| Course Objectives: |
To construct a mathematical infrastructure by teaching basic information about the function, limit, continuity, derivative and integral, to provide the ability to use relevant concepts in practice and to gain the ability to use mathematical knowledge in solving engineering problems. |
| Course Content: |
This course employs the project-based learning approach. In this respect aside from the conventional content the course has a project-based learning component. The project based-learning component aims realising one or more projects designed for learning purposes involving the development of certain intermediary and final deliverables in a step-by-step mannerby the students individually or in project teams. The evaluation of the project-based learning component involves grading the project deliverables and the project works by the instructor and/or a jury.
Functions (Domain and Range Sets, Functions and Graphs, Even-Odd Functions, Operations on Functions, Composition of Functions, Piecewise Functions, Polynomial and Rational Functions, Trigonometric Functions); Limit (Limit of a Function and Limit Rules, Sandwich Theorem, Definition of Limit, One Sided Limits, Limits Containing Infinity, Infinite Limits); Continuity (Continuity at a Point, Continuous Functions, Intermediate Value Theorem, Types of Discontinuity); Derivative (Tangent and Normal Lines, Derivative on a Point, Derivative on a Range, Derivative Rules, Higher Order Derivatives, Derivatives of Trigonometric Functions, Chain Rule, Increasing and Decreasing Functions, Transcendent Functions, Derivatives of Inverse Functions, Properties and Derivatives of Exponential and Logarithmic Functions, Derivatives of Inverse Trigonometric Functions, Derivatives of Hyperbolic and Inverse Hyperbolic Functions, Indeterminates and L'Hopital's Rule, Extreme Values of Functions, Critical Points, Rolle Theorem, Mean Value Theorem, Local First Derivative Test for Extremes, Concavity, Second Derivative Test for Concavity, Inflection Points, Second Derivative Test for Local Extremum, Asymptotes of Graphs, Curve drawing); Indefinite Integral (Integral: Estimating with Area and Finite Sums, Sigma Notation and Limits of Finite Sums, Riemann Sums, Definite Integral, Properties of a Definite Integral, Area Under the Graph of a Non-Negative Function, Mean Value Theorem for Definite Integrals, Fundamental Theorem of Calculus, Integration Techniques, Trigonometric Integrals, Reduction Formulas, Integration of Rational Functions with Partial Fractions, Applications: Calculation of Areas of Plane Regions, Area Between Two Curves, Calculation of Volumes of Rotational Bodies (Disk Method, Shell Method, Cylindrical Shell Method), Arc Length, Areas of Revolving Surfaces, Generalized (Improper) Integrals. |
Course Learning Outcomes (CLOs) are those describing the knowledge, skills and competencies that students are expected to achieve upon successful completion of the course. In this context, Course Learning Outcomes defined for this course unit are as follows:
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| Knowledge
(Described as Theoritical and/or Factual Knowledge.)
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| Skills
(Describe as Cognitive and/or Practical Skills.)
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1) Learn to use the concepts of limit, continuity, derivative and integral in the functions having a single variable.
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2) Sketch the graph of a function using asymptotes, critical points and the derivative test for increasing/decreasing and concavity properties.
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3) Set up max/min problems and use differentiation to solve them.
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4) Evaluate integrals by using the Fundamental Theorem of Calculus and apply integration to compute areas and volumes by slicing, volumes of revolution, and length.
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5) Work with transcendental functions and evaluate integrals using techniques of integration.
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6) Use L'Hospital's rule.
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| Competences
(Described as "Ability of the learner to apply knowledge and skills autonomously with responsibility", "Learning to learn"," Communication and social" and "Field specific" competences.)
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| Week |
Subject |
Materials Sharing * |
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Related Preparation |
Further Study |
| 1) |
Introduction |
Reading assignment, Preparatory study
|
Project work, Homework assignment |
| 2) |
Functions |
Reading assignment, Preparatory study
|
Project work, Homework assignment |
| 3) |
Functions |
Reading assignment, Preparatory study
|
Project work, Homework assignment |
| 4) |
Limit |
Reading assignment, Preparatory study
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| 5) |
Continuity |
Reading assignment, Preparatory study
|
Project work, Homework assignment |
| 6) |
Derivatives |
Reading assignment, Preparatory study
|
Project work, Homework assignment |
| 7) |
Applications of Derivatives |
Reading assignment, Preparatory study
|
Project work, Homework assignment |
| 8) |
Mid Term Exam |
Reading assignment, Preparatory study
|
Project work, Homework assignment |
| 9) |
L’Hopital’ s Rule |
Reading assignment, Preparatory study
|
Project work, Homework assignment |
| 10) |
Integration |
Reading assignment, Preparatory study
|
Project work, Homework assignment |
| 11) |
Applications of Integrals |
Reading assignment, Preparatory study
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Project work, Homework assignment |
| 13) |
Integration Techniques |
Reading assignment, Preparatory study
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Project work, Homework assignment |
| 14) |
Integration Techniques |
Reading assignment, Preparatory study
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| 15) |
Review of term |
Reading assignment, Preparatory study
|
Project work, Homework assignment |
(KPLOs and SPLOs are the abbreviations for Key & Sub- Programme Learning Outcomes, respectively. )
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Programme Learning Outcomes |
Contribution Level (from 1 to 5) |
1) |
Uses and applies theoretical and applied sciences in the field of basic science subjects for the solution of computer engineering problems. |
3 |
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1.1 Has sufficient knowledge in mathematics, science, computer science and computer engineering; use theoretical and applied knowledge in these fields together to solve computer engineering problems |
3 |
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2) |
Analyzes computer engineering applications, designs and develops models to meet specific requirements under realistic constraints and conditions. For this purpose, selects and uses appropriate methods, tools and technologies. |
3 |
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2.1 Identify, define, formulate and solve complex computer engineering problems; for this purpose select and apply appropriate analytical and modeling methods |
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2.2 Designs a complex computer and software based system, process, device or product to meet certain requirements under realistic constraints and conditions, including economics, environmental issues, sustainability, manufacturability, ethics, health, safety, social and political issues; For this purpose, it applies modern design methods. |
3 |
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2.3 Selects and effectively uses modern techniques and tools and information technologies required for computer science and computer engineering applications. |
3 |
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2.4 Designs and conducts experiments, collects data, analyzes and interprets the results for the study of computer science and computer engineering problems and research topics. |
3 |
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3) |
Owns the competencies required by the constantly developing field of computer engineering and the global competitive environment. |
3 |
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3.1 Works effectively individually and in multi-disciplinary teams, takes responsibility. |
3 |
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3.2 Accesses the information and for this purpose searches for resources, uses databases and other information resources. |
5 |
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3.3 Awares of the necessity of lifelong learning, follows developments in science and technology and renews itself continuously. |
4 |
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3.4 Communicates effectively in Turkish, both orally and in writing, has at least one foreign language knowledge at the level of European Language Portfolio B1. |
5 |
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3.5 Manage projects, has conscious of workplace practices, employee health, environmental and work safety; aware of the legal consequences of engineering applications. |
3 |
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3.6 Has awareness of the universal and social effects of engineering solutions and applications; has awareness of entrepreneurship and innovativeness and knowledgeable about contemporary issues. |
2 |
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3.7 Has professional and ethical responsibility. |
1 |
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3.8 Has information about the standards used in computer engineering applications. |
5 |
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3.9 Has quality consciousness. |
1 |
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3.10 Has the capacity to work in at least one of the important application areas of computer science and computer engineering. |
5 |
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4) |
Applies the theoretical knowledge in business life during a semester. |
2 |
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4.1 Experiences all processes in business life. |
2 |
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4.2 Takes part in activities related to the field of education in a business operating in the field. |
3 |
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4.3 Questions the application with theoretical knowledge. |
4 |
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4.4 Compiles the knowledge and experience gained in the field. |
4 |
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5) |
S/he acquires the competencies that develop by the expectations of business world and the society defined as the institutional outcomes of our university on the advanced level in relation with his/her field. |
5 |
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5.1 Acquires the analyzing solving the problems and managing the conflicts. |
5 |
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5.2 Participates as a team member and takes responsibility in the environments that require the solving of the conflicts and acts as a leader when necessary. |
3 |
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5.3 Has awareness for ethical and social responsivity. |
1 |
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5.4 By supporting the learnt courses with quantitative and qualitative data; and by using verbal and visual communication means, s/he transfers them to the groups within and outside his/her group in a systematical and effective way. |
2 |
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5.5 Evaluates the norms and standards present in the works in which s/he takes responsibility in a critical point of view. |
2 |
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5.6 Develops strategical, innovative and entrepreneurial ideas. |
2 |
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5.7 Acquires competence of managing the change. |
3 |
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5.8 Shows development personally and socially with and awareness for lifelong learning. |
2 |
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5.9 Follows advanced technologies and developments about digital transformation. |
1 |
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5.10 Has cultural awareness and s/he transfers this to the groups within and outside his/her field. |
1 |
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5.11 Has awareness about citizenship competency. |
1 |
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5.12 Acquires communication in a Foreign Language (English) competence defined on the level of at least B1 in European Language Portfolio. (In programs whose medium of instruction is English, on the level of B2/B2+). |
3 |
ECTS Information Package / Course Catalogue