MATH 101 COURSE SYLLABUS

Transcription

1 TOPICS OF THE COURSE 2. LIMITS AND RATE OF CHANGE : (8 Hours) Introduction to Limits, Definition of Limit, Techniques for Finding Limits, Limits Involving Infinity, Continuous functions. 3. THE DERIVATIVE : (8 Hours) Tangent Lines and Rates of Change, Definition of Derivative, Techniques of Differentiation, Derivatives of the Trigonometric Functions, The Chain Rule, Implicit Differentiation, Related Rates, Linear Approximation and Differentials. 4. APPPLICATIONS OF THE DERIVATIVE : (8 Hours) Extrema of Functions, The Mean Value Theorem, The First Derivative Test, Concavity and the Second Derivative Test, Summary of Graphical Methods, Optimization Problem. 5. INTEGRALS : (9 Hours) Antiderivatives, Indefinite Integrals, and Simple Differential Equations Change of Variables in Indefinite Integrals, Summation Notation and Area, The Definite Integral, Properties of the Definite Integral, The Fundamental Theorem of Calculus 6. APPLICATIONS OF THE DEFINITE INTEGRAL(8Hours) Area, Solids of Revolution, Volumes by Cylindrical Shells, Arc Length (41 Hours)

2 - CALCULUS I CHAPTER 2-LIMITS AND CONTINUITY 2.4 Definition of Limit 2.3 Techniques for Finding Limits 3.5 Techniques for finding limits of Trigonometric functions 2.3 Squeeze theorem 4.4 Limits Involving Infinity 4.4 Vertical And Horizontal Asymptotes 2.5 Continuous Functions 2.5 Discontinuous Functions 2.5 Intermediate Value Theorem CHAPTER 3-THE DERIVATIVE 3.1 Definition of Derivative 3.3 Techniques of Differentiation 3.5 Derivatives of the Trigonometric Functions 3.6 The Chain Rule 3.* Tangent Line; Corner 3.7 Implicit Differentiation 3.10 Linear Approximation and Differentials 3.9 Related Rates CHAPTER 4-APPPLICATIONS OF THE DERIVATIVE 4.1 Extrema of Functions 4.2 The Mean Value Theorem 4.3 The First Derivative Test 4.3 Concavity and the Second Derivative Test 4.5 Summary of Graphical Methods 4.7 Optimization Problem CHAPTER 5-INTEGRALS 4.10 Antiderivatives, Indefinite Integrals, and Simple Differential Equations 5.4 Change of Variables in Indefinite Integrals 5.1 Summation Notation and Area 5.2 The Definite Integral 5.2 Properties of the Definite Integral 5.3 The Fundamental Theorem of Calculus CHAPTER 6-APPLICATIONS OF THE DEFINITE INTEGRAL 6.1 Area 6.2 Solids of Revolution 6.2 volumes by washer 6.3 Volumes by Cylindrical Shells 6.3 Arc Length P2 (9 Hours) (10 Hours) (8 Hours) (6 Hours) (5 Hours) (38 Hours)

3 P3 - CALCULUS I First Mid Term Examination CHAPTER 2-LIMITS AND RATES OF CHANGE (9 Hours) 1) 2.4 Definition of Limit 2) 2.3 Techniques for Finding Limits 3) 3.5 Techniques for finding limits of Trigonometric functions 4) 2.3 squeeze theorem 5) 4.4 Limits Involving Infinity 6) 4.4 Vertical And Horizontal Asymptotes 7) 2.5 Continuous Functions 8) 2.5 Discontinuous Functions 9) 2.5 Intermediate Value Theorem CHAPTER 3- DERIVATIVES (5 Hours) 10) 3.2 Definition of Derivative 11) 3.3 Techniques of Differentiation 12) 3.5 Derivatives of the Trigonometric Functions 13) 3.6 The Chain Rule 14 ) 3.* Tangent Line; Corner (14 Hours)

4 P4 - CALCULUS I Second Mid Term Examination CHAPTER 3- DERIVATIVES (5 Hours) 15) 3.7 Implicit Differentiation 16) 3.8 The Higher Derivative 17) 3.10 Linear Approximation and Differentials 18) 3.9 Related Rates CHAPTER 4-APPPLICATIONS OF DIFFERENTIATION (8 Hours) 20) 4.5 Summary of Graphical Methods 24) 4.2 The Rolle's Theorem 25) 4.2 The Mean Value Theorem 26) 4.7 Optimization Problem (13 Hours)

5 P5 - CALCULUS I Final Examination CHAPTER 5-INTEGRALS (6 Hours) 28) 4.10 Antiderivatives, Indefinite Integrals, and Simple Differential Equations 29) 5.4 Indefinite Integrals 30) 5.4 indefinite integrals Trigonometric Functions 31) 5.3 The fundamental Theorem Of Calculus (A) 32) 5.3 The fundamental Theorem Of Calculus (B) 33) 6.5 Mean Value Theorem for Definite Integrals CHAPTER 5-APPLICATIONS OF INTEGRATION (5 Hours) 34) 6.0 Graph 35) 6.1 Areas between curves 36) 6.2 volumes by washer and Cylindrical shells 37) 6.2 volumes by washer and Cylindrical shells 38) 6.0 Arc length (11 Hours)

6 ASSESSMENT METHODS P6 1 Quizzes 10 2 First Mid Term Examination 25 3 Second Mid Term Examination 25 4 Final Examination Suggested grading : A A B B B C C C D D 0 49 F

7 No Definition of limit Lecture Table Lecture P7 Notes Techniques for finding limits (A) 2.3 Techniques for finding limits (B) 3.5 Techniques for finding limits of Trigonometric function (A) 3.5 Techniques for finding limits of Trigonometric function (B). 2.3 Squeeze theorem. 4.4 Limits involving infinity (A) 4.4 Limits involving infinity (B) 4.4 Vertical And Horizontal Asymptotes (A) 4.4 Vertical And Horizontal Asymptotes (B) 2.5 Continuous Functions (A) 2.5 Continuous Functions (B) 2.5 Discontinuous Functions (A) 2.5 Discontinuous Functions (B) 2.5 Intermediate Value Theorem (A) 2.5 Intermediate Value Theorem (B) 3.2 Definition of Differentiation (A) 3.2 Definition of Differentiation (B) 3.3 Techniques of differentiation and 3.5 Derivatives of the Trigonometric Functions.docx 3.6 The Chain Rule 3.x TANGENT LINE; CORNER (A) 22 3.x TANGENT LINE; CORNER (B)

8 Lecture Table P8 No Implicit Differentiation (A) Lecture Notes Implicit Differentiation (B) linear Approximations and differentials Related rates (A) Related rates (B) Summary of Graphical Methods (A) Summary of Graphical Methods (B) Summary of Graphical Methods (C) Summary of Graphical Methods (D) The Rolle's Theorem (A) The Rolle's Theorem (B) The Mean Value Theorem (A) The Mean Value Theorem (B) Optimization Problems (A) Optimization Problems (B)

9 Lecture Table P9 No 38 Lecture 4.10 Antiderivatives, indefinite integrals, and simple differential equations. Notes indefinite integrals indefinite integrals Trigonometric Functions The fundamental Theorem Of Calculus (A) The fundamental Theorem Of Calculus (B) The fundamental Theorem Of Calculus (C) The fundamental Theorem Of Calculus (D) The average value of the function Mean Value Theorem for Definite Integrals Graph Areas between curves volumes by washer volumes Cylindrical shells volumes