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Week
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Topics
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Study Metarials
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1
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Real numbers, absolute value, equation and inequalities, properties of linear point sets, basic definitions related to functions
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R1- Section P.1, Section P.2, Section P.3, Section P.4
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2
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Polynomials, rational functions, piecewise functions,
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R1- Section P.5, Section P.6
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3
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Trigonometric functions, exponential and logarithmic functions
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R1- Section P.7
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4
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Limits of functions, one sided limits, limit theorems
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R1- Section 1.1, Section1.2
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5
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Limits at infinity and infinite limits, indeterminate forms, examples related to limits
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R1-Section 1.3
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6
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Limits of trigonometric, exponential and logarithmic functions
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R1- Section 1.3
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7
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Continuous functions and basic properties, properties of continuous functions defined on a closed and bounded interval
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R1- Section 1.4
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8
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Uniform continuity
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R1-Section 1.5
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9
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The concept of derivative and its geometric interpretation, differential concept,
rules of derivation,
derivative of trigonometric functions
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R1- Section 2.1, Section 2.2, Section 2.3, Section2.5
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10
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Chain rule, higher order derivatives,
derivative of inverse functions
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R1- Section 2.4, Section2.6, Section 3.1
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11
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Derivatives of exponential and
logarithmic functions, implicit
differentiation, derivatives of
parametric functions
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R1- Section 3.2, Section 3.3, Section 2.9
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12
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Mean-value theorem, increasing
and decreasing functions,
maximum and minumum
values, first derivative test.
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R1- Section 2.8, Section 4.4
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13
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Concavity and inflection points,
second derivative test,
asymptotes, curve sketching, polar coordinates
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R1- Section 4.5, Section 4.6
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14
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Maximum, Minimum problems,
related rates, L`hospital rule
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R1-Section 4.8, Section 4.3
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