Mathematics Describing the Real World: Precalculus and Trigonometry

Course Overview

Prepare yourself for success with this course on precalculus and trigonometry, authored by one of the most widely used textbooks on the subject, taught by award-winning Professor Bruce Edwards of the University of Florida. This course serves as your unrivaled introduction to precalculus, a crucial subject for mastering calculus, and aids in overcoming common challenges that students face.

With 36 intensively illustrated half-hour lectures, accompanied by a workbook containing additional explanations and problems, you will cover all major topics typical of a precalculus course. Professor Edwards employs realistic problems to illustrate concepts, helping you to engage with mathematics in the context of the real world.

Video Lectures

1. An Introduction to Precalculus-Functions – 31 min
   Review the essential concept of functions and get recommendations for the course.
2. Polynomial Functions and Zeros – 31 min
   Investigate polynomial functions, including techniques for finding their zeros.
3. Complex Numbers – 31 min
   Step into the realm of complex numbers and learn about their applications.
4. Rational Functions – 31 min
   Analyze rational functions, including domains and asymptotes.
5. Inverse Functions – 32 min
   Discover the concept of inverse functions and their graphical representations.
6. Solving Inequalities – 31 min
   Study how to graph and solve various types of inequalities.
7. Exponential Functions – 32 min
   Explore properties of exponential functions and their applications.
8. Logarithmic Functions – 30 min
   Learn about the inverse relationship between logarithmic and exponential functions.
9. Properties of Logarithms – 32 min
   Review properties of logarithms and their practical applications.
10. Exponential and Logarithmic Equations – 31 min
    Practice solving equations involving logarithms and exponents.
11. Exponential and Logarithmic Models – 31 min
    Model real-life phenomena using exponential and logarithmic equations.
12. Introduction to Trigonometry and Angles – 30 min
    Learn the techniques for measuring angles in degrees and radians.
13. Trigonometric Functions-Right Triangle Definition – 32 min
    Discover how trigonometric functions relate to right triangles.
14. Trigonometric Functions-Arbitrary Angle Definition – 32 min
    Calculate trigonometric values for any angles using the coordinate plane.
15. Graphs of Sine and Cosine Functions – 32 min
    Analyze the wave-like patterns of sine and cosine graphs.
16. Graphs of Other Trigonometric Functions – 32 min
    Study the graphs of other trigonometric functions like tangent and cotangent.
17. Inverse Trigonometric Functions – 32 min
    Understand the concept and applications of inverse trigonometric functions.
18. Trigonometric Identities – 32 min
    Learn about trigonometric identities and their importance in solving equations.
19. Trigonometric Equations – 31 min
    Hone your skills in identifying values that satisfy trigonometric equations.
20. Sum and Difference Formulas – 31 min
    Study the formulas for adding and subtracting trigonometric functions.
21. Law of Sines – 30 min
    Investigate the law of sines and its applications in triangle geometry.
22. Law of Cosines – 31 min
    Learn about the law of cosines for finding angles and sides in triangles.
23. Introduction to Vectors – 32 min
    Explore the representation of vectors and their operations.
24. Trigonometric Form of a Complex Number – 32 min
    Utilize trigonometric representation for complex numbers.
25. Systems of Linear Equations and Matrices – 31 min
    Introduction to solving systems of linear equations using matrices.
26. Operations with Matrices – 31 min
    Learn and practice various operations involving matrices.
27. Inverses and Determinants of Matrices – 30 min
    Understand how to calculate the inverse and determinant of matrices.
28. Applications of Linear Systems and Matrices – 32 min
    Explore practical problems solvable with linear systems and matrices.
29. Circles and Parabolas – 30 min
    Examine the properties of circles and parabolas through their equations.
30. Ellipses and Hyperbolas – 31 min
    Study the properties and applications of ellipses and hyperbolas.
31. Parametric Equations – 31 min
    Learn how to model motion with parametric equations.
32. Polar Coordinates – 32 min
    Explore graphing techniques using polar coordinates.
33. Sequences and Series – 32 min
    Delve into infinite sequences and series, leading to limits.
34. Counting Principles – 30 min
    Distinguish between permutations and combinations in counting problems.
35. Elementary Probability – 30 min
    Understand the basics of probability with real-world applications.
36. GPS Devices and Looking Forward to Calculus – 31 min
    Use precalculus concepts in practical applications like GPS, seeing how precalculus prepares you for calculus.