
Offered: B.Tech
Offered: B.Tech
Course Learning Objectives:
To impart knowledge on the basic concepts of probability.
To understand random variables and distribution functions.
To acquaint with joint density function and generating functions.
To introduce sampling techniques and estimation.
To perform hypothesis testing and draw inference.
Syllabus : MAD 2182 / MADX 03 - Probability & Statistics
Text Books : 1) Fundamentals of Mathematical Statistics - S.C.Gupta & V.K.Kapoor
2) Probability and Statistics for Engineers - Miller & Freund's
Module-1 : Basic Probability Concepts
1.1 Lecture Notes
Module-2 : Random Variables and Distribution Functions
2.1 Lecture Notes: Discrete & Continuous Random Variables
2.2 Lecture Notes: Standard Probability Distributions
Module-3 : Two Dimensional Random Variables
3.1 Lecture Notes
Module-4 : Sampling & Estimation
Module-5 : Theory Of Inference
Assignments : Assignment-01 (July 2025) : On Basic Definitions & Formulas Solutions
Assignment-02 (Aug 2025) : MCQ Test-01 Solutions
Assignment-03 (Oct 2025) : Problem Set
Assignment-04 (Nov 2025) : Problem Set Solutions
Old Question Papers : CAT-1 (September 2025) & Answer Key
CAT-1 (September 2023) & Answer Key
CAT-2 (October 2023) & Answer Key
Sem Exam (January 2023) & Answer Key
Partial Differential Equations and Transforms
Partial Differential Equations and Transforms
Semester: Even
Semester: Even
Offered: B.Tech
Offered: B.Tech
Course Learning Objectives:
To formulate and solve partial differential equation of first, second and higher orders.
To introduce basics and engineering applications of Fourier series.
To develop Fourier transforms techniques.
To introduce techniques and engineering applications of Laplace Transforms.
To acquaint with Z -Transform techniques for discrete time systems.
MAD 1283 - Partial Differential Equations and Transforms
Module-1 : Partial Differential Equations
1.1 Lecture Notes
Module-2 : Fourier Series
2.1 Lecture Notes
2.2 3D Animations of Fourier Series
2.3 Video Lecture - 01 (Introduction)
2.4 Video Lecture - 02 (RMS Value)
2.5 Video Lecture - 03 (Harmonic Analysis)
Module-3 : Fourier Transform
3.1 Lecture Notes
3.2 3D Animations of Fourier Transforms
3.3 Video Lecture - 01 (Fourier Integral Theorem)
3.4 Video Lecture - 02 (Fourier Sine and Cosine Transforms)
Module-4 : Laplace Transform
Module-5 : Z-Transform
Assignments : Assignment-01 (Jan 2025) : Basic Definitions & Formulas
Assignment-02 (Feb 2025) : Problem Set Solutions
Assignment-03 (Feb 2025) : MCQ Test-01
Assignment-04 (April 2025) : Problem Set Solutions
Old Question Papers : CAT-1 (March 2024) & Answer Key
Biomathematics
Biomathematics
Semester: Odd
Semester: Odd
Offered: B.Tech Biotechnology
Offered: B.Tech Biotechnology
Course Learning Objectives:
To develop the skills in the areas of Biotechnology necessary to become a successful biologist.
To serve as basic tools for specialized studies in biological fields.
To facilitate the students to apply basic mathematical tools to solve biological problems.
To familiarize problem solving techniques using Numerical methods.
To demonstrate the students with mathematical modeling in Biological models.
Syllabus : MAD 1182 - Biomathematics
Module - I : Matrices
1.1 Lecture Notes
1.2 Video Lectures
1.2.1 Eigenvalues : Link-01
1.2.2 Eigenvectors : Link-02 Link-03 Link-04
1.2.3 Orthogonal Diagonalization : Link-05 Link-06 Link-07
1.2.4 Cayley-Hamilton Theorem : Link-08
Module - II : Calculus
2.1 Lecture Notes
2.2 Video Lectures
2.2.1 Derivatives & Partial Derivatives : Link-01 Link-02
2.2.2 Optima of Two Variables : Link-03 Link-04
2.2.3 Integration : Link-05
2.2.4 Multiple Integrals : Link-06
Module - III : Ordinary Differential Equations (ODE)
3.1 Lecture Notes
3.2 Video Lectures
3.2.1 First Order ODE : Link-01 Link-02
3.2.2 Homogeneous First Order Linear ODE : Link-03
3.2.3 Higher Order ODE : Link-04
Module - IV : Numerical Methods
4.1 Lecture Notes
4.2 Video Lectures
4.2.1 Numerical Solutions of Algebraic & Transcendental Equations : Link-01 Link-02 Link-03
4.2.2 Numerical Solutions of Simultaneous Equations : Link-04 Link-05
Module - V : Applications in Biology
5.1 Lecture Notes
5.2 Video Lectures
5.2.1 Pattern Biology : Link-01 Link-02
Assignments :
Old Question Papers : CAT-1 : 2023 2022 2021
SEE : 2023 2022 2021
Reference Books :
1) B.V. Ramana, "Higher Engineering Mathematics"
Business Mathematics and Statistics
Business Mathematics and Statistics
Semester: Odd
Semester: Odd
Offered: B.B.A. General
Offered: B.B.A. General
Course Learning Objectives:
To analyse the applications of Mathematics and Statistical techniques used business decision making.
To acquire proficiency in calculus in solving real life business problems.
To find the roots of uni-variate Analysis using different techniques.
To demonstrate the concepts of limits, continuity and application of bi-variate analysis.
To develop the use of time series necessary for applications.
Module - I : Introduction to Business Mathematics
1.1 Study Material
1.2 Video Lectures
1.2.1 Matrix Multiplication : Link-01
1.2.2 Determinant : Link-02
1.2.3 Matrix Inverse Method : Link-03
1.2.4 Cramer's Rule : Link-04
Module - II : Differential Calculus
2.1 Study Material
2.2 Video Lectures
2.2.1 Limits & Continuity : Link-01 Link-02 Link-03
2.2.2 Derivatives & Its Rules : Link-04 Link-05
2.2.3 Applications of Differentiation : Link-06 Link-07
Module - III : Uni-Variate Analysis
3.1 Lecture Notes
3.2 Video Lectures
Module - IV : Bi-Variate Analysis
4.1 Lecture Notes
4.2 Video Lectures
Module - V : Index Numbers and Time Series
5.1 Lecture Notes
5.2 Time Series
Assignments :
Assignment - 02
Question Bank: QB (Module - 1, 2, 3 & 4)
Old Question Papers :
Reference Books :
1) B.V. Ramana, "Higher Engineering Mathematics"
Numerical Methods
Numerical Methods
Semester: Odd
Semester: Odd
Offered: B.Tech
Offered: B.Tech
Course Learning Objectives:
To familiarize with the methods of solving equations numerically.
To introduce interpolation techniques and finite difference concepts.
To acquire knowledge on Numerical differentiation and integration.
To solve ordinary differential equations numerically.
Syllabus : MADX 05 - Numerical Methods
Module - I : Numerical Solutions of Equations
1.1 Lecture Notes
1.2 Video Lectures
1.2.1 Regula Falsi Method : Link-01
1.2.2 Fixed Point Iteration : Link-02 Link-03
1.2.3 Newton-Raphson Method : Link-04 Link-05
1.2.4 Gauss-Elimination Method : Link-06
1.2.5 Gauss-Jordan Method : Link-07
1.2.6 Gauss-Jacobi Method : Link-08
1.2.7 Gauss-Seidel Method : Link-09
Module - II : Interpolation
2.1 Lecture Notes
2.2 Video Lectures
2.2.1 Newton's Forward Difference Interpolation : Link-01 Link-02
2.2.2 Newton's Backward Difference Interpolation : Link-03 Link-04
2.2.3 Newton's Divided Difference Interpolation : Link-05 Link-06
2.2.4 Lagrange's Interpolation : Link-07
2.2.5 Cubic Spline Interpolation : Link-08
Module - III : Numerical Differentiation and Integration
3.1 Lecture Notes
3.2 Video Lectures
3.2.1 Numerical Differentiation : Link-01 Link-02
3.2.2 Numerical Integration : Link-03
3.2.3 Numerical Multiple Integrations : Link-04
Module - IV : Initial Value Problems for 1st Order Ordinary Differential Equations
4.1 Lecture Notes
4.2 Video Lectures
Module - V : Boundary Value Problems for Partial Differential Equations
5.1 Lecture Notes
5.2 Video Lectures
Assignments :
Assignment - 01 Solutions of Assignment - 01
Assignment - 02
Old Question Papers :
Question Bank: M-01 M-1&2 QB (All Modules)
Reference Books :
1) M.K Jain, S.R.K Iyengar & R.K Jain, "Numerical Methods (Problems & Solutions)"
2) B.V. Ramana, "Higher Engineering Mathematics"
Study Material for Arrear Courses
Study Material for Arrear Courses
Regulations-2013
1) MAB 1182
2) MAB 2181 : Module - I, II, III, IV, V
Regulations-2017
3) MAC 2181 : Module - I, II, III, IV, V Solutions of Assignment Problems
4) MAC 2281 : Module - I, II, III, IV, V Solutions of Assignment Problems
5) MACX 02 : Module - I, II, III, IV, V Solutions of Assignment Problems
6) MACX 04 : Module - I, II, III, IV, V Solutions of Assignment Problems
7) MACX 07 : Module - I, II, III, IV, V Solutions of Assignment Problems
Regulations-2021
8) MAD 1181 : Module - I, II, III, IV, V Solutions of Assignment Problems
9) MAD 1187 : Module - I, II, III, IV, V Solutions of Assignment Problems
10) MAD 1281 : Module - I, II, III, IV, V Solutions of Assignment Problems
11) MAD 1288 : Module - I, II, III, IV, V Solutions of Assignment Problems
12) MAD 2181 : Module - I, II, III, IV, V Solutions of Assignment Problems
13) MADX 03 : Module - I, II, III, IV, V
14) MADX 05 : Module - I, II, III, IV, V
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