# Plane Curves, Lecture Notes - Mathematics

Plane curves, multivariable calculus, integration along curve. green's theorem , frenet serret apparatus in two dimensions, computing t and n, geometric interpretation of k, rotation index, closed curves

# Taylor Series, Lecture Notes - Mathematics

Taylor series, taylor's formula motivation and derivation, estimating the remainder, numerical applications, finite difference approximation, examples of o notation, error in trapezoidal

# Least Square and Orthogonal Functions, Lecture Notes - Mathematics

Least square and orthogonal functions, problems based on least squares, plane least square, approximations, inner product to enforce the desired orthogonality, order of differential and summation

# Plane Curves, Lecture Notes - Mathematics

Plane curves, multivariable calculus, integration along curve. green's theorem , frenet serret apparatus in two dimensions, computing t and n, geometric interpretation of k, rotation index, closed curves

# Least Square and Orthogonal Functions, Lecture Notes - Mathematics

Least square and orthogonal functions, problems based on least squares, plane least square, approximations, inner product to enforce the desired orthogonality, order of differential and summation

# Fixed Point Method, Lecture Notes - Mathematics

Fixed point method, condition for the existence of a fixed point, uniqueness, iteration method, rate of convergence, continued fractions, first order convergence, finding fixed point, higher order

# Taylor Series, Lecture Notes - Mathematics

Taylor series, taylor's formula motivation and derivation, estimating the remainder, numerical applications, finite difference approximation, examples of o notation, error in trapezoidal

# Runge Kutta Method, Lecture Notes - Mathematics

Ranga kutta method, second order, computation solution, fourth order, formulation, multi steps, taylor expand the local truncation error

# Length Minimizers are Geodesics, Lecture Notes - Mathematics

Length minimizers are geodesics, statement and theorem, create a family of variations, differentiate the length, integrate by parts, move the derivative, boundary terms are 0, integrand is identically 0, geodesics on torus, compute coefficient of...

# Parameterization of Surfaces, Lecture Notes - Mathematics

Parameterization of surfaces, reparameterization, jacobian, transforming the tangent plane and normal, tangent vectors form a vector space

# Plane Curves, Lecture Notes - Mathematics

Plane curves, multivariable calculus, integration along curve. green's theorem , frenet serret apparatus in two dimensions, computing t and n, geometric interpretation of k, rotation index, closed curves

# Taylor Series, Lecture Notes - Mathematics

Taylor series, taylor's formula motivation and derivation, estimating the remainder, numerical applications, finite difference approximation, examples of o notation, error in trapezoidal

# Trapezois Rule and Fixed Points, Lecture Notes - Mathematics

Trapezoidal rules and fixed points, trapezoidal approximation to an integral, numerical examples, zeros and fixed points, introduction, method