Foundations of calculus

This class is also called Freshman Mathematics. The subjects below are copied from the list for Ma 1 class in Caltech Institute.

## Subjects

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* Function
* Mathematical Induction
* Sequences and Series
* Completeness

* Integral for Step Functions
* Integral for More General Functions
* Applications of Integration
* Limits
* Continuity
* Intermediate Value Theorem
* Inversion
* Extreme - Value Theorem
* Integrability Theorem
* Mean Value Theorem for Integrals
* Derivatives
* Implicit Differentiation
* Extreme Values
* Mean Value Theorem for Derivatives
* Curve Sketching
* Fundamental Theorem of Calculus
* Integration by Substitution
* Integration by Parts
* Logarithm
* Exponential Function
* Integration by Partial Fractions
* Real Numbers
* Complex Numbers