18.01 | Fall 2005 | Undergraduate

Single Variable Calculus

Lecture Notes

These lecture notes represent a summary of the topics discussed in class. Each lecture includes a list of homework problems from the assigned problem set which can be completed using the material from that session’s lecture. The practice problems for each lecture are not to be written up or turned in. These are assigned only for practice, and are entirely voluntary.

All Lecture Notes in One File (PDF - 1.4 MB)

ses # TOPICS
1 Velocity and Rates of Change (PDF)
2 Slope and Derivative

Limits and Continuity (PDF)

3 Differentiation Formulas: Products and Quotients (PDF)
4 Chain Rule and Implicit Differentiation (PDF)
5 The Derivatives of Exponential and Logarithm Functions (PDF)
6 The Derivatives of Trigonometric Functions (PDF)
7 Review for Exam 1 (PDF)
8 Approximations (PDF)

Mean Value Theorem

9 Curve Sketching (PDF)
10 Max-Min Problems (PDF)
11 Related Rates (PDF)
12 Inequalities, Zeros, and Newton’s Method (PDF)
13 Differentials and Indefinite Integrals (PDF)
14 Definite Integrals (PDF)
15 The Fundamental Theorem of Calculus (PDF)
16 Properties of Definite Integrals (PDF)
17 Differential Equations and Separation of Variables (PDF)
18 Numerical Integration and Review of Unit 3 (PDF)
19 Areas between Curves, Volumes of Revolutions, and Slicing (PDF)
20 Volumes by Shells and Average Values (PDF)
21 Parametric Equations and Arc Length (PDF)
22 Surface Area and Polar Coordinate Graphs (PDF)
23 Area and Arc Length in Polar Coordinates (PDF)
24 Inverse Trigonometric Functions and Hyperbolic Functions (PDF)
25 Integration by Inverse Substitution (PDF)
26 Integration by Partial Fractions (PDF)
27 Integration by Parts (PDF)
28 Indeterminate Forms and L’Hospital’s Rule (PDF)
29 Improper Integrals (PDF)
30 Infinite Series (PDF)
31 Power Series (PDF)
32-33 Final Review (PDF)

Course Info

As Taught In
Fall 2005
Learning Resource Types
grading Exams with Solutions
notes Lecture Notes
assignment_turned_in Problem Sets with Solutions