Jacobians and Transformation
Introduction prerequisite: Elementary Function, Jacobian, Matrix Addition: Addition of two numbers in a real line is Translation $$ x \longmapsto
Calculus, YEM
YEM
Sets and Functions, YEM
Elementary Functions
Introduction Preliminary Reference A large and practically important class of functions — the elementary functions — can be built from
Approximations, YEM
Closed Form, Approximations, and Taylor’s Theorem
Closed Form Expressions and Solutions A closed-form expression is a mathematical expression or a formula that uses only basic, well-known
Calculus, YEM
Parametric Representation
Functions of Single Variable Parametric representations arise from the need to describe relationships where quantities evolve together through an underlying
Calculus, YEM
Derivative of an Inverse Function
Application of the Chain Rule If $f$ has an inverse $f^{-1}$, the defining property of an inverse is that composing
Calculus, YEM
Partial Derivatives
When One Quantity Depends On Two Things At Once Every function of real interest may not always depend on only
Calculus, YEM
Higher-Order Derivatives
Derivatives of Derivative of a Function The derivative $f'(x)$ of a function is itself a function of $x$ — it
Calculus, YEM
Differentiation – Operations and Rules
Preliminary Reading OPERATIONS ON FUNCTIONS The five elementary functions — constant, power, exponential, logarithmic, trigonometric — are not five isolated
Calculus, Sets and Functions, YEM
Study of Rate of Changes
Change — A Daily Idea Change is not a new idea introduced by mathematics — it is something we already
Sets and Functions, YEM
Functions – Further Probing
VALUE OF THE FUNCTION The most direct way to probe a function at a point is to simply evaluate it