calculus-1-introduction-basic-review-limits-continuity-derivatives-integration-ib-ap-ab

This calculus review video tutorial provides an introduction / basic overview of the fundamental principles taught in an IB or AP calculus AB course. This video is also useful for students taking their first semester of college level calculus. It cover topics such as graphing parent functions with transformations, limits, continuity, derivatives, and integration. This video contains plenty of examples and practice problems.

Here is a list of topics:

1. Graphing Parent Functions With Transformations

2. Linear Functions, Quadratic & Cubic Functions

3. Rational Functions, Fractions, Square Roots, and Radical Functions

4. Exponential, Logarithmic and Trigonometric Functions

5. Limits - Direct Substitution, Factoring, Multiplying by the conjugation Given Radicals and Multiplying by the Common Denominator When Given Complex Fractions

6. Continuity - Point Discontinuity, Infinite Discontinuity, and Jump Discontinuity

7. 3 Step Continuity Test and Piecewise Functions

8. Average Rate of Change vs Instantaneous Rate of Change

9. Slope of the Secant Line vs Slope of the Tangent Line

10. Derivative Functions - Differentiation

11. Power Rule, Product & Quotient Rule, Chain Rule

12. Derivatives of Exponential Functions

13. Derivatives of Logarithmic Functions

14. Derivatives of Trigonometric Functions

15. Limit Definition of the Derivative f(x+h)

16. Alternative Form / Version - Limit Process

17. Relative Extreme Values - Local Minimum and Maximum Values - First Derivative Test and Sign Chart

18. Absolute Maxima and Minima

19. Critical Points, Horizontal and Vertical Tangent

20. How to find the critical numbers

21. Increasing and Decreasing Intervals and Functions

22. Concavity and Inflection Points - Second Derivative

23. Mean Value Theorem and Rolle's Theorem

24. Intermediate Value Theorem

25. Differentiation vs Integration

26. Basic Integration Rules

27. Antiderivatives, Definite Integral and Indefinite Integral

28. U-substitution Integration Technique

29. Rectilinear Particle Motion - Position, Velocity, Acceleration

30. Moving to the Right vs Moving to the left

31. When is the particle at rest or changing directions

32. Displacement vs Total Distance Traveled

33. Speeding up vs Slowing down

34. Velocity vs Speed

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