| Week |
Subject |
Related Preparation |
| 1) |
Functions and their graps. Trigonometric Functions. |
Textbook Chapter 1 |
| 2) |
Limit of a Function and Limit Rules. Definition of Limit. Limits at Infinity. |
Textbook Chapter 2 |
| 3) |
Continuity (continuity at a point, continuous functions, intermediate value theorem, asymptotes of graphs), Tangent Lines (Derivative At A Point), Derivatives (differentiable on an interval, one-sided derivatives).
|
Textbook Chapter 2, Chapter 3
|
| 4) |
Differentiation Rules (powers, multiples, sums and differences, products and quotients, higher-order derivatives), Derivatives of Trigonometric Functions, The Chain Rule (derivative of a composite function). Implicit Differentiation.
|
Textbook Chapter 3
|
| 5) |
Linearization and Differentials.
|
Textbook Chapter 3
|
| 6) |
Implicit Differentiation. Linearization and Differentials.
Inverse Functions and Their Derivatives, Natural Logarithms, Exponential Functions, Inverse Trigonometric Functions, Hyperbolic Functions. Indeterminate Forms and L'Hospital Rule.
|
Textbook Chapter 7
|
| 7) |
Extreme values of Functions on Closed Intervals (local extreme values, finding extrama). Rolle Theorem, The Mean Value Theorem.
|
Textbook Chapter 4
|
| 8) |
Midterm |
- |
| 9) |
Monotonic Functions and The First Derivative Test (increasing functions and decreasing functions), Concavity and Curve Sketching (concavity, points of inflection, second derivative test for local extrema). Anti Derivatives (antiderivatives, initial value problems, indefinite integrals).
|
Textbook Chapter 4
|
| 10) |
Area and Estimating with Finite Sums, Sigma Notation and Limits of Finite Sums, Rieman Sums, The Definite Integral, Area Under the Graph of a Nonnegative Function, Average Value of a Continuos Function.
|
Textbook Chapter 5
|
| 11) |
Area and Estimating with Finite Sums, Sigma Notation and Limits of Finite Sums, Rieman Sums, The Definite Integral, Area Under the Graph of a Nonnegative Function, Average Value of a Continuos Function.
The Fundamental Theorem of Calculus, Indefinite Integrals and The Substitution Method, Definite Integral Substitutions. Area Between Curves.
|
Textbook Chapter 5
|
| 12) |
Using Basic Integration Formulas, Integration by Parts. |
Textbook Chapter 8
|
| 13) |
Trigonometric Integrals, Trigonometric Substitutions.
|
Textbook Chapter 8
|
| 14) |
Integration of Rational Functions by Partial Fractions, Integral Tables.
|
Textbook Chapter 8 |
| 15) |
Applications of Definite Integral. |
Textbook Chapter 6
|
| Course Notes / Textbooks: |
*Thomas' Calculus (14th Edition) Thomas’ Calculus, Fourteenth Edition, G.B.Thomas, J.Hass, C.Heil, M.D.Weir, Pearson. 2018.
*Thomas Kalk¨ul¨us 11. baskı, G.B.Thomas, M.D.Weir, J.Hass, F.R.Giordoni.
|
| References: |
*Thomas' Calculus (14th Edition) Thomas’ Calculus, Fourteenth Edition, G.B.Thomas, J.Hass, C.Heil, M.D.Weir, Pearson. 2018.
*Thomas Kalk¨ul¨us 11. baskı, G.B.Thomas, M.D.Weir, J.Hass, F.R.Giordoni. |
| |
Program Outcomes |
Level of Contribution |
| 1) |
PO 1.1) Sufficient knowledge in mathematics, science and computer engineering |
5 |
| 2) |
PO 1.2) Ability to apply theoretical and applied knowledge in mathematics, science and computer engineering for modeling and solving engineering problems. |
|
| 3) |
PO 2.1) Identifying complex engineering problems |
|
| 4) |
PO 2.2) Defining complex engineering problems |
|
| 5) |
PO 2.3) Formulating complex engineering problems |
|
| 6) |
PO 2.4) Ability to solve complex engineering problems |
|
| 7) |
PO 2.5) Ability to choose and apply appropriate analysis and modeling methods |
|
| 8) |
PO 3.1) Ability to design a complex system, process, device or product to meet specific requirements under realistic constraints and conditions. |
|
| 9) |
PO 3.2) Ability to apply modern design methods under realistic constraints and conditions for a complex system, process, device or product |
|
| 10) |
PO 4.1) Developing modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering applications |
|
| 11) |
PO 4.2) Ability to select and use modern techniques and tools necessary for the analysis and solution of complex problems encountered in engineering applications |
|
| 12) |
PO 4.3) Ability to use information technologies effectively. |
5 |
| 13) |
PO 5.1) Examination of complex engineering problems or discipline-specific research topics, designing experiments |
|
| 14) |
PO 5.2) Examination of complex engineering problems or discipline-specific research topics, experimentation |
|
| 15) |
PO 5.3 ) Analysis of complex engineering problems or discipline-specific research topics, data collection |
|
| 16) |
PO 5.4) Analyzing the results of complex engineering problems or discipline-specific research topics |
|
| 17) |
PO 5.5) Examining and interpreting complex engineering problems or discipline-specific research topics |
|
BİLGİ PAKETİ / DERS KATALOĞU
