Extended Calculus I (MATH157) Course Detail

Course Name Course Code Season Lecture Hours Application Hours Lab Hours Credit ECTS
Extended Calculus I MATH157 4 2 0 5 7.5
Pre-requisite Course(s)
Course Language English
Course Type N/A
Course Level Bachelor’s Degree (First Cycle)
Mode of Delivery Face To Face
Learning and Teaching Strategies Lecture, Question and Answer, Problem Solving.
Course Coordinator
Course Lecturer(s)
Course Assistants
Course Objectives The sequence Math 157-158 is an extension of the standard calculus course that contains vector calculus and the line integral in addition to the standard complete introduction to the concepts and methods of differential and integral calculus . It is taken by some of the engineering students who needs these topics in their departments. Math 157 is designed to give them computational skills in one variable differential and integral calculus to handle engineering problems
Course Learning Outcomes The students who succeeded in this course;
  • understand, define and use functions, and represent them by means of graphs
  • understand fundamental concepts of limit and continuity
  • understand the meaning of derivative and calculate derivatives of one-variable functions
  • use derivatives to solve problems involving maxima, minima, and related rates
  • understand integration, know integration techniques, use them to solve area, volume and other problems
  • understand improper integrals and sequences
Course Content Preliminaries, limits and continuity, differentiation, applications of derivatives, L`Hopital?s Rule, integration, applications of integrals,integrals and transcendental functions, integration techniques and improper integrals, sequences.

Weekly Subjects and Releated Preparation Studies

Week Subjects Preparation
1 P.1 Real Numbers and the Real Line P.2 Cartesian Coordinates in the Plane P.3 Graphs of Quadratic Equations P.4 Functions and Their Graphs P.5 Combining Functions to Make New Functions pp:3-39
2 P.6 Polynomials and Rational Functions P.7 Trigonometric Functions 1.1 Examples of Velocity, Growth Rate, and Area pp:39-63
3 1.2 Limits of Functions 1.3 Limits at Infinity and Infinite Limits 1.4 Continuity 1.5 The Formal Definition of Limit pp:63-92
4 2.1 Tangent Lines and Their Slopes 2.2 The Derivative 2.3 Differentiation Rules 2. 4 The Chain Rule 2.5 Derivatives of Trigonometric Functions pp:94-125
5 2.6 Higher-Order Derivatives 2.7 Using Differentials and Derivatives 2.8 The Mean Value Theorem 2.9 Implicit Differentiation pp:125-147
6 3.1 Inverse Functions 3.2 Exponential and Logarithmic Functions 3.3 The Natural Logarithm and Exponential 3.4 Growth and Decay (Theorem 4, Theorem 5, Theorem 6 and Examples for these theorems) pp:163-187
7 Midterm
8 3.5 The Inverse Trigonometric Functions 3.6 Hyperbolic Functions (only their definition and derivatives) 4.1 Related Rates 4.3 Indeterminate Forms pp:190-203 pp:213-219 pp:227-232
9 4.4 Extreme Values 4.5 Concavity and Inflections 4.6 Sketching the Graph of a Function pp:232-252
10 4.8 Extreme-Value Problems 4.9 Linear Approximations 2.10 Antiderivatives and Initial Value Problems (Antiderivatives, The Indefinite Integral) 5.1 Sums and Sigma Notation pp:258-271 pp:147-150 pp:288-293
11 5.2 Areas as Limits of Sums 5.3 The Definite Integral 5.4 Properties of the Definite Integral 5.5 The Fundamental Theorem of Calculus pp:293-316
12 5.6 The Method of Substitution 5.7 Areas of Plane Regions 6.1 Integration by Parts pp:316-337
13 6.2 Integrals of Rational Functions 6.3 Inverse Substitutions 6.5 Improper Integrals pp:337-353 pp:359-367
14 7.1 Volumes by Slicing – Solids of Revolution 7.2 More Volumes by Slicing 7.3 Arc Length and Surface Area (only Arc Length) pp:390-407
15 9.1 Sequences and Convergence pp:495-502
16 Final Exam


Course Book 1. Calculus: A complete Course, R. A. Adams, C. Essex, 7th Edition; Pearson Addison Wesley
Other Sources 2. Thomas’ Calculus Early Transcendentals, 11th Edition.( Revised by M. D. Weir, J.Hass and F. R. Giardano; Pearson , Addison Wesley)
3. Calculus: A new horizon, Anton Howard, 6th Edition; John Wiley & Sons
4. Calculus with Analytic Geometry, C. H. Edwards; Prentice Hall
5. Calculus with Analytic Geometry, R. A. Silverman; Prentice Hall

Evaluation System

Requirements Number Percentage of Grade
Attendance/Participation - -
Laboratory - -
Application - -
Field Work - -
Special Course Internship - -
Quizzes/Studio Critics - -
Homework Assignments - -
Presentation - -
Project - -
Report - -
Seminar - -
Midterms Exams/Midterms Jury 2 60
Final Exam/Final Jury 1 40
Toplam 3 100
Percentage of Semester Work 60
Percentage of Final Work 40
Total 100

Course Category

Core Courses
Major Area Courses
Supportive Courses X
Media and Managment Skills Courses
Transferable Skill Courses

The Relation Between Course Learning Competencies and Program Qualifications

# Program Qualifications / Competencies Level of Contribution
1 2 3 4 5
1 An ability to apply knowledge of mathematics, science, and engineering to solve chemical engineering and applied chemistry problems. X
2 An ability to analyze and model a domain specific problem, identify and define the appropriate requirements for its solution. X
3 An ability to design, implement and evaluate a chemical engineering system or a system component to meet specified requirements. X
4 An ability to use the modern techniques and engineering tools necessary for chemical engineering practices. X
5 An ability to acquire, analyze and interpret data to understand chemical engineering and applied chemistry requirements. X
6 The ability to demonstrate the necessary organizational and business skills to work effectively in inter/inner disciplinary teams or individually. X
7 An ability to communicate effectively in Turkish and English. X
8 Recognition of the need for, and the ability to access information, to follow recent developments in science and technology and to engage in life-long learning. X
9 An understanding of professional, legal, ethical and social issues and responsibilities in chemical engineering and applied chemistry. X
10 Skills in project and risk management, awareness about importance of entrepreneurship, innovation and long-term development, and recognition of international standards and methodologies. X

ECTS/Workload Table

Activities Number Duration (Hours) Total Workload
Course Hours (Including Exam Week: 16 x Total Hours) 16 4 64
Application 16 2 32
Special Course Internship
Field Work
Study Hours Out of Class 14 4 56
Presentation/Seminar Prepration
Homework Assignments
Quizzes/Studio Critics
Prepration of Midterm Exams/Midterm Jury
Prepration of Final Exams/Final Jury 1 16 16
Total Workload 168