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MATH 106
Course Content
· The definite integrals, fundamental theorem of calculus, the indefinite integrals, change of variables, numerical integration.
· Area, volume of revolution, work, arc length.
· Differentiation and integration of inverse trigonometric functions.
· The logarithmic, exponential, hyperbolic and inverse hyperbolic functions.
· Techniques of integration: substitution, by parts, trigonometric substitutions, partial fractions, miscellaneous substitutions.
· Indeterminate forms, improper integrals, polar coordinates.
Text Book
Calculus; Early Transcendental Functions, Third Edition.
By Robert T. Smith and Roland B. Minton.
There will be two mid term exams each out of 20 points and weekly home works out of 10 points. Then a final exam out of 50 points.
Syllabus
· Chapter 4
4.1. Anti Derivatives.
4.2. Sum and Sigma Notation.
4.3. Area.
4.4. The Definite Integral.
4.5. The Fundamental Theorem of Calculus.
4.6. Integration by Substitution.
4.7. Numerical Integration (only the Trapezoidal Rule and Simpson’s Rule).
4.8. The Natural Logarithm as Integral.
· Chapter 6
6.2. Integration by Parts.
6.3. Trigonometric Techniques of Integration.
6.4. Integration of Rational Functions (Partial Fractions).
6.6. Improper Integrals.
6.1. Review Problems of Integration by Substitution and Completing the Squares.
· Chapter 5
5.1. Area Between Curves.
5.2. Volume (by Disk or Washer).
5.3. Volume (by Cylindrical Shell).
5.4. Arc Length and Surface Area.
· Chapter 9
9.1. Plane Curves and Parametric Equations.
9.2. Calculus and Parametric Equations.
9.3. Arc Length and Surface Area in Parametric Equations.
9.4. Polar Coordinates.
9.5. Calculus and Polar Coordinates.
Exercises
· Chapter 4
Section 4.1: 1,3,5,7,9,10,15,16,29,34,40,43.
Section 4.2: 1,5,7,11,13,17,19,21,23,35,38.
Section 4.3: 5,9,10,11,13,15.
Section 4.4: 5,7,33,34,35,37.
Section 4.5: 53,55,57.
Section 4.6: 5,10,14,16,20,24,31,33,36,40.
Section 4.7: 1,4,9,12.
Section 4.8: 9,10,12,13,15,17,19,24,26,28,30,31,31.
· Chapter 6
Section 6.2: 1,4,7,11,16,19,25,27.
Section 6.3: 1,4,7,10,14,17,22,24,28,30.
Section 6.4: 1,4,7,10,14,17,24,28,30,32.
Section 6.6: 1,6,8,11,16,20,24,30.
Section 6.1: 1,7,9,17,22,23,29,30,35.
· Chapter 5
Chapter 5.1: 1,3,5,8,9,12,19,21,23,24.
Chapter 5.2: 17,19,21,25,27,32.
Chapter 5.3: 1,3,5,9,11,14,17,19,23,25.
Chapter 5.4: 5,7,8,11,14,35,37,40.
· Chapter 9
Chapter 9.1: 1,4,7,10,31,33,36,39,41,43.
Chapter 9.2: 1,3,5,8,9,11,15,17,21,25,28.
Chapter 9.3: 1,4,5,7,11,21,23,25.
Chapter 9.4: 1,2,3,5,7,9,11,12,13,15,18,19,21,23,25,27,30,31,32,33,36,57,60,62.
Chapter 9.5: 1,3,5,8,15,20,25,29,31,33,35,38,40.
The excat number of examples and theorems that we wil cover in each section is as follows:
CHAPTER 4
Section 4.1: All except Example 1.12.
Section 4.2: Examples 2.1, 2.2 and 2.3. Theorem 2.1 and Theorem 2.2, Example 2.4. Principle of Mathematical Induction (غير مطلوب).
Section 4.3: From page 362 to page 365 except Example 3.4.
Section 4.4: Definition 4.1, Example 4.2, Theorem 4.1, Theorem 4.2, Example 4.6, Theorem 4.3, Theorem 4.4, and Example 4.8.
Section 4.5: Theorem 5.1, Remark 5.1. From Example 5.1 to Example 5.6, Theorem 5.2, Examples 5.7, 5.8 and 5.9.
Section 4.6: All
Section 4.7: Example 7.1, 7.5, 7.6.
Section 4.8: All.
CHAPTER 6
Section 6.2: All.
Section 6.3: All.
Section 6.4: Example 4.1 and example 4.6 (تقرأه الطالبة). Examples 4.2 to 4.5 (يشرح بالتفصيل).
Section 6.5: غير مطلوب
Section 6.6: Examples 6.1 to 6.13. Comparison test (غير مطلوب).
Section 6.1: All examples
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