Lessons

I will post reviews of in-class lessons and key concepts as I write them.

Single-Variable

1 Limits

  1. 1.1—Relations, Functions, and Graphs (Review)
  2. 1.2—The Limit
  3. 1.3—Continuity
  4. 1.4—More on Limits
  5. 1.5—Evaluating Limits — The Basics
  6. 1.6—Delta-Epsilon: The Formal Definition of a Limit
  7. 1.7—Proofs with Delta-Epsilon
  8. 1.8—Delta-Epsilon with Special Types of Limits

2 The Derivative

  1. 2.1—The Tangent Problem and Its Solution: the Derivative
  2. 2.2—How to Differentiate: Monomials, Sine, and Cosine
  3. 2.3—Differentiating Combinations of Functions
  4. 2.4—The Chain Rule
  5. 2.5—Implicit Differentiation
  6. 2.6—Derivatives of Inverse Trigonometric Functions
  7. 2.7—Exponential and Logarithmic Derivatives
  8. 2.8—Higher-Order Derivatives
  9. Differentiation Formula Summary

3 Applications of the Derivative

  1. 3.1—Related Rates
  2. 3.2—Minima and Maxima
  3. 3.3—The Mean Value Theorem
  4. 3.4—Curve Sketching
  5. 3.5—Optimization
  6. 3.6—Newton’s Method
  7. 3.7—Antiderivatives
  8. 3.8—Indeterminate Forms and L’Hôpital’s Rule

4 The Integral

  1. 4.1—The Area Problem and Its Solution: the Definite Integral
  2. 4.2—The Fundamental Theorem of Calculus
  3. 4.3—Indefinite Integrals
  4. 4.4—Integration by u-Substitution
  5. 4.5—Integration by Parts
  6. 4.6—Integration by Trigonometric Substitution
  7. 4.7—Integration by Partial Fractions
  8. 4.8—Integration Review
  9. 4.9—Approximate Integration and Simpson’s Rule
  10. 4.10—Improper Integrals
  11. Antiderivative Summary

5 Applications of the Integral

  1. 5.1—Volume by Discs and Washers
  2. 5.2—Volume by Cylindrical Shells
  3. 5.3—Average Value
  4. 5.4—Arc Length
  5. 5.5—Surface Area of Surfaces of Revolution

6 Differential Equations

  1. 6.1—Differential Equations: An Introduction
  2. 6.2—Direction Fields and Euler’s Method
  3. 6.3—Solving Differential Equations by Separation of Variables
  4. 6.4—The Logistic Equation

7 Non-Cartesian Coordinate Systems

  1. 7.1—Calculus with Parametric Curves
  2. 7.2—Calculus with Polar Equations

8 Sequences and Series

  1. 8.1—Sequences (Review)
  2. 8.2—Series
  3. 8.3—The Integral Test
  4. 8.4—The Comparison Tests
  5. 8.5—Absolute Convergence and the Ratio Test
  6. 8.6—Functions as Power Series
  7. 8.7—Taylor Series

Multivariable

1 Space Curves (Lessons by Carlo Angiuli)

  1. 1.1—Vectors and Space Curves
  2. 1.2—Derivatives and Integrals of Vector Functions
  3. 1.3—The TNB Frame
  4. 1.4—Curvature

2 Generalizing the Derivative

  1. 2.1—Functions of Several Variables (by Carlo Angiuli)
  2. 2.2—Limits, Again (by Carlo Angiuli)
  3. 2.3—Partial Derivatives
  4. 2.4—The Chain Rule
  5. 2.5—The Second Derivative Test
  6. 2.6—The Gradient
  7. 2.7—Lagrange Multipliers

3 Generalizing the Integral

  1. 3.1—Line Integrals
  2. 3.2—Double Integrals
  3. 3.3—Surface Integrals
  4. 3.4—Triple Integrals
  5. 3.5—Change of Variables with Multiple Integrals

4 Vector Fields and More Integrals

  1. 4.1—Vector Fields
  2. 4.2—Work: Line Integrals II
  3. 4.3—Flux: Surface Integrals II
  4. 4.4—Divergence and Curl
  5. 4.5—Green’s Theorem
  6. 4.6—Stokes’ Theorem
  7. 4.7—The Divergence Theorem

Valid XHTML 1.1!
Valid CSS!