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| MAT1033 | Mathematics - I | 4+0+0 | ECTS:4 | | Year / Semester | Fall Semester | | Level of Course | First Cycle | | Status | Compulsory | | Department | NAVAL ARCHITECTURE and MARINE ENGINEERING | | Prerequisites and co-requisites | None | | Mode of Delivery | | | Contact Hours | 14 weeks - 4 hours of lectures per week | | Lecturer | Öğr. Gör. Dr Şenol DEMİR | | Co-Lecturer | Şenol DEMİR | | Language of instruction | Turkish | | Professional practise ( internship ) | None | | | | The aim of the course: | | The course aims to provide the basic information about functions, limit, derivative, integral as well as their appicaitons in various disciplines including physical and engineering sciences. |
| Learning Outcomes | CTPO | TOA | | Upon successful completion of the course, the students will be able to : | | | | LO - 1 : | clasify numbers and understand functions and their properties | 1 | 1, | | LO - 2 : | know the concepts of limit and continuity of functions | 1 | 1, | | LO - 3 : | know the concepts of derivatives of functions | 1 | 1, | | LO - 4 : | apply of the derivative to some engineering problems | 1 | 1, | | LO - 5 : | know the concepts of integral of functions | 1 | 1, | | LO - 6 : | apply the integration to some engineering problems and to some applications | 1 | 1, | | CTPO : Contribution to programme outcomes, TOA :Type of assessment (1: written exam, 2: Oral exam, 3: Homework assignment, 4: Laboratory exercise/exam, 5: Seminar / presentation, 6: Term paper), LO : Learning Outcome | | |
| Functions, inverse functions, plotting the graphs of basic curves, transformation of graphs. Trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions . Limit, rules of limit, continuity . Derivative of function, geometric meaning of derivative, rules of derivative, derivative of trigonometric functions, inverse trigonometric functions, logarithmic and exponential functions. Higher order derivative, chain rules, derivative of implicit functions, applications of derivative, concept of derivation. L?hospital rule, limit at infinity, Rolle Theorem and Mean Value Theorem, extrema of functions . Asymptotes, plotting graphs by observation of changes in functions . Indefinite integrals . Methods of integration, change of variable, integration by parts, integration of polynomials, algebraic and trigonometric (rational) functions . Riemann sums, definite integration and properties, fundamental theorem of analysis. Applications of definite integrals: areas of regions, length of curves, volumes of rotating objects, surface arease, calculation of mass, moment, gravitational center and work. Change of variables for definite integrals. Generalization of integration . |
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| Course Syllabus | | Week | Subject | Related Notes / Files | | Week 1 | Functions:Domain of a Function,Functions and Graphs, Even-Odd Functions, Symmetry, Operations on Functions (Sum, difference, multiplication, division and powers),Composite Functions, Piecewise Functions, Polynomials and Rational Functions. | | | Week 2 | Trigonometric functions, Inverse trigonometric functions, Logarithmic, exponential and hyperbolic functions | | | Week 3 | Limits and Contiunity: Limit of a Function and Limit Laws, The Sandwich (The Squeeze theorem), The Precise Definition of a Limit, One-sided Limits, , Limits İnvolving İnfinity, Infinity Limits | | | Week 4 | Contiunity at a Point, Continuous Functions, The İntermediate Value Theorem Types of Discontiunity, | | | Week 5 | Differentiation:Tangents ,Normal Lines , The Derivative at a Point, The Derivate as a Function, One sided Derivatives | | | Week 6 | Differentiable on an Interval, Differentiation Rules, High order Derivatives, Derivatives of Trigonometric Functions, The Chain Rule. | | | Week 7 | Implicit Differentiation, Linearization and Differentials, Increasing Functions and Decrasing Functions, Inverse Functions and Their Derivatives, Logarithms and Exponential Functions and Their Derivatives, Logarithmic Differentiation, | | | Week 8 | Inverse Trigonometric Functions and Their Derivatives, Hyperbolic Functions and Their Derivatives,Inverse Hyperbolic Functions and Their Derivatives, Indeterminate Forms and L?Hospitals Rule | | | Week 9 | Midterm exam | | | Week 10 | Extrem Values of Functions, Critical Points, Rolle?s Theorem, The Mean Value Theorem, The First Derivative Test for Local Extrema, Concavity , The Second Derivative Test for Concavity, Point of İnflection, The Second Derivative Test for Local Extrema. | | | Week 11 | Asymptotes of Graphs, Curve Sketching, Antiderivatives, Indefinite Integrals, Integral Tables | | | Week 12 | Integration:Area and Estimating with Finite Sums, Sigma Notation and Limits of Finite Sums, Riemann Sums, Definite İntegral, Properties of Definite İntegral, Area Under the Graph of a
nonnegative Function, Average Value of Continuous Functions | | | Week 13 | Mean Value Theorem fo Definite İntegrals, The Fundamental Theorem of Calculus: Fundamental Theorem Part 1, Fundamental Theorem Part 2, Techniques of Integration: Integration by Substitution, Integration by Parts, Trigonometric Integrals, Reduction Formulas | | | Week 14 | Trigonometric Substitutions, Tan (?/2) subtitutions, Integrations of Rational Functions by Partial Fractions | | | Week 15 | Applications of definite integrals:Area between two curves, Volumes Using Cross-sections, The Disk Method, the Washer Method, The Ccylindrical Shell method, Arch Length, Areas of Surfuces of Revolution | | | Week 16 | Final exam | | | |
| 1 | Thomas, G.B., Weir, M.D., Hass, J., Thomas' Calculus, 12th Edition, 2009, Pearson, USA. | | | |
| 1 | Stewart, James, Calculus(Early transcendentals), 6th Edition, Thomson Brooks/Cole, 2008, USA.
| | | 2 | Adams, R.A., Essex, C., Calculus a Complete Course, 2010, Pearson, USA. | | | 3 | Genel Matematik, Ekrem KADIOĞLU | | | |
| Method of Assessment | | Type of assessment | Week No | Date | Duration (hours) | Weight (%) | | Mid-term exam | 9 | 29/11/2023 | 1,30 | 50 | | End-of-term exam | 16 | 17/01/2024 | 1,40 | 50 | | |
| Student Work Load and its Distribution | | Type of work | Duration (hours pw) | No of weeks / Number of activity | Hours in total per term | | Yüz yüze eğitim | 4 | 14 | 56 | | Sınıf dışı çalışma | 5 | 14 | 70 | | Arasınav için hazırlık | 9 | 1 | 9 | | Arasınav | 15 | 1 | 15 | | Dönem sonu sınavı için hazırlık | 10 | 1 | 10 | | Dönem sonu sınavı | 2 | 1 | 2 | | Total work load | | | 162 |
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