Syllabus of lectures:
- Sets. Mathematical induction.
- Rational numbes. Which numbers have rational square roots? What is a real number? Complex numbers.
- The formal rules of algebra. Completing the square. Solving a quadratic equation by completing the square. The quadratic formula. Synthetic division by x − a. The fundamental theorem of algebra.
- Functions. What is a function? Functional notation. A function of a function. The graph of a function. Coördinate pairs of a function. Odd and even functions.
- Basic graphs. The constant function. The identity function. The absolute value function. A parabola. The square root function. The cubic function. Translations of a graph.
- Linear functions. The graph of a first degree equation -- a straight line. Polynomials of the second degree. Solving a quadratic equation by factoring. A double root. Quadratic inequalities. The sum and product of the roots.
- Polynomial functions. Definition of a polynomial in x. The degree of a term and of a polynomial. The leading coefficient. The general form of a polynomial. The roots, or zeros, of a polynomial. The polynomial equation. The roots of a polynomial.
- The slope of a straight line. Definition of the slope. Positive and negative slope. A straight line has only one slope. Perpendicular lines.
- Rational functions.
- Inverse functions. Definition of inverses. Constructing the inverse. The graph of an inverse function.
- Logarithmic and exponential functions.
Logarithms.The system of common logarithms. The system of natural logarithms. The three laws of logarithms. Change of base.
- Trigonometric functions.
- Analytic geometry.
- Sets. Mathematical induction.
- Rational numbes. Which numbers have rational square roots? What is a real number? Complex numbers.
- The formal rules of algebra. Completing the square. Solving a quadratic equation by completing the square. The quadratic formula. Synthetic division by x − a. The fundamental theorem of algebra.
- Functions. What is a function? Functional notation. A function of a function. The graph of a function. Coördinate pairs of a function. Odd and even functions.
- Basic graphs. The constant function. The identity function. The absolute value function. A parabola. The square root function. The cubic function. Translations of a graph.
- Linear functions. The graph of a first degree equation -- a straight line. Polynomials of the second degree. Solving a quadratic equation by factoring. A double root. Quadratic inequalities. The sum and product of the roots.
- Polynomial functions. Definition of a polynomial in x. The degree of a term and of a polynomial. The leading coefficient. The general form of a polynomial. The roots, or zeros, of a polynomial. The polynomial equation. The roots of a polynomial.
- The slope of a straight line. Definition of the slope. Positive and negative slope. A straight line has only one slope. Perpendicular lines.
- Rational functions.
- Inverse functions. Definition of inverses. Constructing the inverse. The graph of an inverse function.
- Logarithmic and exponential functions.
Logarithms.The system of common logarithms. The system of natural logarithms. The three laws of logarithms. Change of base.
- Trigonometric functions.
- Analytic geometry.