1、Advanced Mathematics,Wan Yuan School of Science, WHUT My mailbox: My phone: 13971622102 Class mailbox: ,Some rules for our class,Please take notes Please turn off your cell-phones If you are late, just come in and join us Ask questions as soon as possible Do homework by yourself Hand up your homewo
2、rk in time,Introduction,Advanced mathematics is a primary course for collage student.,In this class, we will introduce some basic concepts and some useful tools of mathematics for your further study or research.,Part one Theoretical basis of Calculus The differential Calculus and its Application The
3、 integral Calculus and its Application,I. The Integers and the Rational Numbers,1. Set (集合),Def: A collection of numbers which share the same property.,1.1 Preliminaries for Calculus,I. The Integers and the Rational Numbers,1.1 Preliminaries for Calculus,II. Inequalities,1. Intervals （区间）,1.1 Prelim
4、inaries for Calculus,2. Neighborhood of point a (点 a 的邻域）,Geometric Interpretation: The set of point x whose distance from point a is less than,a is the center of this neighborhood, and is the radius.,II. Inequalities,1.1 Preliminaries for Calculus,II. Inequalities,3. Solve Inequalities,Solution,The
5、n the solution set is .,1.1 Preliminaries for Calculus,III. Absolute Values （绝对值）,1. Absolute value,Solution,Then we choose .,1.1 Preliminaries for Calculus,III. Absolute Values,2. Square Roots,principal roots,Quadratic Formula,are the roots for equation,1.1 Preliminaries for Calculus,IV. The Rectan
6、gular Coordinate System,1. Cartesian Coordinate （笛卡尔坐标系）,1.1 Preliminaries for Calculus,IV. The Rectangular Coordinate System,2. Distance formula,1.1 Preliminaries for Calculus,IV. The Rectangular Coordinate System,3. The Equation of a Circle,Standard form,General form,1.1 Preliminaries for Calculus,V. The Straight Line,1. The Slope of a Line （直线的斜率）,1.1 Preliminaries for Calculus,V. The Straight Line,2. The Forms of a Line,The point-slope form,The slope-intercept form,The general linear form,1.1 Preliminaries for Calculus,
