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الخطة الدراسية لمقرر 150 ريض |
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Syllabus and Contents of Math 150 |
Introduction to Differentiation
3 Credit Hours ( 2 + 2)
Text Book: Calculus Made Simple (First Edition)
Authors: Khashan A., Khashan K., Obeidat S.
Year: 2012, 1E
Course Coordinators:
· Dr: Ayman Khashan: mathcoo2@py.ksu.edu.sa
· Dr: Mahmmod Al-Khateeb: khateeb62jo@yahoo.com
The Students Should Study the Following Topics:
|
Chapter No. |
Chapter Name |
Description |
|
Chapter 1 |
Limits and Continuity of Functions |
Concept of Limit, Computation of Limits, Infinite Limits, Limits at Infinity, Continuity and Consequences, Limits of Trigonometric Functions, Formal definition of limit. |
|
Chapter 2 |
Derivatives of Functions |
The Derivative, Computation of Derivatives, The Chain Rule, Derivatives of Trigonometric Functions, Derivatives of Logarithmic and Exponential Functions, Implicit Differentiation, The Mean Value Theorem. |
|
Chapter 3 |
Applications of Derivatives |
Indeterminate Forms and L'Hopital's Rule, Monotonic Behavior of Functions, Concavity and Inflection Points, Absolute Extrema, Curve Sketching |
The evaluation of the students will be continuous during the course and depends on the following:
|
First Mid Term exam |
15 |
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Second Mid Term exam |
15 |
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Quizzes & Activities |
10 |
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Self-learning |
10 |
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Final Exam |
50 |
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The Total Degrees |
100 |
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Electronic Homeworks |
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Homework |
Week |
Start Date |
End Date |
|
1 |
3 |
19-3-1433 |
30-3-1433 |
|
2 |
5 |
3-4-1433 |
14-4-1433 |
|
3 |
7 |
17-4-1433 |
27-4-1433 |
|
4 |
9 |
8-5-1433 |
19-5-1433 |
|
5 |
11 |
22-5-1433 |
4-6-1433 |
|
6 |
12 |
7-6-1433 |
18-6-1433 |
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This course is intended for students who have a thorough knowledge of analytic geometry and elementary functions in addition to college preparatory algebra, geometry, and trigonometry. The purpose of the course is to prepare the student for advanced placement in college calculus. In this course:
· The student will define and apply the properties of limits of functions. This will include limits of a constant, sum, product, quotient, one-sided limits, limits at infinity, infinite limits, and nonexistent limits.
· The student will state the definition of continuity and determine where a function is continuous or discontinuous. This will include continuity at a point; continuity over a closed interval; application of the Intermediate Value Theorem; and graphical interpretation of continuity and discontinuity.
· The student will find the derivative of an algebraic function by using the definition of a derivative. This will include investigating and describing the relationship between differentiability and continuity.
· The student will apply formulas to find the derivative of algebraic, trigonometric, exponential, and logarithmic functions and their inverses.
· The student will apply formulas to find the derivative of the sum, product, quotient, inverse, and composite (chain rule) of elementary functions.
· The student will find the derivative of an implicitly defined function.
· The student will find the higher order derivatives of algebraic, trigonometric, exponential, and logarithmic functions.
· The student will use logarithmic differentiation as a technique to differentiate non logarithmic functions.
· The student will state (without proof) the Mean Value Theorem for derivatives and apply it both algebraically and graphically.
· The student will use L'Hopital's rule to find the limit of functions whose limits yield the indeterminate forms: 0/0 and infinity/infinity
· A Calculus, these functions will also include functions whose limits yield the indeterminate forms: 0 to the 0th power, 1 to the infinity power, infinity to the infinity power, infinity minus infinity.
· The student will apply the derivative to solve problems, including tangent and normal lines to a curve, curve sketching, velocity, acceleration, related rates of change, and optimization problems. |
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Contents |
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Chapter |
Section |
Examples for Teacher |
Exercises for Students |
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1
Limits and Continuity of Functions |
1.1 Concept of Limit |
1,2,4,5,6,7 |
1 |
6 |
10 |
11 |
12 |
16 |
17 |
18 |
19 |
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Self test |
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1.2 Computation of Limits |
1,2,3,4,5,7,8,9,10,11,
13,15,16,17,18,19 |
3 |
4 |
5 |
10 |
11 |
21 |
23 |
24 |
33 |
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36 |
39 |
41 |
42 |
43 |
45 |
48 |
55 |
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|
Self Test |
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1.3 Infinite Limits |
1,2,3,5,6,7,8,9,10 |
1 |
3 |
4 |
5 |
6 |
9 |
11 |
17 |
18 |
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19 |
22 |
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Self Test |
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1.4 Limits at Infinity |
1,2,3,4,5,6,7,8,9,10,11,
12,13 |
1 |
3 |
5 |
7 |
8 |
10 |
12 |
13 |
17 |
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Self Test |
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1.5 Continuity and Consequences |
1,3,4,5,6,7,9,10,12,14,
16,18,19,20,21 |
1 |
6 |
14 |
16 |
23 |
25 |
26 |
30 |
33 |
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41 |
43 |
49 |
50 |
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Self Test |
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1.6 Limits of Trigonometric Functions |
1,2,3,4,5,6,7,8.9,11,
12,13 |
2 |
8 |
9 |
12 |
13 |
14 |
15 |
16 |
23 |
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Self Test |
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1.7 Formal definition of limit |
1,3,4 |
1,4,8 |
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2
Derivatives of Functions |
2.1 The Derivative |
1,2,3,5,7,8,9,10,
11,12 |
1 |
3 |
5 |
8 |
12 |
13 |
15 |
18 |
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Self Test |
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2.2 Computation of Derivatives |
1,2,3,4,5,6,8,9,10,13,
14,15,16,17 |
1 |
3 |
5 |
11 |
15 |
18 |
22 |
23 |
28 |
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31 |
32 |
34 |
38 |
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Self Test |
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2.3 The Chain Rule |
1,2,3,4,6,7,8,9,10 |
3 |
8 |
9 |
11 |
19 |
25 |
28 |
30 |
33 |
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Self Test |
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2.4 Derivatives of Trigonometric Functions |
1,2,4,6,7,8,9,10 |
1 |
5 |
8 |
12 |
13 |
16 |
28 |
33 |
38 |
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40 |
42 |
47 |
51 |
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Self Test |
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2.6 Derivatives of Logarithmic and Exponential Functions |
1,2,3,4,5,6,7 |
1 |
3 |
8 |
11 |
15 |
20 |
26 |
28 |
36 |
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40 |
42 |
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Self Test |
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2.7 Implicit Differentiation |
1,3,4,5,6,7,8,9 |
3 |
9 |
11 |
15 |
19 |
21 |
26 |
30 |
34 |
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39 |
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Self Test |
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2.8 The Mean Value Theorem |
1,2,3,4,5,6, |
3 |
5 |
7 |
8 |
9 |
12 |
16 |
18 |
20 |
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Self Test |
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3
Applications of Derivatives |
3.1 Indeterminate Forms and L'Hopital Rule |
1,2,3,4,5,7 |
1 |
3 |
4 |
5 |
7 |
10 |
13 |
15 |
16 |
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17 |
18 |
27 |
28 |
29 |
30 |
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Self Test(1,2,3,4,5,6,7,14) |
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3.2 Monotonic Behavior of Functions |
1,2,3,4,5,7,8,9,10 |
1 |
2 |
3 |
4 |
5 |
6 |
8 |
9 |
12 |
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15 |
19 |
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Self Test |
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3.3 Concavity and Inflection Points |
1,2,3,4,5,6 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
11 |
13 |
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15 |
19 |
20 |
22 |
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Self Test |
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3.4 Absolute Extrema |
1,2,3,5,6,7,8,10,11 |
2 |
5 |
8 |
10 |
11 |
12 |
14 |
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Self Test |
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3.6 Curve Sketching |
1,3,4,5,6 |
1 |
3 |
6 |
8 |
10 |
12 |
21 |
24 |
25 |
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27 |
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Self Test |
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Weekly Plan |
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Week |
Section(s) to be Covered |
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1 |
1.1 Concept of Limit |
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2 |
1.2 Computation of Limits |
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3 |
1.3 Infinite Limits
1.4 Limits at Infinity |
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4 |
1.5 Continuity and Consequences |
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5 |
1.6 Limits of Trigonometric Functions
1.7 Formal definition of limit |
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6 |
2.1 The Derivative |
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7 |
2.2 Computation of Derivatives |
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8 |
2.3 The Chain Rule
2.4 Derivatives of Trigonometric Functions |
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9 |
2.6 Derivatives of Logarithmic and Exponential Functions |
|
10 |
2.7 Implicit Differentiation |
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11 |
2.8 The Mean Value |
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12 |
3.1 Indeterminate Forms and L'Hopital's Rule
3.2 Monotonic Behavior of Functions |
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13 |
3.3 Concavity and Inflection Points |
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14 |
3.4 Absolute Extrema |
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15 |
3.6 Curve Sketching |
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16 |
Final Exam |
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