| 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. |
|
| 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. |
|
| 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. |
|
| |
Program Outcomes |
Level of Contribution |
| 1) |
Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in complex engineering problems. |
3 |
| 2) |
Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modelling methods for this purpose. |
3 |
| 3) |
Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way as to meet the desired result; ability to apply modern design methods for this purpose. |
2 |
| 4) |
Ability to devise, select, and use modern techniques and tools needed for analysing and solving complex problems encountered in engineering practice; ability to employ information technologies effectively. |
1 |
| 5) |
Ability to design and conduct experiments, gather data, analyse and interpret results for investigating complex engineering problems or discipline specific research questions. |
2 |
| 6) |
Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually. |
1 |
| 7) |
Ability to communicate effectively in Turkish, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instructions. |
1 |
| 8) |
Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself. |
2 |
| 9) |
Consciousness to behave according to ethical principles and professional and ethical responsibility; knowledge on standards used in engineering practice. |
1 |
| 10) |
Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development. |
1 |
| 11) |
Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions |
1 |
Istanbul Health and Technology University INFORMATION PACKAGE / COURSE CATALOGUE