Calculus for Mathematics Students I
Math 153 - Spring 2021
Announcements
This page contains some information that can be helpful before you register for the course. After the registration, we will be using ODTUClass. You should follow ODTUClass and check your emails regularly for important announcements during the semester.
Course Objectives
At the end of this course, the student will learn the concepts limit, continuity, derivative of a function of one variable and some of their applications to real life problems.
Lectures and Office Hours
All lectures will be live. The meeting links will be announced on ODTUClass. The lecture notes will be uploaded to ODTUClass and can be accessed by the students at any time. For steady progress, students are advised to read the lecture notes on the day of the lecture even if they cannot attend the live lectures.
Students are welcome to attend the office hours. The meeting links will be announced on ODTUClass.
Grading
Your final letter grade will be determined by three exams, several quizzes, and homework.
Midterm 1, 30 points. April 26, Monday at 10:40
Midterm 2, 30 points. June 7, Monday at 10:40
Final, 40 points.
Quizzes and Homework, 10 points.
The midterms will be written exams, and the students will be proctored by the camera. The final exam will be a combination of a written exam and an oral exam. The details of the examination procedures will be announced before each exam. A reliable internet connection will be necessary during all exams.
Course Policy
Only one make-up examination will be offered for each student. The excuse for not attending an examination must be proved with documents. A make-up examination will take place a few days after the missed exam.
The quizzes will be given in recitations. The time of the quizzes will be announced in advance. A portion of quiz scores will be dropped, and there will be no make-up for quizzes.
Each homework must be submitted as group work. The procedure for forming the homework groups will be announced during the first week of classes. No late homework will be accepted throughout the semester.
Textbook
The suggested textbook: Robert A. Adams, Christopher Essex - CALCULUS, A Complete Course Calculus. Eight Edition.
Course Outline
Preliminaries: (2 weeks):
Week 1 - Real numbers and the real line. Equations and inequalities. Cartesian coordinates. Graphs of quadratic equations.
Week 2 - Functions and their graphs. Combining functions to make new functions. Polynomials and rational functions. Trigonometric functions.
Limits and Continuity: (3 weeks):
Week 3 - Motivating examples. The formal epsilon-delta definition. One-sided limits.
Week 4 - Rules for calculating limits. The squeeze Theorem. Limits at infinity and infinite limits.
Week 5 - Continuity and the substitution rule. Properties of continuous functions; intermediate value and extreme value theorems.
Differentiation: (3 weeks):
Week 6 - Tangent lines and their slopes. The definition of the derivative. Differentiation rules.
Week 7 - Midterm 1. The chain rule. Derivatives of trigonometric functions.
Week 8 - Higher-order derivatives. The mean value Theorem. Increasing and decreasing functions. Implicit Differentiation.
Transcendental Functions: (2 weeks):
Week 9 - Inverse functions. Exponential and the logarithmic functions.
Week 10 - Growth and decay. Inverse trigonometric functions. Hyperbolic functions.
Applications of Derivatives: (4 weeks):
Week 11 - Related Rates. Indeterminate forms.
Week 12 - Midterm 2. Extreme values. Concavity and inflections.
Week 13 - Graph sketching. Extreme-value problems.
Week 14 - Extreme-value problems. Linear approximations.