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Course Outline /Schedule (Weekly) Planned Learning Activities |
| Week | Subject | Student's Preliminary Work | Learning Activities and Teaching Methods |
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1 |
Numbers, rational and real numbers. Order. Absolute Value, number line, Intervals, inequalities. |
Required readings and solving problems |
Lecturing and discussion |
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2 |
Functions, Finding the domain and range. Composition, inverse function, graphs. trigononmetric functions. |
Required readings and solving problems |
Lecturing and discussion |
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3 |
Limit of a function of one variable, Limit theorems, One sided limits |
Required readings and solving problems |
Lecturing and discussion |
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4 |
Infinite limits, Indefinite forms, limits at infinity, Continuity |
Required readings and solving problems |
Lecturing and discussion |
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5 |
Limit criterion, Intermediate Value and Maximum-Minimum Theorems. Types of discontinuity. |
Required readings and solving problems |
Lecturing and discussion |
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6 |
Derivative, slope of the tangent. Rules of differentiation. Chain Rule |
Required readings and solving problems |
Lecturing and discussion |
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7 |
Higher order derivatives, Implicit differentiation. Differential and approximation using differential. |
Required readings and solving problems |
Lecturing and discussion |
|
8 |
Rolle´s Theorem, Mean Value Theorem. Finding maxima and minima. |
Required readings and solving problems |
Lecturing and discussion |
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9 |
Mid Term Exam |
Review and Solving Problems |
Written Exam |
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10 |
First derivative Test, Second derivative and convexity. Second derivative test. Asymptotes. |
Required readings and solving problems |
Lecturing and discussion |
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11 |
Graphing. Solving applied maxima and minima problems. Derivative of the inverse functions. |
Required readings and solving problems |
Lecturing and discussion |
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12 |
Logarithm function, properties of the logarithm |
Required readings and solving problems |
Lecturing and discussion |
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13 |
Exponential function. Properties of the exponential function. |
Required readings and solving problems |
Lecturing and discussion |
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14 |
Trigonometric and inverse trigonometric functions. Hyperbolic functions, inverse hyperbolic functions. |
Required readings and solving problems |
Lecturing and discussion |
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15 |
L´Hospital rule and Taylor´s Theorem with remainder. Applications. |
Required readings and solving problems |
Lecturing and discussion |
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16/17 |
FINAL EXAM |
Review and Solving Problems |
WRITTEN EXAM |
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