MAT1214 Calculus

1. MAT1214 Calculus University of Texas @ San Antonio

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. Mathematics of change • Changing • Steepness of incline • Amount of energy • Unchanging • Force • Speed

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. Things You Should Already Know! Review material

9. Linear equations • Equation of a line y = 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. Cubic Function Quadratic 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. See trigonometric formula sheet • Angles • Identities • Formulas • Sum/Difference • Double-Angle • Half-Angle • Sum-to-Product • Right-Triangles • Law of Sines/Cosines