University of Texas @ San Antonio

MAT1214 CALCULUS

WHERE TO FIND INFORMATION• Class Website

• http://www.mathematicalminds.net

• 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 MATERIALThings You Should Already Know!

LINEAR EQUATIONS• Equation of a line y = mx + b

• Slope of a line = m

• Y-Intercept = b

12

12

change

change

xx

yy

x

y

xin

yin

run

risem

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