Single Variable Calculus

Lecture Notes

SES #	TOPICS	LECTURE NOTES
Derivatives
1	Derivatives, slope, velocity, rate of change	(PDF - 1.1 MB)	Ses #1-7 complete (PDF - 5.2 MB)
2	Limits, continuity Trigonometric limits	(PDF - 2.6 MB)
3	Derivatives of products, quotients, sine, cosine	(PDF)
4	Chain rule Higher derivatives	(PDF)
5	Implicit differentiation, inverses	(PDF)
6	Exponential and log Logarithmic differentiation; hyperbolic functions	(PDF)
7	Exam 1 review	(PDF)
8	Exam 1 covering Ses #1-7	(No Lecture Notes)
Applications of Differentiation
9	Linear and quadratic approximations	(PDF)	Ses #9-16 complete (PDF - 6.9 MB)
10	Curve sketching	(PDF - 1.8 MB)
11	Max-min problems	(PDF - 1.1 MB)
12	Related rates	(PDF - 1.0 MB)
13	Newton’s method and other applications	(PDF - 1.2 MB)
14	Mean value theorem Inequalities	(PDF)
15	Differentials, antiderivatives	(PDF)
16	Differential equations, separation of variables	(PDF)
17	Exam 2 covering Ses #8-16	(No Lecture Notes)
Integration
18	Definite integrals	(PDF)	Ses #18-25 complete (PDF - 8.6 MB)
19	First fundamental theorem of calculus	(PDF)
20	Second fundamental theorem	(PDF)
21	Applications to logarithms and geometry	(PDF - 1.4 MB)
22	Volumes by disks and shells	(PDF - 1.7 MB)
23	Work, average value, probability	(PDF - 2.2 MB)
24	Numerical integration	(PDF - 1.1 MB)
25	Exam 3 review	(PDF)
Techniques of Integration
26	Trigonometric integrals and substitution	(PDF)	Ses #26-38 complete (PDF - 8.6 MB)
27	Exam 3 covering Ses #18-24	(No Lecture Notes)
28	Integration by inverse substitution; completing the square	(PDF)
29	Partial fractions	(PDF)
30	Integration by parts, reduction formulae	(PDF - 1.4 MB)
31	Parametric equations, arclength, surface area	(PDF)
32	Polar coordinates; area in polar coordinates Exam 4 review	(PDF - 2.0 MB) (PDF)
33	Exam 4 covering Ses #26-32	(No Lecture Notes)
34	Indeterminate forms - L’Hôspital’s rule	(PDF)
35	Improper integrals	(PDF)
36	Infinite series and convergence tests	(PDF - 1.4 MB)
37	Taylor’s series	(PDF)
38	Final review	(PDF)