Unit 1: Differentiation

Part A: Definition and Basic Rules

» Session 1: Introduction to Derivatives
» Session 2: Examples of Derivatives
» Session 3: Derivative as Rate of Change
» Session 4: Limits and Continuity
» Session 5: Discontinuity
» Session 6: Calculating Derivatives
» Session 7: Derivatives of Sine and Cosine
» Session 8: Limits of Sine and Cosine
» Session 9: Product Rule
» Session 10: Quotient Rule
» Session 11: Chain Rule
» Session 12: Higher Derivatives
» Problem Set 1

Part B: Implicit Differentiation and Inverse Functions

» Session 13: Implicit Differentiation
» Session 14: Examples of Implicit Differentiation
» Session 15: Implicit Differentiation and Inverse Functions
» Session 16: The Derivative of a^x
» Session 17: The Exponential Function, its Derivative, and its Inverse
» Session 18: Derivatives of other Exponential Functions
» Session 19: An Interesting Limit Involving e
» Session 20: Hyperbolic Trig Functions
» Problem Set 2

Exam 1

» Session 21: Review for Exam 1 - Computing Derivatives Using Differentiation Rules
» Session 22: Materials for Exam 1

Unit 2: Applications of Differentiation

Part A: Approximation and Curve Sketching

» Session 23: Linear Approximation
» Session 24: Examples of Linear Approximation
» Session 25: Introduction to Quadratic Appoximation
» Session 26: Using Quadratic Approximations
» Session 27: Sketching Graphs I - Polynomials and Rational Functions
» Session 28: Sketching Graphs II - General Strategies
» Problem Set 3

Part B: Optimization, Related Rates and Newton's Method

» Session 29: Optimization Problems
» Session 30: Optimization Problems II
» Session 31: Related Rates
» Session 32: Ring on a String
» Session 33: Newton's Method
» Problem Set 4

Part C: Mean Value Theorem, Antiderivatives and Differential Equations

» Session 34: Introduction to the Mean Value Theorem
» Session 35: Using the Mean Value Theorem
» Session 36: Differentials
» Session 37: Antiderivatives
» Session 38: Integration by Substitution
» Session 39: Introduction to Differential Equations
» Session 40: Separation of Variables
» Problem Set 5

Exam 2

» Session 41: Review for Exam 2
» Session 42: Materials for Exam 2

Unit 3: The Definite Integral and its Applications

Part A: Definition of the Definite Integral and First Fundamental Theorem

» Session 43: Definite Integrals
» Session 44: Adding Areas of Rectangles
» Session 45: Some Easy Integrals
» Session 46: Riemann Sums
» Session 47: Introduction of the Fundamental Theorem of Calculus
» Session 48: The Fundamental Theorem of Calculus
» Session 49: Applications of the Fundamental Theorem of Calculus
» Session 50: Combining the Fundamental Theorem and the Mean Value Theorem
» Problem Set 6

Part B: Second Fundamental Theorem, Areas, Volumes

» Session 51: The Second Fundamental Theorem of Calculus
» Session 52: Proving the Fundamental Theorem of Calculus
» Session 53: New Functions From Old
» Session 54: The Second Fundamental Theorem and ln(x)
» Session 55: Creating New Functions Using the Second Fundamental Theorem
» Session 56: Geometric Interpretation of Definite Integrals
» Session 57: How to Calculate Volumes
» Session 58: Volume of a Sphere, Revolving About x-axis
» Session 59: Volume of a Parabaloid, Revolving About y-axis
» Problem Set 7

Part C: Average Value, Probability and Numerical Integration

» Session 60: Integrals and Averages
» Session 61: Integrals and Weighted Averages
» Session 62: Integrals and Probability
» Session 63: Numerical Integration
» Session 64: Numerical Integration, Continued
» Session 65: Bell Curve, Conclusion
» Problem Set 8

Exam 3

» Session 66: Review for Exam 3
» Session 67: Materials for Exam 3

Unit 4: Techniques of Integration

Part A: Trigonometric Powers, Trigonometric Substitution and Completing the Square

» Session 68: Integral of sinⁿ(x) cos^m(x), Odd Exponents
» Session 69: Integral of sinⁿ(x) cos^m(x), Even Exponents
» Session 70: Preview of Trig Substitution and Polar Coordinates
» Session 71: Integrals Involving secant, cosecant and cotangent
» Session 72: Trig Substitution
» Session 73: Completing the Square
» Problem Set 9

Part B: Partial Fractions, Integration by Parts, Arc Length, and Surface Area

» Session 74: Integration by Partial Fractions
» Session 75: Advanced Partial Fractions
» Session 76: Integration by Parts
» Session 77: Volume of a Wine Glass
» Session 78: Computing the Length of a Curve
» Session 79: Surface Area
» Problem Set 10

Part C: Parametric Equations and Polar Coordinates

» Session 80: Parametric Curves
» Session 81: Examples Using Parametrized Curves
» Session 82: Polar Coordinates
» Session 83: Polar Coordinates, Continued
» Session 84: Polar Coordinates and Graphing
» Problem Set 11

Exam 4

» Session 85: Review for Exam 4
» Session 86: Materials for Exam 4

Unit 5: Exploring the Infinite

Part A: L'Hospital's Rule and Improper Integrals

» Session 87: L'Hospital's Rule
» Session 88: Examples of L'Hospital's Rule
» Session 89: L'Hospital's Rule and Rates of Growth
» Session 90: Advanced Examples of L'Hospital's Rule
» Session 91: Improper Integrals
» Session 92: Integral Comparison
» Session 93: Indefinite Integrals and Singularities

Part B: Taylor Series

» Session 94: Infinite Series
» Session 95: Series Comparison
» Session 96: Stacking Blocks
» Session 97: Power Series
» Session 98: Taylor's Series
» Session 99: Taylor's Series, Continued
» Session 100: Operations on Power Series
» Session 101: Conclusion

Final Exam

» Session 102: Materials for Final Exam