My question is: usually, a partial differential equation, for example, those coming from physics, is written in a language of vector calculus in a local coordinate. Is there anyway (or any algorithm) that we can use to rewrite it using language of differential forms, tensor, exterior calculus, Hodge star and other operators which are coordinate independent? An example, the Grad f can be rewritten as a geometric form: (df)#, where # is a sharp operator turning a one-form into a vector. I am currently facing this problem to turn a partial differential equation into its coordinate-independent form, which involves forms, tensors, exterior calculus and other operators.

Thank you for anyone who help me about this problem!

My question is: usually, a partial differential equation, for example, those coming from physics, is written in a language of vector calculus in a local coordinate. Is there any way (or any algorithm) that we can use to rewrite it using language of differential forms, tensor, exterior calculus, Hodge star and other operators which are coordinate independent? An example, the Grad f can be rewritten as a geometric form: (df)#, where # is a sharp operator turning a one-form into a vector. I am currently facing this problem to turn a partial differential equation into its coordinate-independent form, which involves forms, tensors, exterior calculus and other operators.

Thank you for anyone who help me about this problem!

My question is: usually, a partial differential equation, for example, those coming from physics, is written in a lauguage of vector calculus in a local coordinate, is there anyway (or any algorithm) that we can use to rewrite it using language of differential forms, tensor, exterior calculus, hodge star and other operators which are coordinate independent. An example, the Grad f can be rewritten as a geometric form: (df)#, where # is a sharp operator turing a one-form into a vector. I am currently facing this problem to turn a partial differential equation into its coordinate-independent form, which involves forms, tensors, exterior calculus and other operators.

Thank you for oneany who help me about this problem!

My question is: usually, a partial differential equation, for example, those coming from physics, is written in a language of vector calculus in a local coordinate. Is there anyway (or any algorithm) that we can use to rewrite it using language of differential forms, tensor, exterior calculus, Hodge star and other operators which are coordinate independent? An example, the Grad f can be rewritten as a geometric form: (df)#, where # is a sharp operator turning a one-form into a vector. I am currently facing this problem to turn a partial differential equation into its coordinate-independent form, which involves forms, tensors, exterior calculus and other operators.

Thank you for anyone who help me about this problem!