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MAT1214 CALCULUS University of Texas @ San Antonio WHERE TO FIND INFORMATION • Class Website • http://www.mathematicalminds.net • PowerPoint Slides • Formula Sheets • Free Textbook • MyMathLab • Videos • More to Come….. WHAT IS CALCULUS? MATHEMATICS OF CHANGE • Unchanging • Changing • Force • Steepness of incline • Speed • Amount of energy MAKE IT LINEAR WHO USES THIS STUFF? • Electric company • • Determining length of cable between two towers Construction • Football stadium • Calculate area of a complicated, non spherical shape • Cost of material, maximum force to withstand • Businesses • The sensitivity of demand to changes in price varies with product. • Light bulbs (need) vs. iPad (want) WHO USES THIS STUFF? • Automobile industry • Maximum impact on car crash to avoid head injury (thus air bags were born) • Forensic Scientists • Estimated time of death using “Newton’s Law of Cooling” • Musicians • Approximate wave functions (detect tones on guitar, pianos, etc.) Things You Should Already Know! REVIEW MATERIAL LINEAR EQUATIONS • Equation of a line • Slope of a line = m • Y-Intercept = b y = mx + b rise changein y y y2 y1 m run changein x x x2 x1 Greek “delta” symbol SLOPE PROPERTIES • Positive Slope • Graph: Lines Goes Up • Function: Increasing • Negative Slope • Graph: Line Goes Down • Function: Decreasing • Zero Slope • Graph: Flat • Function: Constant FUNCTIONS • Math Models • Equation, graph, table, verbal representation • Relation • Input/Outputs FUNCTIONS GRAPHS OF COMMON FUNCTIONS Quadratic Function Cubic Function PIECEWISE FUNCTION INCREASING/DECREASING FUNCTIONS MINIMUM/MAXIMUM FUNCTIONS TRANSFORMATIONS COMPOSITE FUNCTIONS AVERAGE RATE OF CHANGE LOGARITHMS & EXPONENTIAL FUNCTIONS CIRCLES ANGLES & TRIGONOMETRY SEE TRIGONOMETRIC FORMULA SHEET • Angles • Identities • Formulas • Sum/Difference • Double-Angle • Half-Angle • Sum-to-Product • Right-Triangles • Law of Sines/Cosines