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.

https://www.patreon.com/MathScienceTutor

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