Calculus ICalculus I

The function toolkit calculus runs on: composition and inverses, trig in radians, and exponentials with their logarithms.

1. 1Functions and Inverse Functions
2. 2Trig Functions and Equations
3. 3Exponential and Logarithm Functions

What a function approaches, from either side and at infinity: the idea every derivative and integral is built on.

1. 4Tangent Lines and Rates of Change
2. 5The Limit
3. 6One-Sided Limits
4. 7Limit Properties
5. 8Computing Limits
6. 9Infinite Limits
7. 10Limits at Infinity
8. 11Limits at Infinity: Exponentials and Logarithms
9. 12Continuity
10. 13The Precise Definition of a Limit

The instantaneous rate of change as a function in its own right, and every rule for computing it: powers, products, quotients, the chain rule and implicit differentiation.

1. 14The Definition of the Derivative
2. 15Interpreting the Derivative
3. 16Differentiation Formulas
4. 17Product and Quotient Rules
5. 18Derivatives of Trig Functions
6. 19Derivatives of Exponential and Logarithm Functions
7. 20Derivatives of Inverse Trig Functions
8. 21Derivatives of Hyperbolic Functions
9. 22The Chain Rule
10. 23Implicit Differentiation
11. 24Related Rates
12. 25Higher Order Derivatives
13. 26Logarithmic Differentiation

Using derivatives to find peaks and valleys, read the shape of a graph, optimize, approximate, and solve equations numerically.

1. 27Critical Points
2. 28Minimum and Maximum Values
3. 29Finding Absolute Extrema
4. 30Increasing, Decreasing and the First Derivative Test
5. 31Concavity and the Second Derivative Test
6. 32The Mean Value Theorem
7. 33Optimization
8. 34More Optimization Problems
9. 35L'Hôpital's Rule and Indeterminate Forms
10. 36Linear Approximations
11. 37Differentials
12. 38Newton's Method
13. 39Business Applications

Antiderivatives, the area under a curve, and the Fundamental Theorem of Calculus that ties them together.

1. 40Indefinite Integrals
2. 41Computing Indefinite Integrals
3. 42The Substitution Rule
4. 43More Substitution
5. 44The Area Problem
6. 45The Definite Integral
7. 46The Fundamental Theorem of Calculus
8. 47Substitution with Definite Integrals

Slice, approximate, add: average values, areas between curves, volumes of solids, and the work done by a changing force.

1. 48Average Function Value
2. 49Area Between Curves
3. 50Volumes by Disks and Washers
4. 51Volumes by Cylindrical Shells
5. 52Volumes by Cross-Sections
6. 53Work