COURSE OUTLINE - MFSacedon's website



COURSE OUTLINE

Revised: 2008

COURSE NO. : MATH 101

COURSE TITLE : ELEMENTARY CALCULUS

COURSE DESCRIPTION : Functions and graphs, linear and quadratic functions, polynomial functions, exponential and logarithmic functions, limits and continuity, theories of differential and integral calculus and their applications to all sciences.

PREREQUISITE : MATH 12 (Plane Trigonometry)

CREDIT : 3 units

3 hours a week (lecture)

CHAPTER I. Mathematical Functions and Their graphs

1. Definitions (1 hr)

1.11 Function and relation

1.12 Range and domain

2. Linear function (2 hrs)

21. Standard form of linear equation

22. Forms of linear equation & their graphs

3. Quadratic function (2 hrs)

1.31 Imaginary numbers

32. Solutions of quadratic functions

33. General form of quadratic function & their graphs

4. Polynomial function (1.5 hrs)

41. Synthetic division

42. Solutions of selected polynomial functions & their graphs

5. Exponential function (2hrs)

51. Laws of exponent

52. Standard form of Exponential model

53. Solutions of exponential function by One-to-One correspondence & their graphs

6. Logarithmic function (2 hrs)

61. Exponential and inverse exponential theorem

62. Properties of logarithm

63. Solutions of logarithmic & exponential equations, & their graphs

7. Application problems to all sciences (1.5 hrs)

CHAPTER 2. Limits and Continuity (3 hrs)

1. Theorems of limit

2. One sided limits

3. Two sided limits

4. Limits evaluation

2.41 Limits at a point

2.42 Limits at infinity

2.43 Infinite limit

5. Continuity and discontinuity of a function

CHAPTER 3. Differential Calculus

1. Introduction

2. Slope of a tangent line of a function (1.5 hrs)

3. Theorems of differentiation (4 hrs)

31. Constant and Identity

32. Power rule

33. Constant and a function

34. Sum rule

35. Product and quotient rule

36. The chain rule and power rule

4. The derivative as a rate of change (1.5 hr)

5. Implicit differentiation (1.5 hrs)

6. Higher order derivatives (1.5 hr)

7. Curve Sketching (2 hrs)

1. Definitions of Symmetry, Asymptotes

2. Critical points

3. Concavity

4. Derivative test

1. The first derivative test

2. The second derivative test

5. Curve sketching

8. Application of derivatives to all sciences (4 hrs)

9. Partial Derivatives (3 hrs)

CHAPTER 4. INTEGRAL CALCULUS

1. Antiderivative (1.5 hr)

2. The indefinite and definite integrals (1.5 hr)

3. Area as a definite integral (1 hr)

4. Rules of integration (2 hrs)

5. Techniques of integration (3 hrs)

5.51 By Substitution

5.52 By Parts

5.6 Applications of integral calculus (2 hrs)

5.7 Multiple Integrals (3 hrs)

Text Book:

References

1. reter

Grading System:

• Final Grade = 1/3 Midterm Grade + 2/3 Post Midterm grade

• Term Grade = 1/3 Lecture Grade + 2/3 Laboratory Grade

• Lecture Grade = (Quizzes, Long exams, & Attendance) ÷ Total Points

Requirements: Assignments, & Problems Sets

Prepared by:

MARLON F. SACEDON

DMPS Instructor

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