Math

Calculus

A complete calculus course covering limits, differentiation, integration, vectors, and their applications. From evaluating limits to solving differential equations and mastering vectors. 92 lessons across 10 units.

1

Limits

8 lessons — Evaluating limits, continuity, and discontinuities

Lesson 1: Limits by Direct Evaluation Coming Soon
Lesson 2: Limits at Jump Discontinuities and Kinks Coming Soon
Lesson 3: Limits at Removable Discontinuities Coming Soon
Lesson 4: Limits at Removable Discontinuities with Trig Coming Soon
Lesson 5: Limits at Essential Discontinuities Coming Soon
Lesson 6: Limits at Infinity Coming Soon
Lesson 7: Continuity Coming Soon
Lesson 8: Determining & Classifying Discontinuities Coming Soon
2

Differentiation Basics

6 lessons — Rates of change, derivative definition, and basic rules

Lesson 9: Average Rates of Change Coming Soon
Lesson 10: Definition of the Derivative Coming Soon
Lesson 11: Instantaneous Rates of Change Coming Soon
Lesson 12: Power, Constant, and Sum Rules Coming Soon
Lesson 13: Higher Order Derivatives Coming Soon
Lesson 14: Product Rule Coming Soon
3

Differentiation Advanced

8 lessons — Chain rule, quotient rule, and logarithmic differentiation

Lesson 15: Quotient Rule Coming Soon
Lesson 16: Chain Rule Coming Soon
Lesson 17: Differentiation Rules with Tables Coming Soon
Lesson 18: Chain Rule with Trig Coming Soon
Lesson 19: Chain Rule with Inverse Trig Coming Soon
Lesson 20: Chain Rule with Natural Logarithms and Exponentials Coming Soon
Lesson 21: Chain Rule with Other Base Logs and Exponentials Coming Soon
Lesson 22: Logarithmic Differentiation Coming Soon
4

Implicit & Inverse Differentiation

2 lessons — Implicit differentiation and derivatives of inverse functions

Lesson 23: Implicit Differentiation Coming Soon
Lesson 24: Derivatives of Inverse Functions Coming Soon
5

Applications of Differentiation Part 1

10 lessons — Tangent lines, theorems, and extrema

Lesson 25: Derivative at a Value Coming Soon
Lesson 26: Slope at a Value Coming Soon
Lesson 27: Tangent Lines Coming Soon
Lesson 28: Normal Lines Coming Soon
Lesson 29: Points of Horizontal Tangents Coming Soon
Lesson 30: Rolle's Theorem Coming Soon
Lesson 31: Mean Value Theorem Coming Soon
Lesson 32: Intervals of Increase and Decrease Coming Soon
Lesson 33: Intervals of Concavity Coming Soon
Lesson 34: Relative Extrema Coming Soon
6

Applications of Differentiation Part 2

10 lessons — Optimization, curve sketching, and L'Hopital's Rule

Lesson 35: Absolute Extrema Coming Soon
Lesson 36: Optimization Coming Soon
Lesson 37: Curve Sketching Coming Soon
Lesson 38: Comparing a Function and its Derivatives Coming Soon
Lesson 39: Motion Along a Line Coming Soon
Lesson 40: Related Rates Coming Soon
Lesson 41: Differentials Coming Soon
Lesson 42: Newton's Method Coming Soon
Lesson 43: Limits in Form of Definition of Derivative Coming Soon
Lesson 44: L'Hopital's Rule Coming Soon
7

Indefinite Integration

9 lessons — Antiderivatives, substitution, and integration by parts

Lesson 45: Power Rule Coming Soon
Lesson 46: Logarithmic Rule and Exponentials Coming Soon
Lesson 47: Trigonometric Functions Coming Soon
Lesson 48: Inverse Trigonometric Forms Coming Soon
Lesson 49: Substitution with Power Rule Coming Soon
Lesson 50: Substitution with Logarithms and Exponentials Coming Soon
Lesson 51: Substitution with Trigonometric Functions Coming Soon
Lesson 52: Substitution with Inverse Trigonometric Forms Coming Soon
Lesson 53: Integration by Parts Coming Soon
8

Definite Integration

7 lessons — Riemann sums, Fundamental Theorem, and substitution

Lesson 54: Approximating Area Under a Curve Coming Soon
Lesson 55: Area Under a Curve by Limit of Sums Coming Soon
Lesson 56: Riemann Sum Tables Coming Soon
Lesson 57: First Fundamental Theorem of Calculus Coming Soon
Lesson 58: Substitution for Definite Integrals Coming Soon
Lesson 59: Mean Value Theorem for Integrals Coming Soon
Lesson 60: Second Fundamental Theorem of Calculus Coming Soon
9

Applications & Differential Equations

10 lessons — Area, volume, slope fields, and separable equations

Lesson 61: Area Under a Curve Coming Soon
Lesson 62: Area Between Curves Coming Soon
Lesson 63: Volume by Slicing — Washers and Disks Coming Soon
Lesson 64: Volume by Cylinder Method Coming Soon
Lesson 65: Volume Using Known Cross Sections Coming Soon
Lesson 66: Motion Along a Line Revisited Coming Soon
Lesson 67: Slope Fields Coming Soon
Lesson 68: Introduction to Differential Equations Coming Soon
Lesson 69: Separable Equations Coming Soon
Lesson 70: Exponential Growth and Decay Coming Soon
10

Vectors

22 lessons — Use vectors to describe moves in space, program games, and design logos

Lesson 71: Meet Vectors Coming Soon
Lesson 72: Adding Vectors Coming Soon
Lesson 73: From One to Another Coming Soon
Lesson 74: Length of a Vector Coming Soon
Lesson 75: Scaling Vectors Coming Soon
Lesson 76: Between Two Vectors Coming Soon
Lesson 77: Moving Along a Line Coming Soon
Lesson 78: Transformations with Vectors Coming Soon
Lesson 79: Translations Coming Soon
Lesson 80: Dilations Coming Soon
Lesson 81: Reflections Coming Soon
Lesson 82: Length and Direction Coming Soon
Lesson 83: Polar Coordinates Coming Soon
Lesson 84: Polar to Rectangular Coming Soon
Lesson 85: Cosine and Sine Coming Soon
Lesson 86: Vectors in Any Direction Coming Soon
Lesson 87: Rotations Coming Soon
Lesson 88: Speed Boosts Coming Soon
Lesson 89: The Dot Product Coming Soon
Lesson 90: A Formula for Dot Product Coming Soon
Lesson 91: Dot Product and Direction Coming Soon
Lesson 92: Dot Product with Components Coming Soon