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Linear Algebra and Univariate Calculus { F. Y. B. Tech, Sem-I }
Linear Algebra and Univariate Calculus { F. Y. B. Tech, Sem-I }
F. Y. B. Tech, Sem-I (Compulsory Course) (Click Unit name for Material)
Unit-I : Matrices-I : Rank, normal form, system of linear equations with applications in Electrical circuits, linear dependence and independence, linear and orthogonal transformations.
Unit-II : Matrices-II : Eigenvalues, Eigen vectors, Cayley – Hamilton theorem, diagonalization, application to problems in the mass spring system.
Unit-III : Differential Calculus-I : Rolle‟s theorem, Lagrange's mean value theorem, Cauchy's mean value theorem, Successive differentiation, Leibnitz theorem, application to find curvature.
Unit-IV : Differential Calculus-II : Taylor's series, Maclaurin's series, Indeterminate forms, L' Hospital rule, evaluation of limits.
Unit-V : Differential equations : Exact differential equations, differential equations reducible to Exact form, Linear differential equations, differential equations reducible to Linear form.
Unit-VI : Application of DE : Applications of differential equations to orthogonal trajectories, Kirchoff's law of electrical circuits, rectilinear motion, one-dimensional conduction of heat, Newton's law of cooling.
Multivariate Calculus { F. Y. B. Tech, Sem-II }
Multivariate Calculus { F. Y. B. Tech, Sem-II }
F. Y. B. Tech, Sem-II (Compulsory Course) (Click Unit name for Material)
Partial Differentiation: Partial derivatives, Euler's theorem on homogeneous functions, implicit functions, and variables treated as constant, total derivatives.
Application of Partial Differentiation: Jacobian: Jacobians and their applications, errors, and approximations. Maxima and Minima: maxima and minima of functions of two and three variables.
Fourier Series: Definition, Dirichlet‟s conditions, full range Fourier series, half range Fourier series, Harmonic analysis, and application to engineering.
Integral Calculus: Beta and Gamma functions, differentiation under integral sign (DUIS), Error functions.
Multiple Integration: Introduction of curve tracing,double integration, change of order of integration, conversion into polar form,Triple integration: with limits and without limits, Dirichlet's theorem.
Application of Multiple Integration: Rectification of curves, Area, Volume, CG, and MI
Data Analysis using R- Software { S. Y. B. Tech (IT), Sem-I }
Data Analysis using R- Software { S. Y. B. Tech (IT), Sem-I }
S. Y. B. Tech (IT), Sem-I (Compulsory Course) (Click Unit name for Material)
Unit-I: Introduction to data analytics and R Software fundamentals:
a. Understanding the Data.
b. R Packages for Data Science.
c. Importing and Exporting Data in R Software.
d. Getting Started: Analyzing Data in R Software.
e. Accessing Databases with R Software
Unit-II: Data Wrangling:
a. Pre-processing Data in R Software
b. Dealing with Missing Values in R Software
c. Data Formatting in R Software
d. Data Normalization in R Software
e. Binning in R Software
f. Turning categorical variables into quantitative variables in R Software
Unit-III: Data Visualization in R Software:
a. Histogram.
b. Bar/ Line Chart.
c. Box Plot (including group-by option)
d. Scatter Plot (including 3D and other features)
e. Mosaic Plot.
f. Heat Map.
g. 3D Graphs. h. Correlogram (GUIs)
Unit-IV: Statistical Data Analysis:
Descriptive Statistics: Central tendencies, Dispersion, Skewness, Kurtosis
Probability, Normal Distribution Sampling & Sampling Distributions.
Unit-V: Exploratory Data Analysis:
a. Correlation , Linear Regression and Multiple Linear Regression
b. Hypothesis Testing. c. Analysis of Variance ANOVA.
Unit-VI: Model Development using a dataset from Kaggle (Sample links are given below) and perform the following operation.
a. Make visualization of data set for distribution of at least three attributes.
b. Develop one descriptive model for the data set.
c. Develop a model for Prediction and Decision Making for the data set.
sample links: https://www.kaggle.com/code/cvaisnor/heart-2020/data https://www.kaggle.com/code/kailash068/crop-recommendation/data https://www.kaggle.com/datasets/debajyotipodder/co2-emission-by-vehicles https://www.kaggle.com/datasets/csafrit2/higher-education-students-performance-evaluation
Advance Data Analysis using R- Software { T. Y. B. Tech (Open Elective), Sem-I }
Advance Data Analysis using R- Software { T. Y. B. Tech (Open Elective), Sem-I }
T. Y. B. Tech, Sem-I (Open Elective) (Other Than IT) (Click Unit name for Material)
Introduction to data analysis and R Software fundamentals: Understanding the Data, R Packages for Data Science, Importing and Exporting Data in R Software, Getting Started: Analyzing Data in R Software, Accessing Databases with R Software.
Data Wrangling: Pre-processing Data in R Software, Dealing with Missing Values in R Software, Data Formatting in R Software, Data Normalization in R Software, Binning in R Software, Turning categorical variables into quantitative variables in R Software.
Data Visualization in R Software: Histogram, Bar/ Line Chart, Box Plot (including group-by option), Scatter Plot (including 3D and other features), Mosaic Plot, Heat Map, Correlogram (GUIs)
Data Analysis Statistical Data Analysis: Probability, Sampling & Sampling Distributions Exploratory Data Analysis: Central & Descriptive Statistics, Hypothesis Testing.
Model Development: Linear regression and multiple linear regression, model evaluation using visualization, prediction and decision making
Data Analysis Using R: use a dataset from kaggle (Link is given below). Identify the problem statement for the given data and by applying data analysis techniques analyze the data. Draw inferences from the data.
https://www.kaggle.com/code/cvaisnor/heart-2020/data
https://www.kaggle.com/code/kailash068/crop-recommendation/data
https://www.kaggle.com/datasets/debajyotipodder/co2-emission-by-vehicles
https://www.kaggle.com/datasets/csafrit2/higher-education-students-performance-evaluation
Neural Network and Fuzzy Logics { S. Y. B. Tech (Open Elective), Sem-II }
Neural Network and Fuzzy Logics { S. Y. B. Tech (Open Elective), Sem-II }
S. Y. B. Tech, Sem-II (Open Elective)
Architecture of Neural Network: Introduction, Biological neuron, Artificial neuron, Neuron modeling, Basic learning rules, Single layer, Multi layer feed forward network, Back propagation, Learning factors.
Neural Networks For Control: Feedback networks, Discrete time hop field networks, Schemes of neuro-control, Identification and control of dynamical systems, Case studies-Inverted Pendulum, Articulation Control.
Problem Solving-I: Neural Network (NN) Toolbox, NN Simulink Demos, Neural Network (ANN) implementation, NN Tool Artificial Neural Network (ANN) implementation, Application of NN to Control System.
Fundamental of Fuzzy Logic: Classical sets, Fuzzy Sets, Membership function, Cardinality of fuzzy set, Fuzzy complement, Fuzzy union & intersection, Fuzzy Relation, Fuzzification, Defuzzification, Fuzzy Rule.
Fuzzy Logic Control: Introduction, Knowledge based system, Decision making Logic, Fuzzy optimization, Adaptive fuzzy systems, Introduction to generate a genetic algorithm, Applications to Pattern recognition, Home Heating system.
Problem Solving-II: Fuzzy Logic Toolbox, Fuzzy Logic Simulink Demos, Fuzzy Logic Controller (FLC) implementation, Simulink Fuzzy Logic Controller (FLC) implementation, Applications of FLC to Control System.
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