I am looking for a book recommendations for learning calculus for high school or under graduation level can you suggest me some good books which have the proper theory and can very well be used to self teach yourself.
I am looking for a book in calculus that pose over topics like: [This is the prescribed syllabus for my course]
Real valued functions of a real variable, Into, onto and one-to-one functions, sum difference, product and quotient of two functions, composite functions, absolute value, polynomial, rational, trigonometric, exponential and logarithmic functions. Limit and continuity of a function, limit and continuity of the sum, difference, product and quotient of two functions, L'Hospital rule of evaluation of limits of functions. Even and odd functions, inverse of a function, continuity of composite functions intermediate value property of continuous Functions. Derivative of a function, derivative of the sum, difference, product and quotient of two functions, chain rule, derivatives of polynomial, rational, trigonometric, inverse trigonometric, exponential and logarithmic functions, Derivatives of implicit functions, derivatives up to order two, geometrical interpretation of the derivative, tangents and normals. Increasing and decreasing functions, maximum and minimum values of a function, Rolle's theorem and I lagrange's mean value theorem.
Integration as the inverse process of differentiation, indefinite integrals of standard functions, definite integrals and their properties, fundamental theorem of integral calculus. Integration by parts, integration by the methods of substitution and partial fractions. Application of definite integrals to the determination of areas involving simple Curves Formation of ordinary differential equations, solution of homogeneous differential equations, separation of variables method, lincar first order differential equations.
Please is you know some good books ,please help me !! :)
I am going to study maths in future (I don't want a book that just touches the topics just for the sake of it, but something that goes deep into the concepts to build a very strong foundation which can help me tackle hard problems...
Edit: Actually I am from India , and as far I know in USA , the highschool mathematics is a lot less than what it is in India. I'm still in highschool and just included the Undergrad so that I can get something more . But what I forgot to mention was only the first year maybe... That is why I also included the syllabus . I think something like topological introduction to limits might be too much of an overkill