| 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) |
Ability to utilize advanced theoretical and applied knowledge in the field. |
2 |
| 2) |
Using the advanced knowledge and skills acquired in the field, being able to interpret and evaluate data, identify problems, analyze them, and develop solution proposals based on research and evidence. |
2 |
| 3) |
Being able to organize and implement projects and activities for the social environment in which one lives with a sense of social responsibility. |
1 |
| 4) |
Being able to follow information in one foreign language at least at the European Language Portfolio B1 General Level and communicate with colleagues in the field. |
1 |
| 5) |
Ability to use information and communication technologies together with at least European Computer Driving License Advanced Level computer software, as required by the field. |
2 |
| 6) |
Being able to evaluate advanced knowledge and skills in the field critically. |
1 |
| 7) |
Identifying learning needs and being able to direct learning. |
1 |
| 8) |
Developing a positive attitude towards lifelong learning. |
1 |
| 9) |
Acting in accordance with social, scientific, cultural, and ethical values in the stages of collecting, interpreting, applying, and announcing the results related to the field. |
2 |
| 10) |
Having sufficient awareness about the universality of social rights, social justice, quality culture, preservation of cultural values, as well as environmental protection, occupational health, and safety. |
1 |
| 11) |
Being able to conduct an advanced study independently in the field. |
2 |
| 12) |
To take responsibility individually and as a team member to solve complex problems encountered in the field of application, which are unforeseen. |
2 |
| 13) |
Being able to plan and manage activities for the development of those under their responsibility within the framework of a project. |
2 |
| 14) |
Possess advanced level theoretical and practical knowledge supported by textbooks with updated information, practice equipments and other resources. |
1 |
| 15) |
Being able to inform relevant individuals and institutions about the field; expressing their thoughts and solution proposals for problems both in written and verbal form. |
1 |
| 16) |
Being able to share your thoughts and solutions regarding subjects related to the field with both experts and non-experts, supported by quantitative and qualitative data. |
1 |
Istanbul Health and Technology University INFORMATION PACKAGE / COURSE CATALOGUE