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Week
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Topics
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Teaching and Learning Methods and Techniques
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Study Materials
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1. Week
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Definition of function. Basic elementary functions. Trigonometric functions.
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Brainstorming
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Homework
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2. Week
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Definition of function. Basic elementary functions. Trigonometric functions.
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Lecture
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Homework
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3. Week
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Inverse Trigonometric functions, Exponential and Logarithmic functions.
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Lecture
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Homework
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4. Week
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Hyperbolic and Inverse Hyperbolic Functions. Definition of the limit, one sided limits.
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Lecture
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Homework
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5. Week
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Basic trigonometric limits. The concept of continuity.
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Lecture
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Homework
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6. Week
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Properties of continuous functions on the closed interval-Intermediate value theorem, Bolzano's theorem, local and absolute maxima and minima.
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Lecture
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Homework
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7. Week
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The Derivative. Basic differentiation rules. Derivative of inverse function. Derivative of trigonometric and inverse trigonometric functions.
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Lecture
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Homework
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8. Week
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Derivatives of Logaritmic and exponential functios. Logarithmic differentiation. Derivatives of Hypherbolic functions and their inverses. Implicit differentiation.
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Lecture
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Homework
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9. Week
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Higher derivatives. Increasing, decreasing function. First and second derivative tests for local extrema.
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Lecture
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Homework
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10. Week
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Applied maximum-minimum problems. Mean value theorem, Rolle's Theorem
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Lecture
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Homework
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11. Week
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Concavity, inflection point. Indeterminate forms (L’Hospital's rule)
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Lecture
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Homework
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12. Week
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Curve scetching, asymptotes.
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Lecture
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Homework
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13. Week
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Differential and linear approximation. Antiderivative. Basic properties of integrals. Methods of integrations (Integration by substitution, integration by parts)
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Lecture
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Homework
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14. Week
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Recurrence relations. Integration of rational functions. Trigonometric substitutions.
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Lecture
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Homework
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15. Week
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Integration of irrational functions. Rationalizing substitutions.
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Lecture
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Homework
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