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Single Variable Calculus >> Content Detail



Lecture Notes



Lecture Notes


SES #TOPICSLECTURE NOTES
Derivatives
1Derivatives, 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)
3Derivatives of products, quotients, sine, cosine(PDF)
4

Chain rule

Higher derivatives

(PDF)
5Implicit differentiation, inverses(PDF)
6

Exponential and log

Logarithmic differentiation; hyperbolic functions

(PDF)
7Hyperbolic functions and exam 1 review(PDF)
8Exam 1 covering Ses #1-7(No Lecture Notes)
Applications of Differentiation
9Linear and quadratic approximations(PDF)Ses #9-16 complete (PDF - 6.9 MB)
10Curve sketching(PDF - 1.8 MB)
11Max-min problems(PDF - 1.1 MB)
12Related rates(PDF - 1.0 MB)
13Newton's method and other applications(PDF - 1.2 MB)
14

Mean value theorem

Inequalities

(PDF)
15Differentials, antiderivatives(PDF)
16Differential equations, separation of variables(PDF)
17Exam 2 covering Ses #8-16(No Lecture Notes)
Integration
18Definite integrals(PDF)Ses #18-25 complete (PDF - 8.6 MB)
19First fundamental theorem of calculus(PDF)
20Second fundamental theorem(PDF)
21Applications to logarithms and geometry(PDF - 1.4 MB)
22Volumes by disks and shells(PDF - 1.7 MB)
23Work, average value, probability(PDF - 2.2 MB)
24Numerical integration(PDF - 1.1 MB)
25Exam 3 review(PDF)
Techniques of Integration
26Trigonometric integrals and substitution(PDF)Ses #26-38 complete (PDF - 8.6 MB)
27Exam 3 covering Ses #18-24(No Lecture Notes)
28Integration by inverse substitution; completing the square(PDF)
29Partial fractions(PDF)
30Integration by parts, reduction formulae(PDF - 1.4 MB)
31Parametric equations, arclength, surface area(PDF)
32

Polar coordinates; area in polar coordinates

Exam 4 review

(PDF - 2.0 MB)

(PDF)

33Exam 4 covering Ses #26-32(No Lecture Notes)
34Indeterminate forms - L'Hôspital's rule(PDF)
35Improper integrals(PDF)
36Infinite series and convergence tests(PDF - 1.4 MB)
37Taylor's series(PDF)
38Final review(PDF)

 








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