The Real Numbers and the Cartesian Plane.
- Notation for the logic structure of Mathematics: Quantifiers, Implications and Equivalence.
- The real numbers. The real line.
- Absolute value and distance on the real line. Intervals: segments and rays. Intersection and union of sets. Inequalities.
- Points, distance and the midpoint formula.
- Equations. Straight lines. Slope of line. General equation of a line. Slope-point equation. Equation of a line determined by two points.
- Circles and Intersections.
- Linear system of equations with two unknowns.
- Gauss elimination method for linear systems.
- Regions defined in the plane by linear inequalities and system of inequalities with two unknowns. Solution regions. Geometric interpretation.
Polynomials and Rational expressions.
- Operations with polynomials. Special binomial products.
- Quadratic equations. Parabolas. Biquadratic equations.
- Roots of polynomials. Factoring polynomials. Synthetic division. Integer roots of polynomials. Ruffini¿s rule.
- Rational expressions. Operations.Equations and System of Equations.
Functions, properties and basic functions.
- Concept of a function.
- Domain and range of a function. The graph of a function.
- Inverse function.
- Composite function.
- Linear functions.
- Radical functions.
- Piecewise defined functions.
- Function transformation. Translations, dilations and symmetry. The absolute value of a function.
Exponential, logarithmic and trigonometric functions.
- Exponential functions.
- Logarithm functions.
- Trigonometrically functions.
- Radical equations.
- Exponential and logarithm equations.
Limits of Functions. Continuity.
- Continuity. Types of discontinuities.
- Limits of a function at a point. Continuity.
- Finding limits of a function at a point.
- Infinite limits.
- Asymptotes. Vertical, horizontal and slant (oblique) asymptotes.
- Rational, exponential and logarithmic asymptotes.
- Continuity. Types of discontinuity. Intermediate value Theorem.
- The derivative of a function. Tangent lines. Instantaneous rate of change.
- The derivative function.
- Rules for differentiation. The chain rule. Implicit differentiation.
- Application of the derivative. Growth of a function. Extreme points of a function. Weierstrass¿ Theorem. Optimization problems.
- Rolle¿s Theorem. Mean value Theorem. L¿Hôpital¿s rule.
- Taylor polynomial.
- Concavity and convexity.
- Applications: Curve sketching of polynomial and rational functions.
- Antiderivatives. Finding antiderivatives. Basic integration rules.
- Definite integral. The fundamental Theorem of Calculus.
-Techniques of integration: Integration by substitution. Integration by parts. Simple fractions.
- Applications: Area between two curves.