Functions¶
Part 2 of the lecture notes. Elementary functions and their graphs: powers, exponentials, trigonometric functions, inverses.
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1. Functions
The concept of function · Definition of function, domain, codomain and image · Surjections, injections and bijections
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2. Real functions of a real variable
Real function of a real variable · Bounded functions · Symmetric functions · Monotonic functions · …
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3. Power functions
Power functions · Direct and inverse proportionality functions
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4. Exponential and logarithmic functions
Exponential functions · Logarithmic functions · Change of base
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5. Trigonometric functions
Trigonometric functions · Values of the trigonometric functions · Main trigonometric formulas
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6. Vibration phenomena
Vibration phenomena · Damping and amplification effects
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7. Integer part and fractional part functions
Integer part and fractional part functions · Piecewise-defined functions
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8. Hyperbolic functions
Hyperbolic functions · Main hyperbolic formulas
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9. Operations on graphs
Operations on graphs
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10. Composite functions
Composite functions
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11. Inverse functions
Invertible functions and inverse functions