#AUDIO CIVIL ENGINEERING FORMULAS SERIES#

Decibels in air and water, for instance, have different relative values. Relative units are connected to specific contexts. There are relative units like decibels (dB) and absolute units like meters. Additionally, a sound unit is any acoustic unit used to measure sound. This course attempts to give a broad background to numerical methods common to various branches of civil engineering.A vibration that travels as an acoustic wave through a transmission medium, such as a solid, liquid, or gas, is referred to as sound. Deb, Department of Civil Engineering, IIT Kharagpur. Lecture 37 - Orthogonal Basis Functions for Solving PDEs (cont.) Lecture 36 - Orthogonal Basis Functions for Solving PDEs Lecture 34 - Orthogonal Polynomials (cont.) Lecture 33 - Orthogonal Polynomials (cont.) Lecture 29 - Differential Operators (cont.) Lecture 28 - Differential Operators (cont.)

#AUDIO CIVIL ENGINEERING FORMULAS SERIES#

Lecture 26 - Series Solutions for Elliptic PDEs and Introduction to Differential Operators

Lecture 25 - Analytical Methods for Elliptic PDEs

Lecture 24 - Analytical Methods for Parabolic and Elliptic PDEs Lecture 23 - Analytical Methods for Hyperbolic and Parabolic PDEs Lecture 22 - Analytical Methods for Solving the Wave Equation Lecture 21 - Eigenfunction Solutions for the Wave Equation Lecture 20 - Nonlinear Conjugate Gradient and Introduction to PDEs Lecture 19 - Conjugate Gradient Method (cont.) Lecture 16 - ARC Length and Gradient Based Methods Lecture 15 - Solving Multidimensional Nonlinear Equations (cont.) Lecture 14 - Solving Multidimensional Nonlinear Equations Lecture 13 - Solving Nonlinear Equations (cont.) Lecture 11 - Iterative Methods for Eigenvalue Extraction Lecture 08 - Iterative Methods for Solving Linear Systems Lecture 07 - Error Bounds and Iterative Methods for Solving Linear Systems

Lecture 06 - Linear Systems - Error Bounds Lecture 03 - Introduction to Linear Systems Lecture 01 - Introduction to Numerical Methods Finally we discuss integral equations and introduce numerical techniques for their solution. Numerical integration in the time domain is discussed, emphasizing the key requirements of stability and accuracy of time integration algorithms. The concepts of weak form, finite element discretization, polynomial interpolation using Lagrange polynomials and numerical quadrature are introduced. Following this we introduce the finite element method as a generic method for the numerical solution of partial differential equations. Finite difference operators are introduced and used to solve typical initial and boundary value problems. Next we introduce the numerical solution of partial differential equations, after a brief review of canonical partial differential equations and well known analytical techniques for their solution, stressing when and why numerical solutions are necessary. Both direct and iterative solution methods are discussed. It then introduces the student to methods of solution of linear and nonlinear equations. It starts with core concepts of error estimate and accuracy of numerical solutions. This course attempts to give a broad background to numerical methods common to various branches of civil engineering.

Audio civil engineering formulas