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SCIENCE SERIES

Nanotechnology - Economics / Management / Entrepreneurhip (English)

Thursday, April 03, 2025

Starting a new Lecture Notes Series on Nanotechnology - Economics / Management / Entrepreneurhip

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Nanotechnology - Economics / Management / Entrepreneurhip By Lecture Notes together!

Lecture 1: Mod-01 Lec-01 Introduction

Lecture 2: Mod-02 Lec-02 Market Equilibrium : Demand and Supply

Lecture 3: Mod-03 Lec-03 Elasticity of Demand

Lecture 4: Mod-04 Lec-04 Demand Forecasting

Lecture 5: Mod-05 Lec-05 Production

Lecture 6: Mod-06 Lec-06 Exercises on Economics

Lecture 7: Mod-07 Lec-07 Cost - Volume - Profit Relationships

Lecture 8: Mod-08 Lec-08 Cost Management Systems and Activity Costing Systems

Lecture 9: Mod-09 Lec-09 Relevant Information and Decision Making

Lecture 10: Mod-10 Lec-10 Cost Allocation

Lecture 11: Mod-11 Lec-11 Exercises on Economics (Contd.)

Lecture 12: Mod-12 Lec-12 Double - Entry Bookkeeping

Lecture 13: Mod-13 Lec-13 Job Costing

Lecture 14: Mod-14 Lec-14 Process Costing

Lecture 15: Mod-15 Lec-15 The Master Budget

Lecture 16: Mod-16 Lec-16 Flexible Budegst and Variance Analysis

Lecture 17: Mod-17 Lec-17 Financial Statements

Lecture 18: Mod-17 Lec-18 Financial Statements (Contd.)

Lecture 19: Mod-18 Lec-19 Analysis of Financial Statements

Lecture 20: Mod-19 Lec-20 Exercises (Contd.)

Lecture 21: Mod-20 Lec-21 Time Value of Money

Lecture 22: Mod-21 Lec-22 Comparison of Alternatives

Lecture 23: Mod-21 Lec-23 Comparison of Alternatives (Contd.)

Lecture 24: Mod-21 Lec-24 Comparison of Alternatives (Contd. )

Lecture 25: Mod-22 Lec-25 Depreciation Accounting

Lecture 26: Mod-22 Lec-26 Depreciation Accounting (Contd.)

Lecture 27: Mod-23 Lec-27 Exercises

Lecture 28: Mod-24 Lec-28 Evolution of Management Thoughts

Lecture 29: Mod-25 Lec-29 Functions of Management

Lecture 30: Mod-25 Lec-30 Functions of Management (Contd.)

Lecture 31: Mod-25 Lec-31 Functions of Management (Contd. )

Lecture 32: Mod-26 Lec-32 Directing

Lecture 33: Mod-27 Lec-33 Product Development

Lecture 34: Mod-28 Lec-34 Forecasting Revisited

Lecture 35: Mod-28 Lec-35 Forecasting Revisited (Contd.)

Lecture 36: Mod-28 Lec-36 Forecasting Revisited (Contd. )

Lecture 37: Mod-29 Lec-37 Capacity Planning

Lecture 38: Mod-30 Lec-38 Capacity Planning (Contd.) and Plant Location

Lecture 39: Mod-31 Lec-39 Product Service Strategies and Plant Layout

Lecture 40: Mod-32 Lec-40 Plant Lauout (Contd.) and Production Planning and Control

Lecture 41: Mod-33 Lec-41 Production Planning and Control (Contd.)

Lecture 42: Mod-34 Lec-42 Inventory Management

Lecture 43: Mod-34 Lec 43 Inventory Management (Contd.)

Lecture 44: Mod-35 Lec-44 Supply Chain Management

Lecture 45: Mod-36 Lec-45 Supply Chain Management (Contd.) and Marketing Management

Lecture 46: Mod-37 Lec-46 Marketing Management (Contd.)

Lecture 47: Mod-38 Lec-47 Forms of Ownership

Lecture 48: Mod-39 Lec-48 Starting a New Company and Small - scale Industrial Undertakings

Lecture 49: Mod-40 Lec-49 Capital Financing

Lecture 50: Mod-41 Lec-50 Entrepreneurship - Final Words

SCIENCE SERIES

Aerospace - Space Flight Mechanics (English)

Thursday, April 03, 2025

Starting a new Lecture Notes Series on Aerospace - Space Flight Mechanics

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Lecture 1: Mod-01 Lec-01 Introduction to Space Flight Mechanics

Lecture 2: Mod-01 Lec-02 Particle Kinematics

Lecture 3: Mod-01 Lec-03 Particle Kinematics (Contd.)

Lecture 4: Mod-01 Lec-04 Conic Section

Lecture 5: Mod-01 Lec-05 Two Body Problem

Lecture 6: Mod-01 Lec-06 Two Body Problem (Contd...1)

Lecture 7: Mod-01 Lec-07 Two Body Problem (Contd...2)

Lecture 8: Mod-01 Lec-08 Two Body Problem (Contd...3)

Lecture 9: Mod-01 Lec-09 Two Body Problem (Contd...4)

Lecture 10: Mod-01 Lec-10 Two Body Problem (Contd...5)

Lecture 11: Mod-01 Lec-11 Two Body Problem (Contd...6)

Lecture 12: Mod-01 Lec-12 Two Body Problem (Contd...7) & Three Body Problem

Lecture 13: Mod-01 Lec-13 Three Body Problem (Contd...1)

Lecture 14: Mod-01 Lec-14 Three Body Problem (Contd...2)

Lecture 15: Mod-01 Lec-15 Three Body Problem (Contd...3)

Lecture 16: Mod-01 Lec-16 Three Body Problem (Contd...4)

Lecture 17: Mod-01 Lec-17 Three Body Problem (Contd...5)

Lecture 18: Mod-01 Lec-18 Three Body Problem (Contd...6)

Lecture 19: Mod-01 Lec-19 Three Body Problem (Contd...7)

Lecture 20: Mod-01 Lec-20 Three Body Problem (Contd...8)

Lecture 21: Mod-01 Lec-21 Trajectory Transfer

Lecture 22: Mod-01 Lec-22 Trajectory Transfer (Contd...1)

Lecture 23: Mod-01 Lec-23 Trajectory Transfer (Contd...2)

Lecture 24: Mod-01 Lec-24 Trajectory Transfer (Contd...3)

Lecture 25: Mod-01 Lec-25 Trajectory Transfer (Contd...4)

Lecture 26: Mod-01 Lec-26 Trajectory Transfer (Contd...5)

Lecture 27: Mod-01 Lec-27 Trajectory Transfer (Contd...6)

Lecture 28: Mod-01 Lec-28 Trajectory Transfer (Contd...7)

Lecture 29: Mod-01 Lec-29 Trajectory Transfer (Contd...8)

Lecture 30: Mod-01 Lec-30 Trajectory Transfer (Contd...9)

Lecture 31: Mod-01 Lec-31 Trajectory Transfer (Contd...10)

Lecture 32: Mod-01 Lec-32 Trajectory Transfer (Contd...11) and Attitude Dynamics

Lecture 33: Mod-01 Lec-33 Attitude Dynamics (Contd...1)

Lecture 34: Mod-01 Lec-34 Attitude Dynamics (Contd...2)

Lecture 35: Mod-01 Lec-35 Attitude Dynamics (Contd...3)

Lecture 36: Mod-01 Lec-36 Attitude Dynamics (Contd...4)

Lecture 37: Mod-01 Lec-37 Attitude Dynamics (Contd...5)

Lecture 38: Mod-01 Lec-38 Attitude Dynamics (Contd...6)

Lecture 39: Mod-01 Lec-39 Attitude Dynamics (Contd...7)

Lecture 40: Mod-01 Lec-40 Attitude Dynamics (Contd...8)

Lecture 41: Mod-01 Lec-41 Attitude Dynamics (Contd...9)

Lecture 42: Mod-01 Lec-42 Propulsion

Lecture 43: Mod-01 Lec-43 Propulsion (Contd...1)

Lecture 44: Mod-01 Lec-44 Propulsion (Contd...2)

Lecture 45: Mod-01 Lec-45 Propulsion (Contd...3)

MATHS SERIES

Mathematics - A Basic Course in Real Analysis (English)

Thursday, April 03, 2025

Starting a new Lecture Notes Series on Mathematics - A Basic Course in Real Analysis

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Mathematics - A Basic Course in Real Analysis By Lecture Notes together!

Lecture 1: Mod-01 Lec-01 Rational Numbers and Rational Cuts

Lecture 2: Mod-02 Lec-02 Irrational numbers, Dedekind's Theorem

Lecture 3: Mod-03 Lec-03 Continuum and Exercises

Lecture 4: Mod-03 Lec-04 Continuum and Exercises (Contd.)

Lecture 5: Mod-04 Lec-05 Cantor's Theory of Irrational Numbers

Lecture 6: Mod-04 Lec-06 Cantor's Theory of Irrational Numbers (Contd.)

Lecture 7: Mod-05 Lec-07 Equivalence of Dedekind and Cantor's Theory

Lecture 8: Mod-06 Lec-08 Finite, Infinite, Countable and Uncountable Sets of Real Numbers

Lecture 9: Mod-07 Lec-09 Types of Sets with Examples, Metric Space

Lecture 10: Mod-08 Lec-10 Various properties of open set, closure of a set

Lecture 11: Mod-09 Lec-11 Ordered set, Least upper bound, greatest lower bound of a set

Lecture 12: Mod-10 Lec-12 Compact Sets and its properties

Lecture 13: Mod-11 Lec-13 Weiersstrass Theorem, Heine Borel Theorem, Connected set

Lecture 14: Mod-12 Lec-14 Tutorial - II

Lecture 15: Mod-13 Lec-15 Concept of limit of a sequence

Lecture 16: Mod-14 Lec-16 Some Important limits, Ratio tests for sequences of Real Numbers

Lecture 17: Mod-15 Lec-17 Cauchy theorems on limit of sequences with examples

Lecture 18: Mod-16 Lec-18 Fundamental theorems on limits, Bolzano-Weiersstrass Theorem

Lecture 19: Mod-17 Lec-19 Theorems on Convergent and divergent sequences

Lecture 20: Mod-18 Lec-20 Cauchy sequence and its properties

Lecture 21: Mod-19 Lec-21 Infinite series of real numbers

Lecture 22: Mod-20 Lec-22 Comparison tests for series, Absolutely convergent and Conditional convergent series

Lecture 23: Mod-21 Lec-23 Tests for absolutely convergent series

Lecture 24: Mod-22 Lec-24 Raabe's test, limit of functions, Cluster point

Lecture 25: Mod-23 Lec-25 Some results on limit of functions

Lecture 26: Mod-24 Lec-26 Limit Theorems for functions

Lecture 27: Mod-25 Lec-27 Extension of limit concept (one sided limits)

Lecture 28: Mod-26 Lec-28 Continuity of Functions

Lecture 29: Mod-27 Lec-29 Properties of Continuous Functions

Lecture 30: Mod-28 Lec-30 Boundedness Theorem, Max-Min Theorem and Bolzano's theorem

Lecture 31: Mod-29 Lec-31 Uniform Continuity and Absolute Continuity

Lecture 32: Mod-30 Lec-32 Types of Discontinuities, Continuity and Compactness

Lecture 33: Mod-31 Lec-33 Continuity and Compactness (Contd.), Connectedness

Lecture 34: Mod-32 Lec-34 Differentiability of real valued function, Mean Value Theorem

Lecture 35: Mod-33 Lec-35 Mean Value Theorem (Contd.)

Lecture 36: Mod-34 Lec-36 Application of MVT , Darboux Theorem, L Hospital Rule

Lecture 37: Mod-35 Lec-37 L'Hospital Rule and Taylor's Theorem

Lecture 38: Mod-36 Lec-38 Tutorial - III

Lecture 39: Mod-37 Lec-39 Riemann/Riemann Stieltjes Integral

Lecture 40: Mod-38 Lec-40 Existence of Reimann Stieltjes Integral

Lecture 41: Mod-39 Lec-41 Properties of Reimann Stieltjes Integral

Lecture 42: Mod-39 Lec-42 Properties of Reimann Stieltjes Integral (Contd.)

Lecture 43: Mod-40 Lec-43 Definite and Indefinite Integral

Lecture 44: Mod-41 Lec-44 Fundamental Theorems of Integral Calculus

Lecture 45: Mod-42 Lec-45 Improper Integrals

Lecture 46: Mod-43 Lec-46 Convergence Test for Improper Integrals

SCIENCE SERIES

Aerospace - Introduction to Aerodynamics (English)

Thursday, April 03, 2025

Starting a new Lecture Notes Series on Aerospace - Introduction to Aerodynamics

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Lecture 1: Mod-01 Lec-01 Aircraft and Aerodynamic Forces and Moments

Lecture 2: Mod-01 Lec-02 Aircraft and Aerodynamic Forces and Moments (Contd.)

Lecture 3: Mod-02 Lec-03 Fluids and Forces in Fluids

Lecture 4: Mod-02 Lec-04 Fluids and Forces in Fluids (Contd.)

Lecture 5: Mod-03 Lec-05 Forces in Fluids

Lecture 6: Mod-03 Lec-06 Forces in Fluids (Contd.)

Lecture 7: Mod-04 Lec-07 Kinematics of fluid motion

Lecture 8: Mod-04 Lec-08 Kinematics of fluid motion (Contd.)

Lecture 9: Mod-04 Lec-09 Kinematics of fluid motion (Contd. )

Lecture 10: Mod-04 Lec-10 Kinematics of fluid motion (Contd.)

Lecture 11: Mod-05 Lec-11 Kinematics of fluid motion - Velocity with specified extension and vorticity

Lecture 12: Mod-05 Lec-12 Kinematics of fluid motion - Velocity with specified extension and vorticity (Contd.)

Lecture 13: Mod-06 Lec-13 Kinematics of fluid motion - Vorticity Distribution

Lecture 14: Mod-07 Lec-14 Kinematics of fluid motion - Velocity without expansion and vorticity

Lecture 15: Mod-08 Lec-15 Irrotational Solenoidal Flow in Multiply Connected region

Lecture 16: Mod-08 Lec-16 Irrotational Solenoidal Flow in Multiply Connected region (Contd.)

Lecture 17: Mod-09 Lec-17 Equations of Fluid Motion - Navier - Stokes Equation

Lecture 18: Mod-09 Lec-18 Equations of Fluid Motion - Navier - Stokes Equation (Contd.)

Lecture 19: Mod-09 Lec-19 Equations of Fluid Motion - Navier - Stokes Equation (Contd. )

Lecture 20: Mod-10 Lec-20 Conservation of Energy and Energy Equation

Lecture 21: Mod-11 Lec-21 Equations of Motions

Lecture 22: Mod-11 Lec-22 Equations of Motion (Contd.)

Lecture 23: Mod-12 Lec-23 Exact Solution for Simple Problems

Lecture 24: Mod-12 Lec-24 Exact Solution for Simple Problems (Contd.)

Lecture 25: Mod-13 Lec-25 Non-dimensional Form of the Equations and Possible Simplifications

Lecture 26: Mod-14 Lec-26 High Reynolds Number Approximation

Lecture 27: Mod-15 Lec-27 Conditions fior Incompressibility

Lecture 28: Mod-16 Lec-28 Potential Flow

Lecture 29: Mod-17 Lec-29 Potential Flow - Combination of Basic Solutions

Lecture 30: Mod-17 Lec-30 Potential Flow - Combination of Basic Solutions (Contd.)

Lecture 31: Mod-17 Lec-31 Potential Flow - Combination of Basic Solutions (Contd. )

Lecture 32: Mod-17 Lec-32 Potential Flow - Combination of Basic Solutions (Contd. ) - Lifting Cylinder

Lecture 33: Mod-18 Lec-33 Conformal Transformation

Lecture 34: Mod-18 Lec-34 Conformal Transformation (Contd.)

Lecture 35: Mod-19 Lec-35 Zhukovsky Transformation

Lecture 36: Mod-19 Lec-36 Zhukovsky Transformation (Contd.)

Lecture 37: Mod-20 Lec-37 Zhukovsky Transformation - Applications

Lecture 38: Mod-20 Lec-38 Zhukovsky Transformation - Applications (Contd.)

Lecture 39: Mod-20 Lec-39 Zhukovsky Transformation - Applications (Contd. )

Lecture 40: Mod-21 Lec-40 Transformation

Lecture 41: Mod-21 Lec-41 Transformation (Contd.)

Lecture 42: Mod-22 Lec-42 Boundary - Layer Theory

Lecture 43: Mod-22 Lec-43 Boundary - Layer Theory (Contd.)

Lecture 44: Mod-22 Lec-44 Boundary - Layer Theory (Contd. )

Lecture 45: Mod-22 Lec-45 Boundary - Layer Theory ( Contd)

Lecture 46: Mod-22 Lec-46 Boundary - Layer Theory (Contd. )

SCIENCE SERIES

Aerospace - High Speed Aero Dynamics (English)

Thursday, April 03, 2025

Starting a new Lecture Notes Series on Aerospace - High Speed Aero Dynamics

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Lecture 1: Mod-01 Lec-01 Introduction and Review of Thermodynamics

Lecture 2: Mod-01 Lec-02 Review of Thermodynamics (Contd.)

Lecture 3: Mod-01 Lec-03 Review of Thermodynamics (Contd.)

Lecture 4: Mod-01 Lec-04 Review of Thermodynamics (Contd.)

Lecture 5: Mod-02 Lec-05 One-dimensional gas dynamics

Lecture 6: Mod-02 Lec-06 One-dimensional gas dynamics (Contd.)

Lecture 7: Mod-02 Lec-07 One-dimensional gas dynamics (Contd.)

Lecture 8: Mod-03 Lec-08 One-dimensional waves

Lecture 9: Mod-03 Lec-09 One-dimensional waves (Contd.)

Lecture 10: Mod-03 Lec-10 One-dimensional waves (Contd.)

Lecture 11: Mod-04 Lec-11 Waves and Supersonic Flow

Lecture 12: Mod-04 Lec-12 Waves and Supersonic Flow (Contd.)

Lecture 13: Mod-04 Lec-13 Waves and Supersonic Flow (Contd.)

Lecture 14: Mod-04 Lec-14 Waves and Supersonic Flow (Contd.)

Lecture 15: Mod-05 Lec-15 Shock Expansion Theory

Lecture 16: Mod-06 Lec-16 Flow through ducts and channels

Lecture 17: Mod-06 Lec-17 Flow in ducts

Lecture 18: Mod-06 Lec-18 Flow in ducts (Contd.)

Lecture 19: Mod-07 Lec-19 Adiabatic Flow in ducts with friction

Lecture 20: Mod-07 Lec-20 Adiabatic flow in ducts with friction (Contd.)

Lecture 21: Mod-08 Lec-21 Isothermal flow in ducts with friction

Lecture 22: Mod-09 Lec-22 Flow in uniform duct with heating

Lecture 23: Mod-10 Lec-23 Multi - dimensional flow problems

Lecture 24: Mod-10 Lec-24 Multi - dimensional flow problems (Contd.)

Lecture 25: Mod-11 Lec-25 Linearized flow problems

Lecture 26: Mod-11 Lec-26 Linearized flow problems (Contd.)

Lecture 27: Mod-11 Lec-27 Linearized flow problems ( Contd.)

Lecture 28: Mod-11 Lec-28 Linearized flow problems (Contd.)

Lecture 29: Mod-11 Lec-29 Linearized flow problems ( Contd.)

Lecture 30: Mod-11 Lec-30 Linearized flow problems ( Contd.)

Lecture 31: Mod-11 Lec-31 Linearized flow problems (Contd.)

Lecture 32: Mod-12 Lec-32 Linearized Problems - Forces on Slender Bodies

Lecture 33: Mod-12 Lec-33 Linearized Problems - Forces on Slender Bodies (Contd.)

Lecture 34: Mod-13 Lec-34 Similarity Rules for High Speed Flows

Lecture 35: Mod-13 Lec-35 Similarity Rules for High Speed Flows (Contd.)

Lecture 36: Mod-13 Lec-36 Similarity Rules for High Speed Flows (Contd.)

Lecture 37: Mod-14 Lec-37 Similarity Rules in Hypersonic Flow

Lecture 38: Mod-15 Lec-38 Transonic Flow

Lecture 39: Mod-15 Lec-39 Transonic Flow (Contd.)

Lecture 40: Mod-15 Lec-40 Transonic Flow (Contd.)

MATHS SERIES

Mathematics - Stochastic Processes (English)

Thursday, April 03, 2025

Starting a new Lecture Notes Series on Mathematics - Stochastic Processes

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Lecture 1: Mod-01 Lec-01 Introduction to Stochastic Processes

Lecture 2: Mod-01 Lec-02 Introduction to Stochastic Processes (Contd.)

Lecture 3: Mod-01 Lec-03 Problems in Random Variables and Distributions

Lecture 4: Mod-01 Lec-04 Problems in Sequences of Random Variables

Lecture 5: Mod-02 Lec-01 Definition, Classification and Examples

Lecture 6: Mod-02 Lec-02 Simple Stochastic Processes

Lecture 7: Mod-03 Lec-01 Stationary Processes

Lecture 8: Mod-03 Lec-02 Autoregressive Processes

Lecture 9: Mod-04 Lec-01 Introduction, Definition and Transition Probability Matrix

Lecture 10: Mod-04 Lec-02 Chapman-Kolmogrov Equations

Lecture 11: Mod-04 Lec-03 Classification of States and Limiting Distributions

Lecture 12: Mod-04 Lec-04 Limiting and Stationary Distributions

Lecture 13: Mod-04 Lec-05 Limiting Distributions, Ergodicity and Stationary Distributions

Lecture 14: Mod-04 Lec-06 Time Reversible Markov Chain

Lecture 15: Mod-04 Lec-07 Reducible Markov Chains

Lecture 16: Mod-05 Lec-01 Definition, Kolmogrov Differential Equations and Infinitesimal Generator Matrix

Lecture 17: Mod-05 Lec-02 Limiting and Stationary Distributions, Birth Death Processes

Lecture 18: Mod-05 Lec-03 Poisson Processes

Lecture 19: Mod-05 Lec-04 M/M/1 Queueing Model

Lecture 20: Mod-05 Lec-05 Simple Markovian Queueing Models

Lecture 21: Mod-05 Lec-06 Queueing Networks

Lecture 22: Mod-05 Lec-07 Communication Systems

Lecture 23: Mod-05 Lec-08 Stochastic Petri Nets

Lecture 24: Mod-06 Lec-01 Conditional Expectation and Filtration

Lecture 25: Mod-06 Lec-02 Definition and Simple Examples

Lecture 26: Mod-07 Lec-01 Definition and Properties

Lecture 27: Mod-07 Lec-02 Processes Derived from Brownian Motion

Lecture 28: Mod-07 Lec-03 Stochastic Differential Equations

Lecture 29: Mod-07 Lec-04 Ito Integrals

Lecture 30: Mod-07 Lec-05 Ito Formula and its Variants

Lecture 31: Mod-07 Lec-06 Some Important SDE`s and Their Solutions

Lecture 32: Mod-08 Lec-01 Renewal Function and Renewal Equation

Lecture 33: Mod-08 Lec-02 Generalized Renewal Processes and Renewal Limit Theorems

Lecture 34: Mod-08 Lec-03 Markov Renewal and Markov Regenerative Processes

Lecture 35: Mod-08 Lec-04 Non Markovian Queues

Lecture 36: Mod-08 Lec-05 Non Markovian Queues Cont,,

Lecture 37: Mod-08 Lec-06 Application of Markov Regenerative Processes

Lecture 38: Mod-09 Lec-01 Galton-Watson Process

Lecture 39: Mod-09 Lec-02 Markovian Branching Process

MATHS SERIES

Mathematics - An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves (English)

Wednesday, April 02, 2025

Starting a new Lecture Notes Series on Mathematics - An Introduction to Riemann Surfaces and Algebraic Curves: Complex 1-Tori and Elliptic Curves

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Lecture 1: The Idea of a Riemann Surface

Lecture 2: Simple Examples of Riemann Surfaces

Lecture 3: Maximal Atlases and Holomorphic Maps of Riemann Surfaces

Lecture 4: A Riemann Surface Structure on a Cylinder

Lecture 5: A Riemann Surface Structure on a Torus

Lecture 6: Riemann Surface Structures on Cylinders and Tori via Covering Spaces

Lecture 7: Moebius Transformations Make up Fundamental Groups of Riemann Surfaces

Lecture 8: Homotopy and the First Fundamental Group

Lecture 9: A First Classification of Riemann Surfaces

Lecture 10: The Importance of the Path-lifting Property

Lecture 11: Fundamental groups as Fibres of the Universal covering Space

Lecture 12: The Monodromy Action

Lecture 13: The Universal covering as a Hausdorff Topological Space

Lecture 14: The Construction of the Universal Covering Map

Lecture 15: Completion of the Construction of the Universal Covering: Universality of the Universal Covering

Lecture 16: ompletion of the Construction of the Universal Covering: The Fundamental Group

Lecture 17: The Riemann Surface Structure on the Topological Covering of a Riemann Surface

Lecture 18: Riemann Surfaces with Universal Covering the Plane or the Sphere

Lecture 19: Mod-04 Lec-18 Classifying Complex Cylinders Riemann Surfaces

Lecture 20: Characterizing Moebius Transformations with a Single Fixed Point

Lecture 21: Characterizing Moebius Transformations with Two Fixed Points

Lecture 22: Torsion-freeness of the Fundamental Group of a Riemann Surface

Lecture 23: Characterizing Riemann Surface Structures on Quotients of the Upper Half-Plane with Abelian

Lecture 24: Classifying Annuli up to Holomorphic Isomorphism

Lecture 25: Orbits of the Integral Unimodular Group in the Upper Half-Plane

Lecture 26: Galois Coverings are precisely Quotients by Properly Discontinuous Free Actions

Lecture 27: Mod-05 Lec-26 Local Actions at the Region of Discontinuity of a Kleinian Subgroup

Lecture 28: Quotients by Kleinian Subgroups give rise to Riemann Surfaces

Lecture 29: The Unimodular Group is Kleinian

Lecture 30: The Necessity of Elliptic Functions for the Classification of Complex Tori

Lecture 31: The Uniqueness Property of the Weierstrass Phe-function associated to a Lattice in the Plane

Lecture 32: The First Order Degree Two Cubic Ordinary Differential Equation satisfied by the Weierstras

Lecture 33: The Values of the Weierstrass Phe-function at the Zeros of its Derivative are nonvanishing

Lecture 34: The Construction of a Modular Form of Weight Two on the Upper Half-Plane

Lecture 35: The Fundamental Functional Equations satisfied by the Modular Form of Weight Two on the Upper Half

Lecture 36: The Weight Two Modular Form assumes Real Values on the Imaginary Axis in the Upper Half-plane

Lecture 37: The Weight Two Modular Form Vanishes at Infinity

Lecture 38: The Weight Two Modular Form Decays Exponentially in a Neighbourhood of Infinity

Lecture 39: A Suitable Restriction of the Weight Two Modular Form is a Holomorphic Conformal Isomorphism

Lecture 40: The J-Invariant of a Complex Torus (or) of an Algebraic Elliptic Curve

Lecture 41: A Fundamental Region in the Upper Half-Plane for the Elliptic Modular J-Invariant

Lecture 42: The Fundamental Region in the Upper Half-Plane for the Unimodular Group

Lecture 43: A Region in the Upper Half-Plane Meeting Each Unimodular Orbit Exactly Once

Lecture 44: Moduli of Elliptic Curves

Lecture 45: Punctured Complex Tori are Elliptic Algebraic Affine Plane Cubic Curves in Complex 2-Space

Lecture 46: The Natural Riemann Surface Structure on an Algebraic Affine Nonsingular Plane Curve

Lecture 47: Complex Projective 2-Space as a Compact Complex Manifold of Dimension Two

Lecture 48: Complex Tori are the same as Elliptic Algebraic Projective Curves

MATHS SERIES

Mathematics - Statistical Inference (English)

Wednesday, April 02, 2025

Starting a new Lecture Notes Series on Mathematics - Statistical Inference

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Lecture 1: Mod-01 Lec-01 Introduction and Motivation

Lecture 2: Mod-02 Lec-02 Basic Concepts of Point Estimations - I

Lecture 3: Mod-03 Lec-03 Basic Concepts of Point Estimations - II

Lecture 4: Mod-04 Lec-04 Finding Estimators - I

Lecture 5: Mod-05 Lec-05 Finding Estimators - II

Lecture 6: Mod-06 Lec-06 Finding Estimators - III

Lecture 7: Mod-07 Lec-07 Properties of MLEs

Lecture 8: Mod-08 Lec-08 Lower Bounds for Variance - I

Lecture 9: Mod-09 Lec-09 Lower Bounds for Variance - II

Lecture 10: Mod-10 Lec-10 Lower Bounds for Variance - III

Lecture 11: Mod-11 Lec-11 Lower Bounds for Variance - IV

Lecture 12: Mod-12 Lec-12 Sufficiency

Lecture 13: Mod-13 Lec-13 Sufficiency and Information

Lecture 14: Mod-14 Lec-14 Minimal Sufficiency, Completeness

Lecture 15: Mod-15 Lec-15 UMVU Estimation, Ancillarity

Lecture 16: Mod-16 Lec-16 Invariance - I

Lecture 17: Mod-17 Lec-17 Invariance - II

Lecture 18: Mod-18 Lec-18 Bayes and Minimax Estimation - I

Lecture 19: Mod-19 Lec-19 Bayes and Minimax Estimation - II

Lecture 20: Mod-20 Lec-20 Bayes and Minimax Estimation - III

Lecture 21: Mod-21 Lec-21 Testing of Hypotheses : Basic Concepts

Lecture 22: Mod-22 Lec-22 Neyman Pearson Fundamental Lemma

Lecture 23: Mod-23 Lec-23 Applications of NP lemma

Lecture 24: Mod-24 Lec-24 UMP Tests

Lecture 25: Mod-25 Lec-25 UMP Tests (Contd.)

Lecture 26: Mod-26 Lec-26 UMP Unbiased Tests

Lecture 27: Mod-27 Lec-27 UMP Unbiased Tests (Contd.)

Lecture 28: Mod-28 Lec-28 UMP Unbiased Tests : Applications

Lecture 29: Mod-29 Lec-29 Unbiased Tests for Normal Populations

Lecture 30: Mod-30 Lec-30 Unbiased Tests for Normal Populations (Contd.)

Lecture 31: Mod-31 Lec-31 Likelihood Ratio Tests - I

Lecture 32: Mod-32 Lec-32 Likelihood Ratio Tests - II

Lecture 33: Mod-33 Lec-33 Likelihood Ratio Tests - III

Lecture 34: Mod-34 Lec-34 Likelihood Ratio Tests - IV

Lecture 35: Mod-35 Lec-35 Invariant Tests

Lecture 36: Mod-36 Lec-36 Test for Goodness of Fit

Lecture 37: Mod-37 Lec-37 Sequential Procedure

Lecture 38: Mod-38 Lec-38 Sequential Procedure (Contd.)

Lecture 39: Mod-39 Lec-39 Confidence Intervals

Lecture 40: Mod-40 Lec-40 Confidence Intervals (Contd.)

SCIENCE SERIES

Ocean - Ocean Structures and Materials (English)

Wednesday, April 02, 2025

Starting a new Lecture Notes Series on Ocean - Ocean Structures and Materials

Youtube Lecture Playlist Credits
Channel Name: nptelhrd

So Let Us Start to This Journey of Learning

Ocean - Ocean Structures and Materials By Lecture Notes together!

Lecture 1: Mod-01 Lec-01 Introduction and objectives

Lecture 2: Mod-01 Lec-02 Fixed type offshore structures

Lecture 3: Mod-01 Lec-03 Compliant type offshore structures-I

Lecture 4: Mod-01 Lec-04 Compliant type offshore structures-II

Lecture 5: Mod-01 Lec-05 Drill ships and basics of drilling

Lecture 6: Mod-01 Lec-06 Subsea production systems

Lecture 7: Mod-01 Lec-07 Environmental loads I

Lecture 8: Mod-01 Lec-08 Environmental loads II

Lecture 9: Mod-01 Lec-09 Types of coastal structures I

Lecture 10: Mod-01 Lec-10 Types of coastal structures II

Lecture 11: Mod-01 Lec-11 Summary of coastal structures

Lecture 12: Mod-01 Lec-12 Tutorials on Module I

Lecture 13: Mod-02 Lec-01 Outline of planning of ocean structures

Lecture 14: Mod-02 Lec-02 Introduction to design

Lecture 15: Mod-02 Lec-03 Construction techniques

Lecture 16: Mod-02 Lec-04 Dredging I

Lecture 17: Mod-02 Lec-05 Dredging II

Lecture 18: Mod-02 Lec-06 Uncertainties in analysis and design

Lecture 19: Mod-02 Lec-07 Design adequacy- Example I

Lecture 20: Mod-02 Lec-08 Design adequacy- Example II

Lecture 21: Mod-02 Lec-09 Dredging equipments' specifications

Lecture 22: Mod-02 Lec-10 Ocean Pollution

Lecture 23: Mod-02 Lec-11 Foundation and sea bed anchors

Lecture 24: Mod-03 Lec-01 Introduction to materials I

Lecture 25: Mod-03 Lec-02 Introduction to materials II

Lecture 26: Mod-03 Lec-03 Concrete in marine environment

Lecture 27: Mod-03 Lec-04 Concrete: problems and solutions

Lecture 28: Mod-03 Lec-05 Repair materials for marine structures

Lecture 29: Mod-03 Lec-06 Corrosion in concrete I

Lecture 30: Mod-03 Lec-07 Corrosion in concrete II

Lecture 31: Mod-03 Lec-08 Material sin repair and rehabilitation

Lecture 32: Mod-03 Lec-09 Materials for special repair

Lecture 33: Mod-03 Lec-10 New materials for coastal embankments I

Lecture 34: Mod-03 Lec-11 New materials for coastal embankments II

Lecture 35: Mod-04 Lec-01 Non-destructive testing

Lecture 36: Mod-04 Lec-02 Structural health monitoring

Lecture 37: Mod-04 Lec-03 Wireless sensor networking

Lecture 38: Mod-04 Lec-04 Repair and rehabilitation- Fenders