MATH 21

Penn State

Course Overview

Lessons & Practice

I. Welcome

6. Quadratic Inequalities [Coming Soon!]
    7. Complex Numbers [Coming Soon!]

      I Welcome

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      Welcome to Calculus & Vectors!

      My name is Jess and I'm the instructor for this course.

      Feel free to go through this course at your own pace
      • Use the table of contents 📃 on the left to skip to parts you need help with
      • Watch the video ▶ or read the written lessons 📖
      • Speed up ⏩ or slow down ⏪ the videos
      • Use the "Ask a question"❓ feature below each lesson/question any time!


      Recommended Study Schedule (Each day is ~40-60 minutes)

      Chapter 1 - Review
      • Day 1 - Allow yourself about a day to complete this review chapter

      Chapter 2 - Rate of Change & Limits
      • Day 2 - 2.1 The Slope of Tangent Lines
      • Day 2 - 2.1 The Slope of Tangent Lines
      • Day 4 - 2.2 Rates of Change
      • Day 5 - 2.3 Limits
      • Day 6 - 2.4 to 2.6 (Evaluating limits of the form 00\frac{0}{0} by factoring and simplifying radicals)
      • Day 7 - 2.7 to 2.8 (Evaluating limits of the form 00\frac{0}{0} by simplifying absolute values and substitution)
      • Day 8 - Continuity

      Chapter 3 - Derivatives of Polynomials
      • Day 9 - 3.1 Intro to Derivatives & Differentiability
      • Day 10 - 3.2 Derivative Rules
      • Day 11 - 3.2 Derivative Rules
      • Day 12 - 3.3 Product Rule
      • Day 13 - 3.3 Product Rule
      • Day 14 - 3.4 Quotient Rule
      • Day 15 - 3.5 Chain Rule
      • Day 16 - 3.5 Chain Rule

      Chapter 4 - Derivative Application
      • Day 17 - 4.1 HIgher Order Derivative
      • Day 18 - 4.2 Max & Min on a Closed Interval
      • Day 19 - 4.3 Optimization Problems
      • Day 20 - 4.3 Optimization Problems

      Chapter 5 - Curve Sketching
      • Day 21 - 5.1 Increasing & Decreasing Intervals
      • Day 22 - 5.2 Critical Points & Local Max/Min
      • Day 23 - 5.3 Inflection Points & Concavity
      • Day 24 - 5.4 Asymptotes
      • Day 25 - 5.5 Curve Sketching

      Chapter 6 - Derivative of Exponential & Logarithmic Functions
      • Day 26 - 6.1 & 6.2 Review and Derivative of Exponential Functions y=bxy=b^x
      • Day 27 - 6.3 & 6.4 Review and Derivative of Exponential Functions y=exy=e^x
      • Day 28 - 6.5 Optimization Problems

      Chapter 7: Derivative of Trig Functions
      • Day 29 - 7.1 & 7.2 Review and Derivative of Trig Functions
      • Day 30 - 7.3 Optimization Problems


      Chapter 8: Vectors
      • Day 31 - 8.1 Introduction to Vectors
      • Day 32 - 8.2 Magnitude of a Vector + 8.3 Vector Operations
      • Day 33 - 8.4 Vector Application

      Chapter 9: Vector Products
      • Day 34 - 9.1 & 9.2 Dot Product and Applications
      • Day 35 - 9.3 & 9.4 Cross Product and Applications

      Chapter 10 - Equations of Lines & Planes
      • Day 36 - 10.1 Equations of a Line in R2 & R3 (10.1.1 - 10.1.7)
      • Day 37 - 10.1 Equations of a Line in R2 & R3 (10.1.8 - 10.1.12)
      • Day 38 - 10.2 Equations of Planes in R3 (10.2.1 - 10.2.5)
      • Day 39 - 10.2 Equations of Planes in R3 (10.2.6 - 10.2.11)

      Chapter 11 - Intersection of Lines & Planes
      • Day 40 - 11.1 Intersection of 2 Lines
      • Day 41 - 11.2 Intersection of a Line & Plane
      • Day 42 - 11.3 Intersection of 2 Planes
      • Day 43 - 11.4 Intersection of 3 Planes

      Chapter 12 - Distance Between Lines & Planes
      • Day 44 - 12.1 Distance from a Point to a Line in R2R^2 and 12.2 Distance from a Point to a Plane inR3R^3
      • Day 45 - 12.3 Distance from a Point to a Line in R3R^3