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Complex Numbers. i. AppxA_01fig_PChem.jpg. Complex Conjugate. AppxA_02fig_PChem.jpg. Complex Numbers Representing Waves. Vectors. AppxA_11fig_PChem.jpg. Vector Addition and Subtraction. AppxA_12fig_PChem.jpg. Vector Products. Dot Product. Cross Product.
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Complex Numbers i AppxA_01fig_PChem.jpg
Complex Conjugate AppxA_02fig_PChem.jpg
Vectors AppxA_11fig_PChem.jpg
Vector Addition and Subtraction AppxA_12fig_PChem.jpg
Vector Products Dot Product Cross Product c – Unit vector perpendicular to a & b AppxA_13fig_PChem.jpg
Matrices and Rotations AppxA_14fig_PChem.jpg
AppxA_14fig_PChem.jpg Matrices and Rotations Rz(120o) = Rz(180o) =
Eigen Representation of ANXN For a general ANXN:
Eigen Representation Real Symmetric Matrix For a symmetric ANXN:
Eigen Representation Hermitian Matrix For a Hermitian ANXN:
Differentiation AppxA_03fig_PChem.jpg
Derivatives of Some Important Functions AppxA_04fig_PChem.jpg
Some Basic Rules Linearity Product Rule Quotient Rule Chain Rule
Higher Order Derivatives And Optimization AppxA_05fig_PChem.jpg
AppxA_05fig_PChem.jpg Higher Order Derivatives And Optimization
AppxA_08fig_PChem.jpg Integration
Integration Linearity Power Rule AppxA_08fig_PChem.jpg
Even and Odd Functions Even Functions Unless f(x) is an even periodic function, Symmetric about x-axis, and a=2p Odd Functions
Power Series Approximation of Functions an = n! Diverges an = 1/n! Converges AppxA_07fig_PChem.jpg
Taylor Series Expansions f(x) = exp(x) about x = 0 f(x) = ln(1+x) about x = 0 AppxA_06fig_PChem.jpg
AppxA_06fig_PChem.jpg Fourier Series
Second Order Linear Differential Equations Trial function
Second Order Linear Differential Equations Initial Conditions: