Mathematical Methods in Engineering and Science (Video) - Study24x7

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# Mathematical Methods in Engineering and Science (Video)

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Applied Linear Algebra. Nonlinear Optimization. Numerical Methods. Vector and Complex Analysis. Differential Equations and Applications. Approximation Techniques.

• Total 8 Modules
• 40 Videos
• Published on 26 June, 2019

## Module I. Solution of Linear Systems

• Introduction

52m
• Basic Ideas of Applied Linear Algebra

52m
• Systems of Linear Equations

51m
• Square Non-Singular Systems

59m
• Ill-Conditioned and Ill-Posed Systems

55m

## Module II. The Algebraic Eigenvalue Problem

• The Algebraic Eigenvalue Problem

55m
• Canonical Forms, Symmetric Matrices

55m
• Methods of Plane Rotations

56m
• Householder Method, Tridiagonal Matrices

1h 60 min
• QR Decomposition, General Matrices

57m

## Module III. Selected Topics in Linear Algebra and Calculus

• Singular Value Decomposition

57m
• Vector Space: Concepts

54m
• Multivariate Calculus

56m
• Vector Calculus in Geometry

1h 63 min
• Vector Calculus in Physics

59m

## Module IV. An Introductory Outline of Optimization Techniques

• Solution of Equations

54m
• Introduction to Optimization

54m
• Multivariate Optimization

55m
• Constrained Optimization: Optimality Criteria

55m
• Constrained Optimization: Further Issues

56m

## Module V. Selected Topics in Numerical Analysis

• Interpolation

58m
• Numerical Integration

53m
• Numerical Solution of ODE's as IVP

53m
• Boundary Value Problems, Question of Stability in IVP Solution?

55m
• Stiff Differential Equations, Existence and Uniqueness Theory

58m

## Module VI. Ordinary Differential Equations

• Theory of First-Order ODE's

53m
• Linear Second Order ODE's

1h 61 min
• Methods of Linear ODE's

1h 61 min
• ODE Systems

53m
• Stability of Dynamic Systems

1h 61 min

## Module VII. Application of ODE\'s in Approximation Theory

• Series Solutions and Special Functions

1h 61 min
• Sturm-Liouville Theory

1h 60 min
• Approximation Theory and Fourier Series

1h 60 min
• Fourier Integral to Fourier Transform, Minimax Approximation

55m

## Module VIII. Overviews: PDE\'s, Complex Analysis and Variational Calculus

• Calculus of Variations

55m
• Separation of Variables in PDE's, Hyperbolic Equations

54m
• Parabolic and Elliptic Equations, Membrane Equation

51m
• Analytic Functions

51m
• Integration of Complex Functions

58m
• Singularities and Residues

57m

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