university of texas @ san antonio mat1214 calculus
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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
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