math 110
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Math 110 (Calculus I)
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Math 110
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Calculus I
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Credits
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Lec.
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Tut.
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3
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3
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1
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Course Summary
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This course is a first Calculus dealing mainly with differential calculus. After a discussion of few mathematical preliminaries, we introduce functions and models, limits and derivatives, differentiation rules, and finally applications of differentiation.
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Prerequisites
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-
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None
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Textbook
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J.Stewart
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Calculus, Early Transcendentals Sixth Edition.
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International Metric Version
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2008
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Objectives:
On completion of the course, the students should be able to
- handle functions occurring in calculus and in the mathematical modeling of real-world problems;
- grasp the central idea of limit and continuity, and its application in a variety of problems;
- understand the main theme of calculus and its applications involving rates of change and the approximation of functions;
- differentiate standard functions by applying the fundamental rules of differentiation;
- compute the optimal values of functions and handle the optimization problems;
- apply the concepts of monotonicity and concavity in sketching the plane curves;
- deal with indeterminate forms and L’Hôpital’s rule;
- understand the connection between derivatives and antiderivatives.
Course description:
1. Mathematical Preliminaries
- a. Numbers, Inequalities, and Absolute Values
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- b.
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- Coordinate Geometry and Lines
- c.
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- Graphs of Second-Degree Equations
- d.
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- Trigonometry
2. Functions and Models
- a.
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- Four Ways to represent a Function
- b.
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- Mathematical Models
- c.
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- New Functions from Old Functions
- d.
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- Graphing Calculators and Computers
- e.
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- Exponential Functions
- f.
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- Inverse Functions and Logarithms
3. Limits and Derivatives
- a.
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- The Tangent and Velocity Problems
- b.
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- The Limit of a Function
- c.
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- Calculating Limits Using the Limit Laws
- d.
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- Continuity
- e.
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- Limits at Infinity; Horizontal Asymptotes
- f.
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- Derivatives and Rates of Change
- g.
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- The Derivative as a Function
4. Differentiation Rules
- a.
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- Derivatives of Polynomials and Exponential Functions
- b.
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- The Product and Quotient Rules
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- Derivatives of Trigonometric Functions
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- The Chain Rule
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- Implicit Differentiation
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- Derivatives of Logarithmic Functions
- g.
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- Rates of Change in the Sciences
- h.
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- Exponential Approximations and Differentials Hyperbolic Functions
5. Applications of Differentiation
- a.
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- Maximum and Minimum Values
- b.
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- The Mean Value Theorem
- c.
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- How derivatives Affect the Shape of a Graph
- d.
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- Intermediate Forms and L’Hospital Rule
- e.
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- Summary of Curve Sketching
- f.
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- Graphing with Calculus and Calculators
- g.
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- Optimization Problems
- h.
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- Antiderivatives
Teaching Schedule:
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Delivery Type
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Number
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Lecture Length (hours)
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Student Hours
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Lecture
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39
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1
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39
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Tutorial
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13
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1
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13
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Private Study Hours
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117
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Total Contact Hours
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52
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Total Hours
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169
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Methods of Assessment:
1- Coursework
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Assessment Type
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Notes (paper HW/Online)
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% of Formal Assessment
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In-course Assessment
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Weekly Paper HW
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10
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Total Percentage
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10
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2- Exams
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Assessment Type
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Notes (MCQ, etc …
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% of Formal Assessment
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First Exam
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Written
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30
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Second Exam
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Written
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30
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Final Exam
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Written
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40
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Total Percentage
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100
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آخر تحديث
2/24/2013 8:01:12 PM
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