Calculus I (0301101)

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Page Content Calculus I
Course Description:
Functions: domain, operations on functions, graphs of functions; trigonometric functions; limits: meaning of a limit, computational techniques, limits at infinity, infinite limits; continuity; limits and continuity of trigonometric functions; the derivative: techniques of differentiation, derivatives of trigonometric functions; the chain rule; implicit differentiation; differentials; Roll’s Theorem; the mean value theorem; the extended mean value theorem; L’Hopital’s rule; increasing and decreasing functions; concavity; maximum and minimum values of a function; graphs of functions including rational functions (asymptotes) and functions with vertical tangents (cusps); antiderivatives; the indefinite integral; the definite integral; the fundamental theorem of calculus; area under a curve; area between two curves; transcendental functions: inverse functions, logarithmic and exponential functions and their derivatives and integrals; limits (the indeterminate forms); hyperbolic functions and their inverses; inverse trigonometric functions; some techniques of integration.
Textbook:
James Stewart (2015) Calculus (Early Transcendentals), 8th Edition, Thomson, Metric international version.
References:
 Saturnino Salas, Einar Hille, Garrett Etgen. Calculus: One and Several Variables, 10th Edition.
 Howard Anton. Calculus: Early Transcendentals, Single Variable. 10th Edition.
Lecture notes:
The following lecturebylecture notes were handwritten by Dr. Baha Alzalg.
These materials might not be used for commercial purposes without my consent.
Topic #

Topic(s)

Scribe

1

Functions

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2

Limits

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3

Continuity

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4

The IVT.
Vertical and horizontal asymptotes

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5

Differentiation

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6

Chain
rule, more on differentiation

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7

Rate of
change, velocity, acceleration

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8

Implicit differentiation

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9

Derivatives
of inverse and hyperbolic functions

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10

Differentials
and linearization

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11

Indeterminate
forms and l'Hospital's rule

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12

The mean
value theorem

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13

Increasing/decreasing
functions and extrema

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14

Concavity

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15

Curve
sketching

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16

The
definite integral

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17

The
fundamental theorem of calculus

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18

The
indefinite integral

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19

Integration
by substitution

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