Polar coordinates and its relation with cartesian coordinates. Study of curves defined by parametric equations.

Limits and derivatives of real functions.

Definition and understanding of the Riemann integral concept. Computation of integrals (by using different rules) and applications (areas between curves and volumes).

Solving differential equations.

Modeling and solving real problems that involve the new concepts.

1. Real functions of a real variable
1.1 Curves defined by parametric equations.
1.2 Polar coordinates
1.3 Hyperbolic functions

2. Differential calculus
2.1 Limits, continuity, asymptotes
2.2 Derivatives, tangents and rates of change
2.3 Implicit differentiation
2.4 Weirstrass theorem of extreme value, Fermat theorem, Rolle theorem, Lagrange mean value theorem
2.5 Maxima and minima values
2.6 Indeterminate forms and L'Hospital rule
2.7 Linear approximations and differentials
2.7 Newton method

3. Integral calculus
3.1 Antiderivatives
3.2 Integration rules: by parts, by substitution, by partial fractions
3.3 Definition and geometric interpretation of integral of Riemann
3.4 The fundamental theorem of calculus
3.5 Total variation theorem
3.6 Improper integrals
3.7 Integrals' applications

4. Differential equations of first order
4.1 Separable equations
4.2 Linear equations
4.3 Euler's method

Basic calculus