Week |
Subject |
Related Preparation |
1) |
Infinite Sequences: Convergence and Divergence of Sequences, Calculating Limits of Sequences, Sandwich Theorem for Sequences, Continuous Function Theorem of Sequences, Frequent Limits, Recursively Defined, Sequences, Bounded Monotone Sequences, Monotone Sequence Theorem. |
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2) |
Infinite Series: For Geometric Series, Divergent Series n. Term Test, Combining Series, Adding or Deleting Terms, Convergence Tests for Series with Positive Terms: Integral Test, p Series, Harmonic Series, Comparison Test, Limit Comparison Test, Ratio Test, Root Test. |
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3) |
Alternating Series: Alternating Harmonic Series, Alternating Series Test (Leibniz Test), Absolute and Conditional Convergence. Power Series: Radius of Convergence of a Power Series, Operations in Power Series, Series Product Theorem for Power Series, Term Term Derivative Theorem, Term Term Integration Theorem, Taylor and Maclaurin Series, n. Taylor Polynomial of Order. |
|
4) |
Applications of Taylor Series: Computing Non-Elementary Integrals, Arctangents, Calculating Limits Under Uncertainty. Parametric Equations and Polar Coordinates: Parametrizing Planar Curves. |
|
5) |
Polar Coordinates: Polar Equations, Relationship Between Polar and Cartesian Coordinates, Graphing with Polar Coordinates (Line, Circle and Cardioid), Areas and Lengths in Polar Coordinates, Area in Plane, Length of Polar Curve. |
|
6) |
Vectors: Three Dimensional Coordinate Systems, Vectors, Dot Product, Angle Between Two Vectors, Perpendicular Vectors, Vector Product, Parallel Vectors, Lines and Planes in Space: Lines and Line Segments in Space, Vector Equation of a Line, Parametric Equations of a Line, A Plane in Space Equation for Intersection Lines. Vector Value Functions: Curves and Tangents in Space, Limit and Continuity, Derivatives, Velocity Vector, Acceleration Vector, Rules of Derivative, Arc Length Along a Space Curve. |
|
7) |
Multivariate Functions: Definition and Value Sets, Functions of Bivariates, Graphs of Functions of Bivariates and Level Curves, Functions of Trivariate, Level Surfaces (plane, sphere, ellipsoid, elliptical paraboloid, cylinder, cone), Limit in Bivariate Functions, Continuity, Limitin Dual Path Test for Absence, Continuity of Resultant Functions, Functions with More than Two Variables. |
|
8) |
Partial Derivatives: Partial Derivatives of Functions of Two Variables, Partial Derivative and Continuity, Second Order Partial Derivatives, Mixed Derivative Theorem, Higher Order Partial Derivatives, Differentiability, Chain Rule: Functions of Two Variables, Chain Rule for Functions Containing Two Independent Variables, Functions of Three Variables, Chain Rule for Functions with Three Arguments, Chain Rule for Two Arguments and Three Intermediate Variables. |
|
9) |
Implicit Derivative, Directional Derivatives and Gradient Vector: Directional Derivatives in the Plane, Computation and Gradients, Tangents of Level Curves and Gradients, Functions of Three Variables. Tangent Planes and Differentials: Tangent Plane of a Surface, Normal Line of a Surface. |
|
10) |
Linearizing Two Variables Function, Differentials, Extreme Values; Local Extreme Values, Critical and Saddle Points, Second Derivative Test for Local Extreme Values. |
|
11) |
Multiple Integrals: Double Integrals on Rectangles, Double Integrals as Volume. Calculation of Double Integrals: Fubini's Theorem (First Shape), Double Integrals over General Regions, Double Integrals over Non-Rectangular Bounded Regions, Volumes (volume between two surfaces), Fubini's Theorem (Extensive Shape) |
|
12) |
Finding the limits of integration: Properties of Double Integrals, Area Calculation of Double Integrals, Mean Value Theorem. Double Integrals in Polar Form: Finding Integration Boundaries, Converting Cartesian Integrals to Polar Integrals. |
|
13) |
Calculation of volume (volume between two surfaces) using polar coordinates, Variable Transformation in Double Integrals. |
|
14) |
Triple Integral: Triple Integral in Cartesian Coordinates, Volume Calculation, Triple Integral Calculation in Spherical Coordinates. |
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Program Outcomes |
Level of Contribution |
1) |
Adequate knowledge in mathematics, science, and related engineering discipline; ability to use theoretical and practical knowledge in these areas in complex engineering problems. |
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2) |
An ability to detect, identify, formulate, and solve complex engineering problems; the ability to select and apply appropriate analysis and modelling methods for this purpose. |
|
3) |
An ability to design a complex system, process, device, or product to meet specific requirements under realistic constraints and conditions; the ability to apply modern design methods for this purpose. |
|
4) |
An ability to develop, select and use modern techniques and tools necessary for the analysis and solution of complex problems in engineering applications. |
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5) |
An ability to use information technologies effectively. |
|
6) |
Ability to design, conduct experiments, collect data, analyse, and interpret results to investigate complex engineering problems or discipline-specific research topics. |
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7) |
Ability to work effectively in disciplinary and multidisciplinary teams; ability to work individually. |
|
8) |
Ability to communicate effectively in oral and written Turkish. |
|
9) |
Knowledge of at least one foreign language. |
|
10) |
Ability to write effective reports and understand written reports, to prepare design and production reports, to make effective presentations, to give clear and understandable instructions. |
|
11) |
Awareness of the necessity of lifelong learning; ability to access information, follow developments in science and technology and ability to renew themselves. |
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