Syllabus for MATH 153 – Calculus I
Objectives
This first part of two-tier course aims to provide basic and some further concepts of Mathematics such as functions and their
graphs, limits and continuity, transcendental functions, derivatives, integrals and their applications.
Textbook
“Calculus, A Complete Course” by Robert A. Adams, Sixth Edition, Addison Wesley.
References
“Calculus, Early Transcendentals” by Howard Anton, Irl Bivens, Stephen Davis, Eighth Edition, Wiley.
Grading
Exam
Midterm I
Midterm II
Final Exam
Quizzes
Ratio
25%
25%
40%
10%
Course Outline
1.
Real Numbers and the Real Line. Cartesian Coordinates in the Plane. Graphs of Quadratic Equations. Functions
and Their Graphs.
2.
Combining Functions to Make New Functions. Polynomials and Rational Functions. The Trigonometric Functions.
Limits of Functions.
3.
Limits at Infinity and Infinite Limits. Continuity. Tangent Lines and Their Slopes.
4.
The Derivative. Differentiation Rules. The Chain Rule. Derivatives of Trigonometric Functions. The Mean-Value
Theorem.
5.
Higher-Order Derivatives. Implicit Differentiation. Antiderivatives and Initial-Value Problems.
6.
Inverse Functions. Exponential and Logarithmic Functions. The Natural Logarithm and Exponential. The Inverse
Trigonometric Functions.
7.
Hyperbolic Functions. Second-Order Linear Differential Equations with Constant Coefficients.Related Rates.
8.
Extreme Values. Concavity and Inflections. Sketching the Graph of a Function. Extreme-Value Problems. Finding
Roots of Equations (Newton’s Method).
9.
Linear Approximations. Taylor Polynomials. Indeterminate Forms. Sums and Sigma Notation.
10. Areas as Limits of Sums. The Definite Integral. Properties of the Definite Integral.
11. The Fundamental Theorem of Calculus. The Method of Substitution. Areas of Plane Regions.
12. Integration by Parts. Inverse Substitutions. Integrals of Rational Functions.
13. Integration using Maple. Improper Integrals. The Trapezoid and Midpoint Rules. Simpson’s Rule.
14. Volumes by Slicing-Solids of Revolution. Arc Length and Surface Area.
Applications by Using Maple
1. Defining and Graphing Functions. Calculating with Trigonometric Functions.
2. Calculating Limits. Solving Equations with fsolve.
3. Finding Derivatives. Higher-Order Derivatives.
4. Derivatives of Implicit Functions. More Graph Plotting.
5. Integrating Functions. Numerical Integration.
Rules
Attendance is an essential requirement of this course and is the responsibility of the student. Class begins promptly and you
are expected to be present at the beginning and at the end of each class session.
Note
* The content of this sylabus can be changed by the instructor at any timeby informing the related department’s head.
* The student is supposed to be aware of the facts and notices written in this sylabus.