Applied Mathematics

Thinking & Problem Solving - Quick Reference Guide

I

Laplace Transform

Definition, Standard Functions, Linearity, Shifting Theorem, Properties, Derivatives & Integrals, Real Integrals

 II

Inverse Laplace Transform

Standard Formulae, Derivatives Method, Partial Fractions, Convolution Theorem, Differential Equations

 III

Fourier Series

Dirichlet's Conditions, Parseval's Identity, Period 2π & 2l, Even/Odd Functions, Half Range Series

 IV

Complex Variables

Analytic Functions, Cauchy-Riemann Equations, Milne-Thomson Method, Harmonic Functions, Orthogonal Trajectories

 V

Statistical Techniques

Karl Pearson's Correlation, Spearman's Rank Correlation, Regression Lines, Curve Fitting (1st & 2nd degree)

 VI

Probability

Random Variables, PDF & PMF, Expectation, Mean, Variance, Standard Deviation, Moment Generating Function

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