Calculus

Calculus topics learn everything from limits to derivatives to integrals to vector calculus. Created by Khan Academy.

Recommended that you have a good foundation in Precalculus before taking this course.

Average Course Length

25 hours

Skill Level

Intermediate

Pick a lesson


1: Newton Leibniz and Usain Bolt
2: Introduction to Limits (HD)
3: Limit Examples (part 1)
4: Limit Examples (part 2)
5: Limit Examples (part3)
6: Limit Examples w/ brain malfunction on first prob (part 4)
7: Squeeze Theorem
8: Proof: lim (sin x)/x
9: More Limits
10: Epsilon Delta Limit Definition 1
11: Epsilon Delta Limit Definition 2
12: Calculus: Derivatives 1 (new HD version)
13: Calculus: Derivatives 2 (new HD version)
14: Calculus: Derivatives 2.5 (new HD version)
15: Derivative Intuition Module
16: The Chain Rule
17: Chain Rule Examples
18: Even More Chain Rule
19: Product Rule
20: Quotient Rule
21: Derivatives (part 9)
22: Proof: d/dx(x^n)
23: Proof: d/dx(sqrt(x))
24: Proof: d/dx(ln x) = 1/x
25: Proof: d/dx(e^x) = e^x
26: Proofs of Derivatives of Ln(x) and e^x
27: Extreme Derivative Word Problem (advanced)
28: Implicit Differentiation
29: Implicit Differentiation (part 2)
30: More implicit differentiation
31: More chain rule and implicit differentiation intuition
32: Trig Implicit Differentiation Example
33: Calculus: Derivative of x^(x^x)
34: Introduction to L'Hopital's Rule
35: L'Hopital's Rule Example 1
36: L'Hopital's Rule Example 2
37: L'Hopital's Rule Example 3
38: Maxima Minima Slope Intuition
39: Inflection Points and Concavity Intuition
40: Monotonicity Theorem
41: Calculus: Maximum and minimum values on an interval
42: Calculus: Graphing Using Derivatives
43: Calculus Graphing with Derivatives Example
44: Graphing with Calculus
45: Optimization with Calculus 1
46: Optimization with Calculus 2
47: Optimization with Calculus 3
48: Optimization Example 4
49: Introduction to rate-of-change problems
50: Equation of a tangent line
51: Rates-of-change (part 2)
52: Ladder rate-of-change problem
53: Mean Value Theorem
54: The Indefinite Integral or Anti-derivative
55: Indefinite integrals (part II)
56: Indefinite Integration (part III)
57: Indefinite Integration (part IV)
58: Indefinite Integration (part V)
59: Integration by Parts (part 6 of Indefinite Integration)
60: Indefinite Integration (part 7)
61: Another u-subsitution example
62: Introduction to definite integrals
63: Definite integrals (part II)
64: Definite Integrals (area under a curve) (part III)
65: Definite Integrals (part 4)
66: Definite Integrals (part 5)
67: Definite integral with substitution
68: Integrals: Trig Substitution 1
69: Integrals: Trig Substitution 2
70: Integrals: Trig Substitution 3 (long problem)
71: Periodic Definite Integral
72: Simple Differential Equations
73: Solid of Revolution (part 1)
74: Solid of Revolution (part 2)
75: Solid of Revolution (part 3)
76: Solid of Revolution (part 4)
77: Solid of Revolution (part 5)
78: Solid of Revolution (part 6)
79: Solid of Revolution (part 7)
80: Solid of Revolution (part 8)
81: Sequences and Series (part 1)
82: Sequences and series (part 2)
83: Maclauren and Taylor Series Intuition
84: Cosine Taylor Series at 0 (Maclaurin)
85: Sine Taylor Series at 0 (Maclaurin)
86: Taylor Series at 0 (Maclaurin) for e to the x
87: Euler's Formula and Euler's Identity
88: Visualizing Taylor Series Approximations
89: Generalized Taylor Series Approximation
90: Visualizing Taylor Series for e^x
91: Polynomial approximation of functions (part 1)
92: Polynomial approximation of functions (part 2)
93: Approximating functions with polynomials (part 3)
94: Polynomial approximation of functions (part 4)
95: Polynomial approximations of functions (part 5)
96: Polynomial approximation of functions (part 6)
97: Polynomial approximation of functions (part 7)
98: Taylor Polynomials
99: Exponential Growth
100: AP Calculus BC Exams: 2008 1 a
101: AP Calculus BC Exams: 2008 1 b&c
102: AP Calculus BC Exams: 2008 1 c&d
103: AP Calculus BC Exams: 2008 1 d
104: Calculus BC 2008 2 a
105: Calculus BC 2008 2 b &c
106: Calculus BC 2008 2d
107: Partial Derivatives
108: Partial Derivatives 2
109: Gradient 1
110: Gradient of a scalar field
111: Divergence 1
112: Divergence 2
113: Divergence 3
114: Curl 1
115: Curl 2
116: Curl 3
117: Double Integral 1
118: Double Integrals 2
119: Double Integrals 3
120: Double Integrals 4
121: Double Integrals 5
122: Double Integrals 6
123: Triple Integrals 1
124: Triple Integrals 2
125: Triple Integrals 3
126: (2^ln x)/x Antiderivative Example
127: Introduction to the Line Integral
128: Line Integral Example 1
129: Line Integral Example 2 (part 1)
130: Line Integral Example 2 (part 2)
131: Position Vector Valued Functions
132: Derivative of a position vector valued function
133: Differential of a vector valued function
134: Vector valued function derivative example
135: Line Integrals and Vector Fields
136: Using a line integral to find the work done by a vector field example
137: Parametrization of a Reverse Path
138: Scalar Field Line Integral Independent of Path Direction
139: Vector Field Line Integrals Dependent on Path Direction
140: Path Independence for Line Integrals
141: Closed Curve Line Integrals of Conservative Vector Fields
142: Example of Closed Line Integral of Conservative Field
143: Second Example of Line Integral of Conservative Vector Field
144: Green's Theorem Proof Part 1
145: Green's Theorem Proof (part 2)
146: Green's Theorem Example 1
147: Green's Theorem Example 2
148: Introduction to Parametrizing a Surface with Two Parameters
149: Determining a Position Vector-Valued Function for a Parametrization of Two Parameters
150: Partial Derivatives of Vector-Valued Functions
151: Introduction to the Surface Integral
152: Example of calculating a surface integral part 1
153: Example of calculating a surface integral part 2
154: Example of calculating a surface integral part 3
155: 2011 Calculus AB Free Response #1a
156: 2011 Calculus AB Free Response #1 parts b c d
157: 2011 Calculus AB Free Response #2 (a & b)
158: 2011 Calculus AB Free Response #2 (c & d)
159: 2011 Calculus AB Free Response #3 (a & b)
160: 2011 Calculus AB Free Response #3 (c)
161: 2011 Calculus AB Free Response #4a
162: 2011 Calculus AB Free Response #4b
163: 2011 Calculus AB Free Response #4c
164: 2011 Calculus AB Free Response #4d
165: 2011 Calculus AB Free Response #5a
166: 2011 Calculus AB Free Response #5b
167: 2011 Calculus AB Free Response #5c.
168: 2011 Calculus AB Free Response #6a
169: 2011 Calculus AB Free Response #6b
170: 2011 Calculus AB Free Response #6c
171: 2011 Calculus BC Free Response #1a
172: 2011 Calculus BC Free Response #1 (b & c)
173: 2011 Calculus BC Free Response #1d
174: 2011 Calculus BC Free Response #3a
175: 2011 Calculus BC Free Response #3 (b & c)
176: 2011 Calculus BC Free Response #6a
177: 2011 Calculus BC Free Response #6b
178: 2011 Calculus BC Free Response #6c
179: Error or Remainder of a Taylor Polynomial Approximation
180: Proof: Bounding the Error or Remainder of a Taylor Polynomial Approximation
181: 2011 Calculus BC Free Response #6d
182: Constructing a unit normal vector to a curve
183: 2 D Divergence Theorem
184: Conceptual clarification for 2-D Divergence Theorem
185: Surface Integral Example Part 2 - Calculating the Surface Differential
186: Surface Integral Example Part 1 - Parameterizing the Unit Sphere
187: Surface Integral Example Part 3 - The Home Stretch
188: Surface Integral Ex2 part 1 - Parameterizing the Surface
189: Surface Integral Ex2 part 2 - Evaluating Integral
190: Surface Integral Ex3 part 1 - Parameterizing the Outside Surface
191: Surface Integral Ex3 part 2 - Evaluating the Outside Surface
192: Surface Integral Ex3 part 3 - Top surface
193: Surface Integral Ex3 part 4 - Home Stretch
194: Conceputal Understanding of Flux in Three Dimensions
195: Constructing a unit normal vector to a surface