University of San Antonio MAT1214 CALCULUS.

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Presentation transcript:

University of San Antonio MAT1214 CALCULUS

WHERE TO FIND INFORMATION Class Website PowerPoint Slides Formula Sheets Free Textbook MyMathLab Videos More to Come…..

WHAT IS CALCULUS?

Unchanging Force Speed Changing Steepness of incline Amount of energy MATHEMATICS OF CHANGE

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.)

REVIEW MATERIAL Things You Should Already Know!

LINEAR EQUATIONS Equation of a liney = mx + b Slope of a line = m Y-Intercept = b 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

Angles Identities Formulas Sum/Difference Double-Angle Half-Angle Sum-to-Product Right-Triangles Law of Sines/Cosines SEE TRIGONOMETRIC FORMULA SHEET