1. University of Texas @ San Antonio MAT1214 CALCULUS

2. WHERE TO FIND INFORMATION Class Website http://www.mathematicalminds.net PowerPoint Slides Formula Sheets Free Textbook MyMathLab Videos More to Come…..

3. WHAT IS CALCULUS?

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

5. MAKE IT LINEAR

6. 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)

7. 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.)

8. REVIEW MATERIAL Things You Should Already Know!

9. LINEAR EQUATIONS Equation of a liney = mx + b Slope of a line = m Y-Intercept = b Greek “delta” symbol

10. SLOPE PROPERTIES Positive Slope Graph: Lines Goes Up Function: Increasing Negative Slope Graph: Line Goes Down Function: Decreasing Zero Slope Graph: Flat Function: Constant

11. FUNCTIONS Math Models Equation, graph, table, verbal representation Relation Input/Outputs

12. FUNCTIONS

13. GRAPHS OF COMMON FUNCTIONS

14. Quadratic Function Cubic Function

16. PIECEWISE FUNCTION

17. INCREASING/DECREASING FUNCTIONS

21. MINIMUM/MAXIMUM FUNCTIONS

24. TRANSFORMATIONS

25. COMPOSITE FUNCTIONS

28. AVERAGE RATE OF CHANGE

31. LOGARITHMS & EXPONENTIAL FUNCTIONS

38. CIRCLES

41. ANGLES & TRIGONOMETRY

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