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Fundamentals of Stress and Vibration 1. Mathematics for Structural mechanics
[A Practical guide for aspiring Designers / Analysts]

Mathematics for

Structural Mechanics

Contents

Introduction ..................................................................................................... 2

Applied calculus ............................................................................................... 4

Vector algebra .................................................................................................. 23

Vector product ................................................................................................. 36

Identifying right handed coordinates ............................................................ 42
Vector differentiation ...................................................................................... 44

Transformation ................................................................................................ 47

Eigen values and Eigen vectors ..................................................................... 56

Engineering curves .......................................................................................... 58
Concept of Gradient ....................................................................................... 62

Lagrangian Multipliers..................................................................................... 63

Concept of Optimization ............................................................................... 65

Fourier Series and Transforms ...................................................................... 70
Routine Engineering hand Calculations ....................................................... 74

QP No. SSC/Q4401, Version 1.0, NSQF Level 7, Compliant with Aero and Auto Industries, Page 1