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Calculus Essentials at UT San Antonio: Resources, Applications, and Fundamentals

Learn about calculus, its applications in real life, and essential concepts like linear equations, functions, graphs, and trigonometry. Access PowerPoint slides, formula sheets, textbook, and videos on the class website. Perfect for students seeking to master calculus fundamentals.

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Calculus Essentials at UT San Antonio: Resources, Applications, and Fundamentals

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  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

  15. Piecewise function

  16. Increasing/decreasing functions

  17. Minimum/maximum functions

  18. transformations

  19. Composite functions

  20. Average rate of change

  21. Logarithms & exponential functions

  22. Circles

  23. Angles & trigonometry

  24. See trigonometric formula sheet • Angles • Identities • Formulas • Sum/Difference • Double-Angle • Half-Angle • Sum-to-Product • Right-Triangles • Law of Sines/Cosines

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