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Numerical Analysis Learning Map

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Concepts

Numerical Analysissubject
Causes and Estimations of Error in Calculationchapter
Introduction To Numerical Analysissection
Numbers: Exact and Approximatesection
Rounding-off Errorsection
Significant Figures and Errorssection
Absolute, Relative and Percentage Errorssection
Relation between Relative Error and Significant Figuressection
General Error Estimation Formulasection
Error Propagation in Arithmetic Operationssection
Solved Problems on Error Analysissection
Exercises on Error Analysissection
Calculus of Finite Differenceschapter
Introduction to Finite Differencessection
Forward Difference Operatorsection
Backward Difference Operatorsection
Properties of Forward Difference Operatorsection
Fundamental Theorem of Difference Calculussection
Shift Operator and Its Relation with Difference Operatorsection
Relation between Difference Operator and Differential Operatorsection
Function Representation Using Leading Differencessection
Factorial Notation in Finite Differencessection
Polynomial Representation in Factorial Notationsection
Solved Problems on Finite Differencessection
Exercises on Finite Differencessection
Interpolation with Equal and Unequal Intervalschapter
Introduction to Interpolationsection
Newton's Forward Interpolation Formulasection
Newton's Backward Interpolation Formulasection
Central Difference Interpolation Methodssection
Gauss Forward Interpolation Formulasection
Gauss Backward Interpolation Formulasection
Modified Gauss Interpolation (Pivotal Entry Method)section
Stirling’s Interpolation Formulasection
Bessel’s Interpolation Formulasection
Everett’s Interpolation Formulasection
Construction of Central Difference Tablessection
Error Analysis in Difference Tablessection
Selection of Suitable Interpolation Formulasection
Lagrange Interpolation Formulasection
Computational Scheme for Lagrange Interpolationsection
Divided Differencessection
Properties of Divided Differencessection
Divided Differences of Polynomialssection
Divided Differences for Equispaced Datasection
Confluent Divided Differencessection
Newton’s Divided Difference Interpolation Formulasection
Applications and Deductions of Divided Difference Formulasection
Construction of Divided Difference Tablessection
Inverse Interpolationsection
Iterative Methods for Inverse Interpolationsection
Lagrange Method for Inverse Interpolationsection
Divided Difference Method for Inverse Interpolationsection
Root Finding using Inverse Interpolationsection
Hermite Interpolationsection
Solved Problems on Interpolationsection
Exercises on Interpolationsection
Numerical Differentiationchapter
Introduction to Numerical Differentiationsection
Differentiation Using Finite Differences (Equally Spaced Data)section
Differentiation for Unequally Spaced Datasection
Error Analysis in Numerical Differentiationsection
Higher Order Derivatives using Numerical Methodssection
Solved Problems on Numerical Differentiationsection
Exercises on Numerical Differentiationsection
Numerical Integrationchapter
Introduction to Numerical Integrationsection
General Quadrature Formulasection
Trapezoidal Rulesection
Simpson’s One-Third Rulesection
Computational Schemes for Trapezoidal and Simpson’s Rulessection
Weddle’s Rulesection
Special Case of Weddle’s Rulesection
Mechanical Quadrature based on Lagrange Interpolationsection
Newton-Cotes Formulas (Closed Type)section
Degree of Precision of Quadrature Formulassection
Derivation of Integration Rules from Newton-Cotes Formulasection
Integration using Central Difference Formulassection
Euler-Maclaurin Summation Formulasection
Error Analysis in Numerical Integrationsection
Solved Problems on Numerical Integrationsection
Exercises on Numerical Integrationsection
Solution of Algebraic and Transcendental Equationschapter
Introduction to Nonlinear Equationssection
Location of Roots and Interval Methodssection
Bisection Methodsection
Fixed Point Iteration Methodsection
Convergence Analysis of Iterative Methodssection
Newton-Raphson Methodsection
Generalized Newton’s Method and Root Extractionsection
Regula-Falsi Methodsection
Computational Algorithms for Root Findingsection
Graeffe’s Root Squaring Methodsection
Comparison of Root-Finding Methodssection
Solved Problems on Root Finding Methodssection
Exercises on Root Finding Methodssection
System of Linear Algebraic Equationschapter
Introduction to Systems of Linear Equationssection
Direct and Iterative Methods Overviewsection
Gauss Elimination Methodsection
Pivoting Techniquessection
Gauss-Jordan Methodsection
Matrix Inversion Methodsection
LU Decompositionsection
Iterative Methodssection
Gauss-Jacobi Iteration Methodsection
Gauss-Seidel Iteration Methodsection
Convergence Criteriasection
Error Analysis in Linear Systemssection
Solved Problemssection
Exercisessection
Numerical Solution of Ordinary Differential Equations (First Order)chapter
Introduction to Numerical Solution of ODEssection
Euler’s Methodsection
Modified Euler Method (Euler-Cauchy Method)section
Picard’s Method of Successive Approximationssection
Taylor Series Methodsection
Runge-Kutta Methodssection
Higher Order Runge-Kutta Methods (RK2, RK4)section
Predictor-Corrector Methodssection
Milne’s Predictor-Corrector Methodsection
Error Analysis in Numerical ODE Methodssection
Step Size and Stability Considerationssection
Solved Problems on Numerical ODE Methodssection
Exercises on Numerical ODE Methodssection
Eigenvalues and Eigenvectorschapter
Introduction to Eigenvalues and Eigenvectorssection
Matrix Polynomials and Characteristic Equationsection
Characteristic (Eigen) Values and Eigenvectorssection
Properties and Relations of Eigenvalues and Eigenvectorssection
Power Method for Dominant Eigenvaluesection
Inverse Power Method for Smallest Eigenvaluesection
Shifted Power Methodsection
Convergence of Eigenvalue Methodssection
Error Analysis in Eigenvalue Computationsection
Solved Problems on Eigenvalues and Eigenvectorssection
Exercises on Eigenvalues and Eigenvectorssection

Relationships

Numerical Analysis --contains--> Causes and Estimations of Error in Calculation
Causes and Estimations of Error in Calculation --contains--> Introduction To Numerical Analysis
Causes and Estimations of Error in Calculation --contains--> Numbers: Exact and Approximate
Causes and Estimations of Error in Calculation --contains--> Rounding-off Error
Causes and Estimations of Error in Calculation --contains--> Significant Figures and Errors
Causes and Estimations of Error in Calculation --contains--> Absolute, Relative and Percentage Errors
Causes and Estimations of Error in Calculation --contains--> Relation between Relative Error and Significant Figures
Causes and Estimations of Error in Calculation --contains--> General Error Estimation Formula
Causes and Estimations of Error in Calculation --contains--> Error Propagation in Arithmetic Operations
Causes and Estimations of Error in Calculation --contains--> Solved Problems on Error Analysis
Causes and Estimations of Error in Calculation --contains--> Exercises on Error Analysis
Numerical Analysis --contains--> Calculus of Finite Differences
Calculus of Finite Differences --contains--> Introduction to Finite Differences
Calculus of Finite Differences --contains--> Forward Difference Operator
Calculus of Finite Differences --contains--> Backward Difference Operator
Calculus of Finite Differences --contains--> Properties of Forward Difference Operator
Calculus of Finite Differences --contains--> Fundamental Theorem of Difference Calculus
Calculus of Finite Differences --contains--> Shift Operator and Its Relation with Difference Operator
Calculus of Finite Differences --contains--> Relation between Difference Operator and Differential Operator
Calculus of Finite Differences --contains--> Function Representation Using Leading Differences
Calculus of Finite Differences --contains--> Factorial Notation in Finite Differences
Calculus of Finite Differences --contains--> Polynomial Representation in Factorial Notation
Calculus of Finite Differences --contains--> Solved Problems on Finite Differences
Calculus of Finite Differences --contains--> Exercises on Finite Differences
Numerical Analysis --contains--> Interpolation with Equal and Unequal Intervals
Interpolation with Equal and Unequal Intervals --contains--> Introduction to Interpolation
Interpolation with Equal and Unequal Intervals --contains--> Newton's Forward Interpolation Formula
Interpolation with Equal and Unequal Intervals --contains--> Newton's Backward Interpolation Formula
Interpolation with Equal and Unequal Intervals --contains--> Central Difference Interpolation Methods
Interpolation with Equal and Unequal Intervals --contains--> Gauss Forward Interpolation Formula
Interpolation with Equal and Unequal Intervals --contains--> Gauss Backward Interpolation Formula
Interpolation with Equal and Unequal Intervals --contains--> Modified Gauss Interpolation (Pivotal Entry Method)
Interpolation with Equal and Unequal Intervals --contains--> Stirling’s Interpolation Formula
Interpolation with Equal and Unequal Intervals --contains--> Bessel’s Interpolation Formula
Interpolation with Equal and Unequal Intervals --contains--> Everett’s Interpolation Formula
Interpolation with Equal and Unequal Intervals --contains--> Construction of Central Difference Tables
Interpolation with Equal and Unequal Intervals --contains--> Error Analysis in Difference Tables
Interpolation with Equal and Unequal Intervals --contains--> Selection of Suitable Interpolation Formula
Interpolation with Equal and Unequal Intervals --contains--> Lagrange Interpolation Formula
Interpolation with Equal and Unequal Intervals --contains--> Computational Scheme for Lagrange Interpolation
Interpolation with Equal and Unequal Intervals --contains--> Divided Differences
Interpolation with Equal and Unequal Intervals --contains--> Properties of Divided Differences
Interpolation with Equal and Unequal Intervals --contains--> Divided Differences of Polynomials
Interpolation with Equal and Unequal Intervals --contains--> Divided Differences for Equispaced Data
Interpolation with Equal and Unequal Intervals --contains--> Confluent Divided Differences
Interpolation with Equal and Unequal Intervals --contains--> Newton’s Divided Difference Interpolation Formula
Interpolation with Equal and Unequal Intervals --contains--> Applications and Deductions of Divided Difference Formula
Interpolation with Equal and Unequal Intervals --contains--> Construction of Divided Difference Tables
Interpolation with Equal and Unequal Intervals --contains--> Inverse Interpolation
Interpolation with Equal and Unequal Intervals --contains--> Iterative Methods for Inverse Interpolation
Interpolation with Equal and Unequal Intervals --contains--> Lagrange Method for Inverse Interpolation
Interpolation with Equal and Unequal Intervals --contains--> Divided Difference Method for Inverse Interpolation
Interpolation with Equal and Unequal Intervals --contains--> Root Finding using Inverse Interpolation
Interpolation with Equal and Unequal Intervals --contains--> Hermite Interpolation
Interpolation with Equal and Unequal Intervals --contains--> Solved Problems on Interpolation
Interpolation with Equal and Unequal Intervals --contains--> Exercises on Interpolation
Numerical Analysis --contains--> Numerical Differentiation
Numerical Differentiation --contains--> Introduction to Numerical Differentiation
Numerical Differentiation --contains--> Differentiation Using Finite Differences (Equally Spaced Data)
Numerical Differentiation --contains--> Differentiation for Unequally Spaced Data
Numerical Differentiation --contains--> Error Analysis in Numerical Differentiation
Numerical Differentiation --contains--> Higher Order Derivatives using Numerical Methods
Numerical Differentiation --contains--> Solved Problems on Numerical Differentiation
Numerical Differentiation --contains--> Exercises on Numerical Differentiation
Numerical Analysis --contains--> Numerical Integration
Numerical Integration --contains--> Introduction to Numerical Integration
Numerical Integration --contains--> General Quadrature Formula
Numerical Integration --contains--> Trapezoidal Rule
Numerical Integration --contains--> Simpson’s One-Third Rule
Numerical Integration --contains--> Computational Schemes for Trapezoidal and Simpson’s Rules
Numerical Integration --contains--> Weddle’s Rule
Numerical Integration --contains--> Special Case of Weddle’s Rule
Numerical Integration --contains--> Mechanical Quadrature based on Lagrange Interpolation
Numerical Integration --contains--> Newton-Cotes Formulas (Closed Type)
Numerical Integration --contains--> Degree of Precision of Quadrature Formulas
Numerical Integration --contains--> Derivation of Integration Rules from Newton-Cotes Formula
Numerical Integration --contains--> Integration using Central Difference Formulas
Numerical Integration --contains--> Euler-Maclaurin Summation Formula
Numerical Integration --contains--> Error Analysis in Numerical Integration
Numerical Integration --contains--> Solved Problems on Numerical Integration
Numerical Integration --contains--> Exercises on Numerical Integration
Numerical Analysis --contains--> Solution of Algebraic and Transcendental Equations
Solution of Algebraic and Transcendental Equations --contains--> Introduction to Nonlinear Equations
Solution of Algebraic and Transcendental Equations --contains--> Location of Roots and Interval Methods
Solution of Algebraic and Transcendental Equations --contains--> Bisection Method
Solution of Algebraic and Transcendental Equations --contains--> Fixed Point Iteration Method
Solution of Algebraic and Transcendental Equations --contains--> Convergence Analysis of Iterative Methods
Solution of Algebraic and Transcendental Equations --contains--> Newton-Raphson Method
Solution of Algebraic and Transcendental Equations --contains--> Generalized Newton’s Method and Root Extraction
Solution of Algebraic and Transcendental Equations --contains--> Regula-Falsi Method
Solution of Algebraic and Transcendental Equations --contains--> Computational Algorithms for Root Finding
Solution of Algebraic and Transcendental Equations --contains--> Graeffe’s Root Squaring Method
Solution of Algebraic and Transcendental Equations --contains--> Comparison of Root-Finding Methods
Solution of Algebraic and Transcendental Equations --contains--> Solved Problems on Root Finding Methods
Solution of Algebraic and Transcendental Equations --contains--> Exercises on Root Finding Methods
Numerical Analysis --contains--> System of Linear Algebraic Equations
System of Linear Algebraic Equations --contains--> Introduction to Systems of Linear Equations
System of Linear Algebraic Equations --contains--> Direct and Iterative Methods Overview
System of Linear Algebraic Equations --contains--> Gauss Elimination Method
System of Linear Algebraic Equations --contains--> Pivoting Techniques
System of Linear Algebraic Equations --contains--> Gauss-Jordan Method
System of Linear Algebraic Equations --contains--> Matrix Inversion Method
System of Linear Algebraic Equations --contains--> LU Decomposition
System of Linear Algebraic Equations --contains--> Iterative Methods
System of Linear Algebraic Equations --contains--> Gauss-Jacobi Iteration Method
System of Linear Algebraic Equations --contains--> Gauss-Seidel Iteration Method
System of Linear Algebraic Equations --contains--> Convergence Criteria
System of Linear Algebraic Equations --contains--> Error Analysis in Linear Systems
System of Linear Algebraic Equations --contains--> Solved Problems
System of Linear Algebraic Equations --contains--> Exercises
Numerical Analysis --contains--> Numerical Solution of Ordinary Differential Equations (First Order)
Numerical Solution of Ordinary Differential Equations (First Order) --contains--> Introduction to Numerical Solution of ODEs
Numerical Solution of Ordinary Differential Equations (First Order) --contains--> Euler’s Method
Numerical Solution of Ordinary Differential Equations (First Order) --contains--> Modified Euler Method (Euler-Cauchy Method)
Numerical Solution of Ordinary Differential Equations (First Order) --contains--> Picard’s Method of Successive Approximations
Numerical Solution of Ordinary Differential Equations (First Order) --contains--> Taylor Series Method
Numerical Solution of Ordinary Differential Equations (First Order) --contains--> Runge-Kutta Methods
Numerical Solution of Ordinary Differential Equations (First Order) --contains--> Higher Order Runge-Kutta Methods (RK2, RK4)
Numerical Solution of Ordinary Differential Equations (First Order) --contains--> Predictor-Corrector Methods
Numerical Solution of Ordinary Differential Equations (First Order) --contains--> Milne’s Predictor-Corrector Method
Numerical Solution of Ordinary Differential Equations (First Order) --contains--> Error Analysis in Numerical ODE Methods
Numerical Solution of Ordinary Differential Equations (First Order) --contains--> Step Size and Stability Considerations
Numerical Solution of Ordinary Differential Equations (First Order) --contains--> Solved Problems on Numerical ODE Methods
Numerical Solution of Ordinary Differential Equations (First Order) --contains--> Exercises on Numerical ODE Methods
Numerical Analysis --contains--> Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors --contains--> Introduction to Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors --contains--> Matrix Polynomials and Characteristic Equation
Eigenvalues and Eigenvectors --contains--> Characteristic (Eigen) Values and Eigenvectors
Eigenvalues and Eigenvectors --contains--> Properties and Relations of Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors --contains--> Power Method for Dominant Eigenvalue
Eigenvalues and Eigenvectors --contains--> Inverse Power Method for Smallest Eigenvalue
Eigenvalues and Eigenvectors --contains--> Shifted Power Method
Eigenvalues and Eigenvectors --contains--> Convergence of Eigenvalue Methods
Eigenvalues and Eigenvectors --contains--> Error Analysis in Eigenvalue Computation
Eigenvalues and Eigenvectors --contains--> Solved Problems on Eigenvalues and Eigenvectors
Eigenvalues and Eigenvectors --contains--> Exercises on Eigenvalues and Eigenvectors

Numerical Analysis

Learning structure

Numerical Analysis Learning Map

Concepts

Relationships

Chapters

Causes and Estimations of Error in Calculation

Calculus of Finite Differences

Interpolation with Equal and Unequal Intervals

Numerical Differentiation

Numerical Integration

Solution of Algebraic and Transcendental Equations

System of Linear Algebraic Equations

Numerical Solution of Ordinary Differential Equations (First Order)

Eigenvalues and Eigenvectors

Curated pathways

Metric Spaces

Introduction To Discrete Mathematics