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Mathematical Methods in Engineering and Science (Video)
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Mathematical Methods in Engineering and Science (Video)
by Dr Bhaskar Dasgupta

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

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level English
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Program Fee
FREE
About This Course

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


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Course Curriculum
8 Sections | 40 Lecture | 37h 41min total length
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Mathematical Methods in Engineering and Science (Video)

Module I. Solution of Linear Systems

| 04h 31min total length
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    Introduction

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    Basic Ideas of Applied Linear Algebra

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    Systems of Linear Equations

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    Square Non-Singular Systems

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    Ill-Conditioned and Ill-Posed Systems

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Mathematical Methods in Engineering and Science (Video)

Module II. The Algebraic Eigenvalue Problem

| 04h 44min total length
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    The Algebraic Eigenvalue Problem

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    Canonical Forms, Symmetric Matrices

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    Methods of Plane Rotations

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    Householder Method, Tridiagonal Matrices

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    QR Decomposition, General Matrices

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Mathematical Methods in Engineering and Science (Video)

Module III. Selected Topics in Linear Algebra and Calculus

| 04h 50min total length
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    Singular Value Decomposition

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    Vector Space: Concepts

    54m <?php echo $alt; ?>
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    Multivariate Calculus

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    Vector Calculus in Geometry

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    Vector Calculus in Physics

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Mathematical Methods in Engineering and Science (Video)

Module IV. An Introductory Outline of Optimization Techniques

| 04h 36min total length
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    Solution of Equations

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    Introduction to Optimization

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    Multivariate Optimization

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    Constrained Optimization: Optimality Criteria

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    Constrained Optimization: Further Issues

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Mathematical Methods in Engineering and Science (Video)

Module V. Selected Topics in Numerical Analysis

| 04h 39min total length
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    Interpolation

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    Numerical Integration

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    Numerical Solution of ODE's as IVP

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    Boundary Value Problems, Question of Stability in IVP Solution?

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    Stiff Differential Equations, Existence and Uniqueness Theory

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Mathematical Methods in Engineering and Science (Video)

Module VI. Ordinary Differential Equations

| 04h 50min total length
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    Theory of First-Order ODE's

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    Linear Second Order ODE's

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    Methods of Linear ODE's

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    ODE Systems

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    Stability of Dynamic Systems

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Mathematical Methods in Engineering and Science (Video)

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

| 03h 57min total length
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    Series Solutions and Special Functions

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    Sturm-Liouville Theory

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    Approximation Theory and Fourier Series

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    Fourier Integral to Fourier Transform, Minimax Approximation

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Mathematical Methods in Engineering and Science (Video)

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

| 05h 28min total length
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    Calculus of Variations

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    Separation of Variables in PDE's, Hyperbolic Equations

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    Parabolic and Elliptic Equations, Membrane Equation

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    Analytic Functions

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    Integration of Complex Functions

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    Singularities and Residues

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show 5 more sections
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