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 changein y y y2  y1
m



run changein 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