MATH 26
Penn State
Course Overview
Lessons & Practice
I. Welcome
1. Trigonometry
7hr1.9.1. How to Label a Right-Angle Triangle?6 min1.9.2. Practice Level 11 min1.9.3. The Story of the 3 Primary Trig Ratios3 min1.9.4. Primary Trig Ratios--, , 5 min1.9.5. Practice Level 22 min1.9.6. Practice Level 22 min1.9.7. Example2 min1.9.8. Practice Level 11.9.9. Example3 min1.9.10. Practice Level 22 min1.9.11. Practice Level 32 min
2. Trigonometric Equations
22min3. Parametric & Polar Curves
39min4. Vectors
3hr4.1.1. What are Points, Scalars, & Vectors?2 min4.1.2. Practice: Scalar VS Vector?2 min4.1.3. 2D Vectors9 min4.1.4. Practice: 2D Vectors5 min4.1.5. Converting Between Vector Forms7 min4.1.6. Example: Converting Between Vector Forms4 min4.1.7. Practice: Cartesian Polar3 min4.1.8. Practice: Polar Cartesian3 min4.1.9. 3D Vectors3 min
4.3.1. Vector Scalar Multiplication3 min4.3.2. Vector Addition in Cartesian Form4 min4.3.3. Vector Subtraction in Cartesian Form3 min4.3.4. Practice: Vector Operations2 min4.3.5. Practice: Position Vectors3 min4.3.6. Parallelogram Rule3 min4.3.7. Example: Finding Magnitude & Direction5 min4.3.8. Practice: Finding Magnitudes4 min4.3.9. Vector Properties7 min
4.5.1. Dot Product5 min4.5.2. Example: Angle Between Vectors4 min4.5.3. Practice: Dot Product2 min4.5.4. Dot Product Properties3 min4.5.5. Practice: Dot Product Properties3 min4.5.6. Dot Product Application: Projections7 min4.5.7. Practice: Projection4 min4.5.8. Dot Product Application: Work5 min4.5.9. Example: Work5 min
4.6.1. Cross Product9 min4.6.2. Practice: Cross Product5 min4.6.3. Cross Product Properties2 min4.6.4. Practice: Cross Product5 min4.6.5. Cross Product Application: Area & Volume3 min4.6.6. Example: Area of a Parallelogram3 min4.6.7. Practice: Volume of a Parallelopiped2 min4.6.8. Cross Product Application: Torque6 min4.6.9. Example: Torque5 min
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 by factoring and simplifying radicals)
- Day 7 - 2.7 to 2.8 (Evaluating limits of the form 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
- Day 27 - 6.3 & 6.4 Review and Derivative of Exponential Functions
- 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 and 12.2 Distance from a Point to a Plane in
- Day 45 - 12.3 Distance from a Point to a Line in