School of Humanities \ Mathematics
Course Credit
ECTS Credit
Course Type
Instructional Language
Programs that can take the course
Faculty of Engineering Departments
Functions and graphs, limit and continuity of functions, derivative of functions, geometric meaning of derivative, rules of differentiation, chain rule, maximum-minimum problems, derivatives of trigonometric functions, implicit differentiation, mean value theorem, graphing and asymptotes, Riemann sums and definite integrals, the fundamental theorem of calculus, area between two curves, improper integrals.
Textbook and / or References
Course Book:
Thomas’ Calculus- Early Transcendentals (14th Ed.); Joel R. Hass, Maurice D. Weir, George B. Thomas; Pearson, 2019. ISBN: 978-0-13-443902-0
References:
• Kalkülüs Kavram ve Kapsam, 2. Baskı”, James Stewart, TÜBA, ISBN 975–8593–94–3.
• Calculus with Analytic Geometry (5th Ed.)”; C. H. Edwards and D. E. Penney; Prentice Hall, 1998.
Gaining basic mathematical knowledge; developing mathematical thinking and modeling techniques, giving information about limits, derivatives and integrals of functions and their applications.
1. Gain fundamental mathematical knowledge and apply it to different disciplines.
2. Understand and apply the basic concepts of functions, limits, and continuity for mathematical modeling in engineering.
3. Apply derivatives to analyze rates of change, solve maximum-minimum problems, and use optimization techniques in engineering.
4. Use integral techniques to calculate area, volume, and physical quantities.
5. Contribute to the modeling and analysis of engineering systems using differential and integral calculus.
Week 1: The set of real numbers, equations, inequalities, intervals, absolute value, functions, composite functions, and some important functions. Basic graphs (translation and shifting). Exponential and logarithmic functions and their fundamental properties.
Week 2: The limit of a function and limit rules. One-sided limits, limits at infinity, and infinite limits.
Week 3: Continuous functions, their properties, and related theorems. The derivative of a function and its geometric interpretation.
Week 4: Differentiation rules. The derivative of trigonometric functions. The chain rule.
Week 5: The derivative of implicit functions, tangent and normal equations. Derivatives of inverse functions, logarithmic and exponential functions. The derivative of inverse trigonometric functions. Hyperbolic and inverse hyperbolic functions and their derivatives.
Week 6: Related rates. Linear approximations and differentials. Applications of derivatives. Maximum and minimum values of a function. The Mean Value Theorem.
Week 7: The first derivative test. Concavity, the second derivative test, and graph sketching (symmetry and asymptotes). Indeterminate forms and L'Hôpital's rule. Exponential indeterminate forms.
Week 8: Applied maximum and minimum problems (optimization). Newton’s method. Antiderivatives (inverse derivatives, primitives).
Week 9: Summation notation and area as a limit of a sum. The concept of the definite integral. Fundamental theorems of calculus. The substitution method in definite integrals and the area between two curves.
Week 10: Defining logarithms through integration. Integration techniques. Basic integral formulas. The substitution method and integration by parts.
Week 11: Trigonometric integrals and trigonometric substitutions. The integration of rational functions (partial fraction decomposition method).
Week 12: Improper (generalized) integrals.
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